Florentin Smarandache

In this study, we propose a new approach based on fuzzy TODIM (Portuguese acronym for interactive and multicriteria decision-making) for decision-making problems in uncertain environments. Our method incorporates group utility and individual regret, which are often ignored in traditional multicriteria decision-making (MCDM) methods. To enhance the analysis and application of fuzzy sets in decision-making processes, we introduce novel entropy and distance measures for q-rung picture fuzzy sets. These measures include an entropy measure based on the sine function and a distance measure derived from the Jensen-Shannon divergence. In our methodology, incorporating the sine function into the entropy measure stands out as a distinctive decision, grounded in a profound understanding of the inherent characteristics of fuzzy sets. Utilizing the sine function proves especially advantageous when handling fuzzy sets that exhibit cyclical variations or fluctuations in their membership degrees. We effectively weight the criteria for an improved evaluation by using this new entropy measure. The introduced distance measure finds application in the TODIM approach, allowing the execution of TODIM method steps within a fuzzy environment until the determination of one alternative’s dominance over another—an advancement beyond traditional approaches. We apply our enhanced fuzzy TODIM method to a real-life construction project management problem from the literature and compare the results with those in the literature and obtained from other MCDM methods. Our proposed measures are robust, as demonstrated by the sensitivity analysis that varied the weights of group utility and individual regret, with the results visualized in a 3D sensitivity plot. The findings demonstrate the superiority of our method in providing a more comprehensive evaluation of alternatives, making it a useful tool for decision-makers facing complex and uncertain decision-making problems.

We introduce for the first time the appurtenance equation and inclusion equation, which help in understanding the operations with neutrosophic numbers within the frame of neutrosophic statistics. The way of solving them resembles the equations whose coefficients are sets (not single numbers).

We plead for a fluid margin, or mixed/indeterminate buffer zone, between Physical and Non-Physical Causal Closures, and for a Neutrosophic Causal Closure Principle claiming that the chances of all physical effects are determined by their prior partially physical and partially non-physical causes.

The n-th PowerSet of a Set {or P n (S)} better describes our real world, because a system S (which may be a company, institution, association, country, society, set of objects/plants/animals/beings, set of concepts/ideas/propositions, etc.) is formed by subsystems , which in their turn by sub-subsystems , and so on. We prove that the SuperHyperFunction is a generalization of classical Function, SuperFunction, and HyperFunction. And the SuperHyperAlgebra, SuperHyperGraph are part of the SuperHyperStructure. Almost all structures in our real world are Neutrosophic SuperHyperStructures since they have indeterminate/incomplete/uncertain/conflicting data.

In this paper we define the Soft Set Product as a product of many soft sets and afterwards we extend it to the HyperSoft Set. Similarly, the IndetermSoft Product is extended to the IndetermHyperSoft Set. We also present several applications of the Soft Set Product to Fuzzy (and fuzzy-extensions) Soft Set Product and to IndetermSoft Set and IndetermHyperSoft Set.

Recently, a friend of one of these writers told her story of using one of a healthcare product to activate her stem cells as part of regenerative medicine. Regenerative medicine is a field of medicine that seeks to repair or replace damaged or diseased tissues and organs. This can be done through a variety of methods, including stem cell therapy, tissue engineering, and gene therapy. This is a short review article on this rapid field called regenerative medicine, in particular via a new method called photobiomodulation, especially by virtue of lowintensity laser pen treatment. Hopefully it will attract more research in this interesting direction, both for laser/photobiomodulation to boost plant growth as well as in healthcare (see also: Christianto & Smarandache, 2022; Christianto, 2023).

The goal of this short note is to expand the concepts of ‘pluralism’, ‘neutrosophy’, ‘refined neutrosophy’, ‘refined neutrosophic set’, ‘multineutrosophic set’, and ‘plithogeny’ (Smarandache 2002, 2013, 2017, 2019, 2021, 2023a, 2023b, 2023c), into a larger category that I will refer to as MultiAlism (or MultiPolar). As a straightforward generalization, I propose the conceptualization of a MultiPolar System (different from a PluriPolar System), which is formed not only by multiple elements that might be random, or contradictory, or adjuvant, but also by accepting features from more than one basic system (UniPolar, BiPolar, TriPolar, or PluriPolar systems). PluriAlism is a closed dynamic system without neutralities nor indeterminacies, while MultiAlism is an open dynamic system with neutralities and indeterminacies. PluriAlism is a uni-system (formed by elements from a single system), while MultiAlism is a MultiSystem (formed by elements from many systems).

In the real word, in most cases, everything (an attribute, event, proposition, theory, idea, person, object, action, etc.) is evaluated in general by many sources (called experts), not only one. The more sources evaluate a subject, the better accurate result (after fusioning all evaluations). That's why, in this paper, we straightforwardly extend the Refined Neutrosophic Set to the MultiNeutrosophic Set, and we show that the last two are isomorphic. A MultiNeutrosophic Set is a Neutrosophic Set whose all elements' degrees of truth/indeterminacy/falsehood are evaluated by many (Multi) sources. Afterwards, we introduce a total order on the set of n-plets of the form (p, r, s), we build the operators on the (p, r, s)-plets, and show several applications of the MultiNeutrosophic Sets.

We now found nine new topologies, such as: NonStandard Topology, Largest Extended NonStandard Real Topology, Neutrosophic Triplet Weak/Strong Topologies, Neutrosophic Extended Triplet Weak/Strong Topologies, Neutrosophic Duplet Topology, Neutrosophic Extended Duplet Topology, Neutrosophic MultiSet Topology, and recall and improve the seven previously founded topologies in the years (2019-2023), namely: NonStandard Neutrosophic Topology, NeutroTopology, AntiTopology, Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, SuperHyperTopology, and Neutrosophic SuperHyperTopology. They are called avantgarde topologies because of their innovative forms.

As part of our small contribution in dialogue toward better peace development and reconciliation studies, and following Toffler & Toffler’s War and Antiwar (1993), the present article delves into a realm of logic beyond the traditional confines of negation and the excluded middle principle, exploring the nuances of "Otherness" that transcend classical and Nagatomo logics. Departing from the foundational premises of classical Aristotelian logic systems, this exploration ventures into alternative realms of reasoning, specifically examining Neutrosophic Logic and Klein bottle logic (cf. Smarandache, 2005). The study challenges conventional boundaries and explores the implications of embracing paradoxes and self-reference in logic systems, aiming to redefine approaches to understanding truth and reasoning. The paper investigates how these alternative logics open avenues for philosophical inquiry, redefining entropy, and potentially influencing innovative perspectives in free energy systems. Through this exploration, it seeks to expand the discourse on logic, welcoming a broader spectrum of thought beyond established frameworks; and we also discuss shortly a number of possible implementations including in risk management and also Klein bottle entropy redefinition (Tang et al, 2018).

Various sensors play an important role in the monitoring and development of robotic technology. We present a contemporary statistical analysis method for evaluating datasets generated by robotic systems. Specifically, this data set originates from the physical structure of the robot and is acquired by a wireless temperature sensor. The data collection process spans a temporal period of 1 to 10 hours during the operational period of the robot. The collected data is subjected to a rigorous analysis using neutrosophic methodology. To facilitate this, a modern neutrosophic formula has been devised, drawing on definitions established within the field. To benchmark the effectiveness of the proposed approach, a conventional formula is also used for comparison purposes. Our results clearly indicate that the proposed method achieves higher levels of information richness and adaptability compared to classical methods. This indicates the improved utility of the proposed approach in solving the complexities of robotic data analysis.

The present article delves into the extension of Knuth’s fundamental Boolean logic table to accommodate the complexities of indeterminate truth values through the integration of neutrosophic logic (Smarandache & Christianto, 2008). Neutrosophic logic, rooted in Florentin Smarandache’s groundbreaking work on Neutrosophic Logic (cf. Smarandache, 2005, and his other works), introduces an additional truth value, ‘indeterminate,’ enabling a more comprehensive framework to analyze uncertainties inherent in computational systems. By bridging the gap between traditional boolean operations and the indeterminacy present in various real-world scenarios, this extension redefines logic tables, introducing neutrosophic operators that capture nuances beyond the binary realm. Through a thorough exploration of neutrosophic logic's principles and its implications in computational paradigms, this study proposes a novel approach to logic design that accommodates uncertain, imprecise, and incomplete information. This paradigm shift in logic tables not only broadens the spectrum of computing methodologies but also holds promise in fields such as decision-making systems and data analytics.

Sustainable development involves the creation of systems and technologies that not only improve human lives but also enable natural resources to be consumed responsibly. These systems include integration of technologies for efficient resource consumption, better production, and lower negative impacts on the environment. Over the years, humanity has developed these technologies and commercialized through a series of advancements: from prototype creation to commercialization. Even with the promise of sustainable development, these technologies took a long time before being deployed on a large scale. Decisions are needed to be made to create policies, regulations, and implementation strategies for these technologies. These decisions will be based on different economic, environmental, social, and technical factors, among others. In doing these decisions, one of the major factors needed to be addressed is uncertainty. Statistical techniques can be used to manage uncertainties that involve randomness. For instance, the prediction of the leaching behavior of complex coppercobalt-bearing ores is performed using an artificial neural network with a back-forward algorithm (Mbuya and Mulaba-Bafubiandi 2023). However, the existence of uncertainties in new and emerging technologies is due to the lack of information about how technologies can be deployed for use by the society. Policymakers rely on expert judgment to be able to determine which technologies can be scaled up for testing, or which technologies are better than the others.

The purpose of this paper is to introduce new types of neutrosophic crisp sets with three types 1, 2, 3. After given the fundamental definitions and operations, we obtain several properties, and discussed the relation- ship between neutrosophic crisp sets and others. Also, we introduce and study the neutrosophic crisp point and neu- trosophic crisp relations. Possible applications to data- base are touched upon.

Our universe is but one page in a large book. For example, things and Beings can travel between Universes, intentionally or unintentionally. In this short remark, we revisit and offer short remark to Neil's ideas and trying to connect them with geometrization of musical chords as presented by D. Tymoczko and others, then to Escher staircase and then to Jacob's ladder which seems to point to possibility to interpret Jacob's vision as described in the ancient book of Genesis as inter dimensional or heavenly staircase, e.g. an inter dimensional bridge between heaven and earth (see also classic book: Hofstadter, Godel, Escher, Bach). Jacob's vision of angels going down to earth from that staircase has been depicted for instance in William Blake art etc. In our communication with others via physics literature and discussions etc, we came to several conclusions as follows: Firstly, possibility of quantum wormhole effect to mirror particle universe, which sometimes it is termed non-orientable wormhole. While such mirror particles effect have been more than 50 years predicted with the so-called parity violation (cf. Lee & Yang, 1950s), and that is called symmetry breaking. Secondly, a series of extended experiments on laser irradiated cold water may suggest possible transition from a phase of water to be at least partially fourth phase of water, which may be composed of crystalline water (see e.g. Gerald Pollack, and also Harold Aspden on liquid crystalline). If we can imagine laser cooling effect can be done in protracted time, then we can achieve a physical representation of Aspden's liquid crystalline. Therefore, in subsequent article (Part II) we outlined simple model of such an effect of tunneling via quantum liquid crystalline Universe, which may likely be modeled with iced-water. It is interesting to remark here that certain experiments by Stockholm University scientists have shown that X-ray triggered water can exhibit properties just like liquid crystal (cf. PRL, 2020). That is why we consider it possible that there can be quantum phase transition where liquid water (comprised of iced cubes and water) can exhibit effects such as tunneling in quantum liquid crystalline Universe. Last but not least, we admit that what we outlined here is just an initial phase; and if you wish, perhaps we can call such experiments as "wormhole-at-lab" experiments (abbreviated: WHALE).

The present article was partly inspired by G. Pollack's book, and also Dadoloff, Saxena & Jensen (2010). As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1, No. 2, 2022), for example, things and Beings can travel between Universes, intentionally or unintentionally [4]. In this short remark, we revisit and offer short remark to Neil Boyd's ideas and trying to connect them with geometry of musical chords as presented by D. Tymoczko and others, then to Escherian staircase and then to Jacob's ladder which seems to pointto possibility to interpret Jacob's vision as described in the ancient book of Genesis as interdimensional staircase, e.g. an interdimensional bridge between heaven and earth (cf. classic book: Hofstadter, Godel, Escher, Bach). Jacob's vision of angels going down to earth from that staircase has been depicted for instance in William Blake art etc. In our communication with others via physics literature and discussions etc, we came to several conclusions as follows: Firstly, possibility of wormhole effect to mirror particle universe, which sometimes it is termed non-orientable wormhole. While such mirror particles effect have been more than 50 years predicted with the so-called parity violation (cf. Lee & Yang, 1950s), and that is called symmetry breaking. Secondly, a series of extended experiments on laser irradiated cold water may suggest possible transition from a phase of water to be at least partially fourth phase of water, which may be composed of crystalline water (see e.g. Gerald Pollack, and also Harold Aspden on liquid crystalline). If we can imagine laser cooling effect can be done in protracted time, then we can achieve a physical representation of Aspden's liquid crystalline. Therefore, in this article we outline a series of simple experiments of laser irradiated iced-water along with beryl and selenite crystals in order to see possibility of such a quantum tunneling via quantum liquid crystalline Universe hypothesis, which may likely be modeled with iced-water. It is interesting to remark here that certain experiments by Stockholm University scientists have shown that X-ray triggered water can exhibit properties just like liquid crystal (cf. PRL, 2020). That is why we consider it possible that there can be quantum phase transition where liquid water (comprised of iced cubes and water) can exhibit effects such as tunneling in quantum liquid crystalline Universe. Last but not least, we admit that what we outlined here is just aninitial phase; and if you wish, perhaps we can call such experiments as "wormhole-at-lab" experiments (abbreviated: WHALE).

In the present paper we discuss: a) how Hilbert's unification program failed completely, and b) we outline a new electron model based on Helmholtz's electron vortex and Kolmogorov theory of turbulence. Novelty aspect: we discuss among other things, electron capture event, and von Karman vortex street. We also discuss a new model of origination of charge and matter. This paper is a sequel to a preceding paper on similar theme.

In recent years, apparently the Big Bang as described by the Lambda CDM-Standard Model Cosmology has become widely accepted by majority of physics and cosmology communities. Even some people have concluded that it has no serious alternative in horizon. Is that true? First, as we argued elsewhere, Big Bang story relies on singularity. In other words, when we are able to describe the observed data without invoking singularity, then Big Bang model is no longer required. Therefore, here we explore a few alternative stories other than Big Bang story, which most cosmologists believe it is the nearest to Biblical account of creation. We would argue that rereading of Genesis 1:2 will lead us to another viable story, albeit the alternative has not been developed rigorously as LCDM theories. We also briefly discuss a fluid Maxwell equations of Prof. Tsutomu Kambe based on vortex sound theory.

It has been known for long time that most of the existing cosmology models have singularity problem. Cosmological singularity has been a consequence of excessive symmetry of flow, such as "Hubble's law". More realistic one is suggested, based on Newtonian cosmology model but here we include the vertical-rotational effect of the whole Universe. We review a Riccati-type equation obtained by Nurgaliev, and solve the equation numerically with Mathematica. It is our hope that the new proposed method can be verified with observation data.

In a new paper in recent issue of this journal (PSTJ), Prof. M. Pitkanen describes a solar system model inspired by spiral galaxies. While we appreciate his new approach, we find it lacks substantial discussion on the nature of vortices and chirality in galaxy. Therefore we submit a viewpoint that Gross-Pitaevskii model can be a more complete description of both solar system and also spiral galaxies, especially taking into account the nature of chirality and vortices in galaxies. In this article, we also hope to bring out some correspondence among existing models, so we discuss shortly: the topological vortice approach, Burgers equation in the light of KAM theory, and the Cantorian Navier-Stokes approach. Of course, this short article is far from being complete. We hope further investigation can be done around this line of approach.

Sabine Hossenfelder's recent book "Lost in Math" has attracted numerous responses, including by notable physicists such as Frank Wilczek. In this article we focus on Wilczek's remark on that book, in particular on the perils of postempirical science. We also discuss shortly multiverse hypothesis from philosophical perspective. In last section, we offer a resolution from the perspective of Neutrosophic Logic on this problem of classical tension between mathematics and experience approach to physics, which seems to cause the stagnation of modern physics.

It is known that the Big Bang theory was based on the concept of creation ex nihilo, after ancient Greek philosophers. In this paper, we will make few remark on the concept of creatio ex nihilo (as a commentary to a recent paper by Kalachanis, Athanasios Anastasiou, Ioannis Kostikas, Efstratios Theodossious and Мilan S. Dimitrijevi), as well as two other approaches, i.e. Intelligent Design and Emergence Theory by Clayton/Yong. As continuation of our recent paper to appear in forthcoming issue of J. Asia Mathematika, we argue that beside the above three approaches, a new concept called creatio ex-rotatione offers a resolution to the long standing disputes between beginning and eternity of the Universe. In other words, in this respect we agree with Vaas, i.e. it can be shown: "how a conceptual and perhaps physical solution of the temporal aspect of Immanuel Kant's "first antinomy of pure reason" is possible, i.e. how our universe in some respect could have both a beginning and an eternal existence. Therefore, paradoxically, there might have been a time before time or a beginning of time in time." By the help of computational simulation, we also show how a model of early Universe with rotation can fit this new picture.

This article is an update of our previous article in this SGJ journal, titled: On Gödel's Incompleteness Theorem, Artificial Intelligence & Human Mind [7]. We provide some commentary on the latest developments around AI, humanoid robotics, and future scenario. Basically, we argue that a more thoughtful approach to the future is "techno-realism."

Borges has a rare ability to put wild ideas into detective stories with reporting style. At least that is the impression that we got on his short stories. In particular, one of his short story is worthnoting: Tlon, Uqbar, Orbis Tertius. The story told us about a mysterious country called Uqbar, in apparently an unofficial reprint of Encyclopedia Britannica. It also tells about Tlon, a mysterious planet, created purely by imaginative minds. While this story clearly criticizes Berkeley view and may be not related to our daily reality, a reinterpretation of this story leads us to a long standing discourse in the philosophy of science: to how extent the entire modern physics follow such a Berkeley-antirealism tendency?

Smarandache Hypothesis states that there is no speed limit of anything, including light and particles. While the idea is quite simple and based on known hypothesis of quantum mechanics, called Einstein-Podolski-Rosen paradox, in reality such a superluminal physics seems still hard to accept by majority of physicists. Here we review some experiments to support superluminal physics and also findings to explain Smarandache Quantum Paradoxes and Quantum Sorites Paradox. We also touch briefly on new experiment on magneton, supporting SubQuantum Kinetic Model of Electron.

The Higgs particle has been detected a few years ago, that is what newspapers tell us. For many physicists, the Standard Model of particle physics has accomplished all the jobs. Or to put it simply: The game is over. Is it true? Then some physicists began to ask: can go beyond the Standard Model? Because the supersymmetric extension of the Standard Model has failed. If you feel that theoretical physics is becoming boring, you are not alone. Fortunately, there is good news: a new generation of physicists are doing table-top experiments in their basements. Can we expect new results later? 2 If so, what will the future of physics look like? This article discusses this question, starting with a blunt look at the relationship between mathematics and physical reality, written from the perspectives of a mathematician and a cosmologist.

In the same spirit with the theme of last issue of this SGJ journal ("Ongoing creation"), this paper shortly reviews a plausible mechanism from Aether to become ordinary matter from the perspective of Neutrosophic Logic. We also discuss two other possible applications of Neutrosophic Logic, including a resolution of conflicting paradigms in medicine. We hope that some ideas as outlined herein will be proved useful in the near future.

Despite its enormous practical success, many physicists and philosophers alike agree that the quantum theory is full of contradictions and paradoxes which are difficult to solve consistently. Even after 90 years, the experts themselves still do not all agree what to make of it. The area of disagreement centers primarily around the problem of describing observations. Formally, the so-called quantum measurement problem can be defined as follows: the result of a measurement is a superposition of vectors, each representing the quantity being observed as having one of its possible values. The question that has to be answered is : how this superposition can be reconciled with the fact that in practice we only observe one value. How is the measuring instrument prodded into making up its mind which value it has observed? Among some alternatives to resolve the above QM measurement problem, a very counterintuitive one was suggested by Hugh Everett in his 1955 Princeton dissertation, which was subsequently called the Many-Worlds Interpretation of QM (MWI). In this paper we will not discuss all possible scenarios to solve the measurement problem, but we will only shortly discuss Everett's MWI, because it has led to heated debates on possibility of multiverses, beyond the Universe we live in. We also discuss two alternatives against MWI proposal: (a) the so-called scale symmetry theory, (b) the Maxwell-Dirac isomorphism. In last section, we also discuss shortly MWI hypothesis from philosophical perspective.

While we completely understood that a binary dwarf companion of the Sun has not been accepted by majority of astronomers, allow us to present some new arguments, along with our own serendipitous encounter with such a binary companion of the Sun. We hope that the present note will be found useful for further investigations, in relation to Planet Nine and such a dwarf star companion of the Sun (sometimes dubbed as Nemesis). Nonetheless, this article is not an exhaustive review of such dwarf companion star theories.

Around 3 decades ago, Jayant Narlikar & Halton Arp argued on possible variable mass hypothesis cosmology (VMH). In the meantime, the Earth expansion problem has attracted great interest, and recent study gives geodetic evidence that the Earth has been expanding, at least over the recent several decades. Therefore, in the present article discusses some interesting effects related to varying G, but here we argue that instead of varying G we can think of varying mass (M). Among other things we discuss receding planets from the Sun, calculation of Pioneer spacecraft anomaly as proposed by B.G. Sidharth, and also possible slight change of LAGEOS Satellite. Further observation to verify or refute this conjecture is recommended, especially based on geological evidence of expanding earth.

Inspired by "One Note Samba," a standard jazz repertoire, we present an outline of Bose-Einstein Condensate Cosmology (BECC). Although this approach seems awkward and a bit off the wall at first glance, it is not impossible to connect altogether BEC, Scalar Field Cosmology and Feshbach Resonance with Ermakov-Pinney equation. We also discuss shortly possible link with our previous paper, where we describe Newtonian Universe with Vortex in terms of Ermakov equation.

In some recent papers (G. ‘t Hooft and others), it has been argued that quantum mechanics can arise from classical cellular automata. Nonetheless, G. Shpenkov has proved that the classical wave equation makes it possible to derive a periodic table of elements, which is very close to Mendeleyev’s one, and describe also other phenomena related to the structure of molecules. Hence the classical wave equation complements Schrödinger’s equation, which implies the appearance of a cellular automaton molecular model starting from classical wave equation. The other studies show that the microworld is constituted as a tessellation of primary topological balls. The tessellattice becomes the origin of a submicrospic mechanics in which a quantum system is subdivided to two subsystems: the particle and its inerton cloud, which appears due to the interaction of the moving particle with oncoming cells of the tessellattice. The particle and its inerton cloud periodically change the momentum and hence move like a wave. The new approach allows us to correlate the Klein-Gordon equation with the deformation coat that is formed in the tessellatice around the particle. The submicroscopic approach shows that the source of any type of wave movements including the Klein-Gordon, Schrödinger, and classical wave equations is hidden in the tessellattice and its basic exciations – inertons, carriers of mass and inert properies of matter. We also discuss possible correspondence with Konrad Zuse’s calculating space.

Leschenko presented a new solving procedure for Euler-Poisson equations for solving momentum equations of the CR3BP near libration points for uniformly rotating planets having inclined orbits in the solar system with respect to the orbit of the Earth. The system of equations of the CR3BP has been explored with regard to the existence of an analytic way of presentation of the approximated solution in the vicinity of libration points. A new and elegant ansatz has been suggested in their publication whereby, in solving, the momentum equation is reduced to a system two coupled Riccati ODEs. In this paper, we presented a numerical solution of such coupled Riccati ODEs using Mathematica software package.

It has been known for long time that intuition plays significant role in many professions and human life, including in entrepreneurship, government, and also in detective or law enforcement activities. Even women are known to possess better intuitive feelings or "hunch" compared to men. Despite these examples, such a precognitive interdiction is hardly accepted in established science. In this paper, we discuss briefly the advanced solutions of Maxwell equations, and then make connection between syntropy and precognition from classical perspective. It is our hope that the new proposed method can be verified with experimental data. But we admit that our model is still in its infancy, more researches are needed to fill all the missing details.

While it is known that Euclid's five axioms include a proposition that a line consists at least of two points, modern geometry avoid consistently any discussion on the precise definition of point, line, etc. It is our aim to clarify one of notorious question in Euclidean geometry: how many points are there in a line segment?-from discrete-cellular space (DCS) viewpoint. In retrospect, it may offer an alternative of quantum gravity, i.e. by exploring discrete gravitational theories. To elucidate our propositions, in the last section we will discuss some implications of discrete cellular-space model in several areas of interest: (a) cell biology, (b) cellular computing, (c) Maxwell equations, (d) low energy fusion, and (e) cosmology modelling.

An outline of plausible resolution of this problem is given here, based on: a) Gödel's incompleteness theorem, b) Newton's aether stream model. And in another paper we will present our calculation of receding Moon from Earth based on such a matter creation hypothesis. More experiments and observations are called to verify this new hypothesis, albeit it is inspired from Newton's theory himself. We hear within ourselves the constant cry: There is the problem, seek the solution. You can find it through pure thought.

Some years ago, Hidding et al. suggest that the emergence of intricate and pervasive weblike structure of the Universe on Megaparsec scales can be approximated by a wellknown equation from fluid mechanics, the Burgers' equation. The solution to this equation can be obtained from a geometrical formalism. The resulting Adhesion formalism provides deep insight into the dynamics and topology of the Cosmic Web. It uncovers a direct connection between the conditions in the very early Universe and the complex spatial patterns that emerged out of these under the influence of gravity.

Sound is one of the types of waves that can be felt by the sense of hearing (ears). In physics, the definition of sound is something that is produced from objects that vibrate. Objects that produce sound are called sound sources. The sound source that vibrates will vibrate the molecules into the air around it. Sound is mechanical compression or longitudinal waves that propagate through the medium. This medium or intermediate agent can be liquid, solid, gas. So, sound waves can propagate for example in water, coal, or air. Most sounds are a combination of various vibratory signals composed of harmonic waves, but pure sound can theoretically be explained by oscillating vibrational speed or frequency measured in Hertz (Hz) vibration units and amplitude or loudness of sound with measurements in decibels (dB). The effect sounds can have on us humans is simply astounding. While everyday life becomes stressful, overcrowded and increasingly hectic, we seek ways for inner peace and balance. The power of music, felt through overtone-rich sound therapy and sound massage, can be a solution. No matter how much scientific explanation is behind it, healing through music remains fascinating, even magical. This paper introduces a new field called cymatics and sound healing with their plausible impact to spirituality and consciousness research.

It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such an acoustic model of cosmology is rarely developed fully into a complete framework from the notion of space, cancer therapy up to the sky. This paper may be the first attempt towards such a complete description of the Universe based on classical wave equation of sound. It is argued that one can arrive at a consistent description of space, elementary particles, Sachs-Wolfe acoustic theorem, up to a novel approach for cancer therapy, starting from this simple classical wave equation of sound. We also discuss a plausible extension of Acoustic Sachs-Wolfe theorem based on its analogue with Klein-Gordon equation to become Acoustic Sachs-Wolfe-Christianto-Smarandache-Umniyati (ASWoCSU) equation. It is our hope that the new proposed equation can be verified with observation data. But we admit that our model is still in its infancy, more researches are needed to fill all the missing details.

It is known that most existing cosmology models do not include rotation, with few exceptions such as rotating Bianchi and rotating Godel metrics. Therefore in this paper we aim to discuss four possible ways to model rotating universe, including Nurgaliev's Ermakov-type equation. It is our hope that the new proposed method can be verified with observations, in order to open new possibilities of more realistic nonlinear cosmology models.

Integrating insights from Dokuchaev (2020), Rapoport, Christianto, Chandra, Smarandache (under review), and other pioneering works, this article explores the theoretical foundations linking nonorientable spaces to resolving the Poincaré conjecture and its broader implications in theoretical physics, geology, cosmology, and biology.

In the ancient world, the Greeks believed that all great insights came from one of nine muses, divine sisters who brought inspiration to mere mortals. In the modern world, few people still believe in the muses, but we all still love to hear stories of sudden inspiration. Like Newton and the apple, or Archimedes and the bathtub (both another type of myth), we're eager to hear and to share stories about flashes of insight. But what does it take to be actually creative? How to have such a flash insight? Turns out, there is real science behind "aha moments." We prefer to call it "intuilytics."

The existence of big bang relic neutrinos—exact analogues of the big bang relic photons comprising the cosmic microwave background radiation—is a basic prediction of standard cosmology. The standard big bang theory predicts the existence of 1087 neutrinos per flavour in the visible universe. This is an enormous abundance unrivalled by any other known form of matter, falling second only to the cosmic microwave background (CMB) photon. Yet, unlike the CMB photon which boasts its first (serendipitous) detection in the 1960s and which has since been observed and its properties measured to a high degree of accuracy in a series of airborne/satellite and ground based experiments, the relic neutrino continues to be elusive in the laboratory. The chief reason for this is of course the feebleness of the weak interaction.
At present, the observational evidence for their existence rests entirely on cosmological measurements, such as the light elemental abundances, anisotropies in the cosmic microwave background, and the large-scale matter power spectrum.

Constelatii Diamantine este una dintre cele mai bune reviste literare romanesti ale zilelor noastre. Are o redacție internațională și colaboratori din diaspora românească din întreaga lume. Poezii, proză, eseuri, ilustrații. ---------------------------------------------------------------------------------- Constelatii Diamantine is one of the best Romanian literary journals of today. It has an international editorial board and collaborators from all over Romanian diaspora around the world. Poems, prose, essays, illustrations.

Constelatii Diamantine este una dintre cele mai bune reviste literare romanesti ale zilelor noastre. Are o redacție internațională și colaboratori din diaspora românească din întreaga lume. Poezii, proză, eseuri, ilustrații. ---------------------------------------------------------------------------------- Constelatii Diamantine is one of the best Romanian literary journals of today. It has an international editorial board and collaborators from all over Romanian diaspora around the world. Poems, prose, essays, illustrations.

Constelatii Diamantine este una dintre cele mai bune reviste literare romanesti ale zilelor noastre. Are o redacție internațională și colaboratori din diaspora românească din întreaga lume. Poezii, proză, eseuri, ilustrații. ----------------------------------------------------------------------------------
Constelatii Diamantine is one of the best Romanian literary journals of today. It has an international editorial board and collaborators from all over Romanian diaspora around the world. Poems, prose, essays, illustrations.

This fifth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 (available at fs.unm.edu/DSmT-book4.pdf or www.onera.fr/sites/default/files/297/2015-DSmT-Book4.pdf) in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered.
First Part of this book presents some theoretical advances on DSmT, dealing mainly with modified Proportional Conflict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classifiers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes.
Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identification of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classification.
Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classification, and hybrid techniques mixing deep learning with belief functions as well.

Fotografiile acestui album s-au adunat, neprogramatic și fără pretenții artistice, în timpul recentei vizite pe care am făcut-o în România, în vara anului 2023. O vizită cu inima îngreunată de dor. Drumurile mele s-au întins mai mult pe Dunăre și pe Olt, de-a stânga și de-a dreapta acestor ape care au desenat și determinat o bună parte din istoria românilor. Instanțele foto sunt surprinse în și împrejurul Orșovei, Drobetei Turnu Severin, Cazanelor Dunării, Craiovei și Bălceștilor natali. Textele însoțitoare sunt eboșe cu tentă poetică, așa cum le-au inspirat, instant, locurile văzute, oamenii (re)întâlniți și sentimentele prezente/trezite/reamintite în sufletul autorului.

We all know that problems of transportation and allocation appear frequently in practical life. We need to transfer materials from production centers to consumption centers to secure the areas’ need for the transported material or allocate machines or people to do a specific job at the lowest cost, or in the shortest time. We know that the cost factors Time is one of the most important factors that decision-makers care about because it plays an “important” role in many of the practical and scientific issues that we face in our daily lives, and we need careful study to enable us to avoid losses. For this, the linear programming method was used, which is one of the research methods. Processes, where the problem data is converted into a linear mathematical model for which the optimal solution achieves the desired goal. Since these models are linear models, we can solve them using the direct simplex method and its modifications, but the specificity that these models enjoy has enabled scholars and researchers to find special methods that help us in obtaining the optimal solution. Whatever the method used, the goal is to determine the number of units transferred from any material from production centers to consumption centers, or to allocate a machine or person to do a job so that the cost or time is as short as possible. These issues were addressed according to classical logic, but the ideal solution was a specific value appropriate to the conditions in which the data was collected and does not take into account the changes that may occur in the work environment. In order to obtain results that are more accurate and enjoy a margin of freedom, we present in this book a study of transport issues and neutrosophic allocation issues and some methods for solving them. By neutrosophic issues we mean These are the problems in which the data are neutrosophic values, i.e. the required quantities and the available quantities.

In this book, authors, for the first time, introduce the new notion of special subset linguistic topological spaces using linguistic square matrices. This book is organized into three chapters. Chapter One supplies the reader with the concept of ling set, ling variable, ling continuum, etc. Specific basic linguistic algebraic structures, like linguistic semigroup linguistic monoid, are introduced. Also, algebraic structures to linguistic square matrices are defined and described with examples.

In general, a system S (that may be a company, association, institution, society, country, etc.) is formed by sub-systems Si { or P(S), the powerset of S }, and each sub-system Si is formed by sub-sub-systems Sij { or P(P(S)) = P2(S) } and so on. That’s why the n-th PowerSet of a Set S { defined recursively and denoted by Pn(S) = P(Pn-1(S) } was introduced, to better describes the organization of people, beings, objects etc. in our real world. The n-th PowerSet was used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order to build the SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one in fact encounters SuperHyperStructures. Also, six new types of topologies have been introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology.

Various exploration in astrophysics has revealed many breakthroughs nowadays, not only with respect to James Webb Telescope, but also recent finding related to water and ice deposits in the Moon surface. Those new findings seem to bring us to new questions related to origin of Earth, Moon and the entire Universe.

We all know that problems of transportation and allocation appear frequently in practical life. We need to transfer materials from production centers to consumption centers to secure the areas’ need for the transported material or allocate machines or people to do a specific job at the lowest cost, or in the shortest time. We know that the cost factors Time is one of the most important factors that decision-makers care about because it plays an “important” role in many of the practical and scientific issues that we face in our daily lives, and we need careful study to enable us to avoid losses. For this, the linear programming method was used, which is one of the research methods. Processes, where the problem data is converted into a linear mathematical model for which the optimal solution achieves the desired goal. Since these models are linear models, we can solve them using the direct simplex method and its modifications, but the specificity that these models enjoy has enabled scholars and researchers to find special methods that help us in obtaining the optimal solution. Whatever the method used, the goal is to determine the number of units transferred from any material from production centers to consumption centers, or to allocate a machine or person to do a job so that the cost or time is as short as possible. These issues were addressed according to classical logic, but the ideal solution was a specific value appropriate to the conditions in which the data was collected and does not take into account the changes that may occur in the work environment. In order to obtain results that are more accurate and enjoy a margin of freedom, we present in this book a study of transport issues and neutrosophic allocation issues and some methods for solving them. By neutrosophic issues we mean These are the problems in which the data are neutrosophic values, i.e. the required quantities and the available quantities.

This book extends the concept of linguistic coordinate geometry using linguistic planes or semi-linguistic planes. In the case of coordinate planes, we are always guaranteed of the distance between any two points in that plane. However, in the case of linguistic and semi-linguistic planes, we can not always determine the linguistic distance between any two points. This is the first limitation of linguistic planes and semi-linguistic planes.

Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy.
In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements.
There are about 7,000 neutrosophic researchers, within 89 countries around the globe, that have produced about 4,000 publications and tenths of PhD and MSc theses, within more than two decades.
This is the sixth volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation, with an introduction contains a short history of neutrosophics, together with links to the main papers and books.

ES:
Este es el Sexto volumen de la Enciclopedia de Investigadores Neutróficos, editados a partir de materiales ofrecidos por los autores que respondieron a la invitación del editor. Los autores se enumeran alfabéticamente. La introducción contiene una breve historia de la neutrosófica, y en especial se sus impacto en latinoamérica junto con enlaces a los principales artículos y libros. Conjunto neutrosófico, lógica neutrosófica, probabilidad neutrosófica, estadística neutrosófica, medida neutrosófica, precálculo neutrosófico, cálculo neutrosófico, psicología neutrosófica, sociología neutrosófica etc., están ganando una atención significativa en resolver muchos problemas de la vida real que implican incertidumbre, imprecisión, vaguedad, incompletitud, inconsistencia e indeterminación. En los últimos años, los campos de la neutrosófica se han ampliado y aplicado en diversos campos, tales como: inteligencia artificial, minería de datos, software informática, toma de decisiones en forma incompleta / indeterminada / inconsistente sistemas de información, procesamiento de imágenes, modelado computacional, robótica, diagnóstico médico, ingeniería biomédica, problemas de inversión, previsión económica, ciencias sociales, humanística y la validación y consolidación del conocimiento científico.

Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy.
In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements.
There are about 7,000 neutrosophic researchers, within 89 countries around the globe, that have produced about 4,000 publications and tenths of PhD and MSc theses, within more than two decades.
This is the fifth volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation, with an introduction contains a short history of neutrosophics, together with links to the main papers and books.

This book is written for middle and high school students, for teachers and for those with a passion for math, containing 150+1 problems (which are followed by solutions) to make it more accessible to the reader.
The last problem (150+1), a very interesting one, leaves some space for comments and generalizations.
The book is a collaboration between a multi-awarded student at Romania’s National Mathematics Olympiad (Carina Maria Viespescu, student in year 10 at Liceul International of Informatics Bucuresti), a teacher from Colegiul National “Fratii Buzesti” din Cravoia and prof. Dr. Emeritus Florentin Smarandache from the University of New Mexico.
A couple of problems are proposed by colleagues, and their names indicated in footnotes.

RO:
Cartea se adresează elevilor de gimnaziu și liceu, profesorilor și celor pasionați de matematică, conținând 150+1 probleme, urmate de soluții, pentru a fi mai ușor savurate de cititor.
Ultima problemă (150+1) foarte interesantă lasă loc de comentarii și generalizări.
Lucrarea este o colaborare dintre o elevă multiplu medaliată la Olimpiada Națională de Matematică a României (Carina Maria Viespescu, elevă în clasa a X-a la Liceul Internațional de Informatică din București), un profesor de la Colegiul Național Frații Buzești din Cravioa și prof Dr. Emerit Florentin Smarandache de la University of New Mexico.
Câteva probleme sunt propuse de colegi, iar numele și afilierea lor este precizată în notele de subsol.

Constelatii Diamantine este una dintre cele mai bune reviste literare romanesti ale zilelor noastre. Are o redacție internațională și colaboratori din diaspora românească din întreaga lume. Poezii, proză, eseuri, ilustrații.
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Constelatii Diamantine is one of the best Romanian literary journals of today. It has an international editorial board and collaborators from all over Romanian diaspora around the world. Poems, prose, essays, illustrations.

Constelatii Diamantine este una dintre cele mai bune reviste literare romanesti ale zilelor noastre. Are o redacție internațională și colaboratori din diaspora românească din întreaga lume.

Poezii, proză, eseuri, ilustrații.

Constelatii Diamantine is one of the best Romanian literary journals of today. It has an international editorial board and collaborators from all over Romanian diaspora around the world.

Poems, prose, essays, illustrations.

Constelatii Diamantine is one of the best Romanian literary journals of today. It has an international editorship and collaborators from all over Romanian diaspora around the world. Poems, prose, essays, illustrations.

Constelatii Diamantine este una dintre cele mai bune reviste literare romanesti ale zilelor noastre. Are o redacție internațională și colaboratori din toată diaspora românească din întreaga lume. Poezii, proză, eseuri, ilustrații

In this twelfth book of scilogs – called seed & heed –, one may find topics on Neutrosophy, Superluminal Physics, Mathematics, Information Fusion, Philosophy, or Sociology – email messages to research colleagues, or replies, notes, comments, remarks about authors, articles, or books, spontaneous ideas, and so on.

Exchanging ideas with Pritpal Singh, Mohamed Abobala, Muhammad Aslam, Ervin Goldfain, Dmitri Rabounski, Victor Christianto, Steven Crothers, Jean Dezert, Tomasz Witczak (in order of reference in the book).

In this eleventh book of scilogs – called in-turns and out-turns –, one may find new and old questions and solutions, referring mostly to topics on Neutrosophy, but also Multispace, with miscellaneous addition of topics on Physics, Mathematics, or Sociology – email messages to research colleagues, or replies, notes about authors, articles, or books, spontaneous ideas, and so on.

Exchanging ideas with Prem Kumar Singh, Feng Liu, Nicolae Bălașa, Jimmy Quellet, Minodora Rușchița, Frank Gelli, A. R. Vătuiu, Victor Christianto, Vladimir I. Rogozhin, Robert Neil Boyd, Akira Kanda, Stefan Spaarmann, Oliver Consa, Yabin Shao, Junle Zhuo, Nivetha Martin, Said Broumi, Jean Dezert, Erick González, Tomasz Witczak, B. De Baets, I. Couso, D. Dubois, L. Good, Mihaela Colhon, Atiqe Ur Rahman, Muhammad Saeed, Muhammad Ihsan, Edeline Nancy, Shawkat Alkhazaleh, Shazia Rana, Vasantha Kandasamy, Santanu Acharjee, Mohamed Al-Shmrani, Parimala Manie, Mehmet Unver, Murat Olgun, Adel Aleidhri, Akira Kanda, Ilanthenral Kandasamy, Mircea Zărnescu, R. Tayebi Khorami, Arsham Borumand Saeid, Maisam Jdid, M. Abobala, Riad Hamido, Rafael Rojas, Esmaeil Zarei, Faisal Khan, Rouzbeh Abbassi, Adel Al-Odhari, Henry Garrett, Ackbar Rezaei, Saeid Jafari, Karthika Muthusamy, Harish Garg, Huda E. Khalid, Gonca D. Güngör, Muslim A. Noah Zainal, Fakhry Asad Agusfrianto, Madeleine Al-Tahan, Mariam Hariri, Yudi Mahatma, Masoud Ghods, Marco Brigliadori, Luis Enrique Aponte Pérez, Amr Mohammed, M. Aslam (in order of reference in the book).

This album brings together photos from a documentary trip I made in December 2008-January 2009 in Central America (Guatemala and Honduras), to discover the old Maya civilization. In one of those blurry days caused by Pacaya volcano's debris and ash, along the ruins of Petén, I believe I must have had an encounter with the Maya deity Kʼawiil…

This photo album contains images from a trip to Quebec city and Montreal, on the occasion of an international scientific conference I attended in the sumer of 2006.

Cet album photo contient des images d'un voyage à Québec et Montréal, à l'occasion d'une conférence scientifique internationale à laquelle j'ai participé l’été de l’année 2006.

For the first time, the authors venture to define the notion of
linguistic geometry in this book. It is pertinent to keep in the
record that linguistic geometry differs from classical geometry.
Many basic or fundamental concepts and notions of classical
geometry are not true or extendable in the case of linguistic
geometry. Hence, for simple illustration, facts like two distinct
points in classical geometry always define a line passing
through them; this is generally not true in linguistic geometry.

The authors define the notion of directed linguistic graphs and linguistic-weighted graphs.
Chapter two of the book discusses all types of linguistic graphs, linguistic dyads, linguistic triads, linguistic wheels, complete linguistic graphs, connected linguistic graphs, disconnected linguistic graphs, and linguistic components of the graphs.  Further we define the notion of linguistic subgraphs of a linguistic graph.  The third chapter also introduces the notion of Linguistic Cognitive Maps (LCMs) analogous to Fuzzy Cognitive maps (FCMs).  We also propose Linguistic relational Maps, which are analogous to Fuzzy relational Maps.  These models find applications in problems whose data is unsupervised, but the values are linguistic.

The authors build linguistic matrices only for those linguistic variables which yield a linguistic continuum or an ordered linguistic set.  Most of the properties enjoyed by real and complex matrices are satisfied by these linguistic matrices. However, we see when we try to define operations on linguistic matrices that they behave in different ways.  The possible operations defined on linguistic matrices are only the maximum and minimum.  Further, we have different identities for min and max operations on these matrices for linguistic variable and its associated linguistic words.

In this book, the authors have proved the analogues of the Bolzano Weierstrass theorem for the linguistic version. Several concepts in the case of linguistic continuum are very distinct from the natural classical real continuum. Categorically, we have three linguistic variables: one leading to a continuum, some finite and orderable set, and some not orderable. We define a linguistic plane associated with linguistic variables and give graphs associated with linguistic functions.

0(مقدمة)Degree of membership greater than 1 anddegree of membership less than 0(preface)ّعُرف مفهومفوق/تحت/خلفالمجموعة، والمنطق النيوتروسوفيك للمرة الأولىمن قبل المؤلففيعام𝟏𝟗𝟗𝟓، وقّدم في مختلف المؤتمرات، والندوات الوطنية، والدولية[14 -15]بين عامي𝟏𝟗𝟗𝟓 − 𝟐𝟎𝟏𝟔،ونشر للمرةالأولى[1-9,13]في عام𝟐𝟎𝟎𝟕بّحيث إنًها مختلفة تماماعن المجموعات/المنطق/الاحتمالات/الإحصاءات الأخرى، وتم ّ تعميممجموعة النيوتروسوفيكيةعلى التوالي إلىفوقمجموعة النيوتروسوفيكية}عندمابعض مركبات النيوتروسوفيك أكبر من1{، وتحتمجموعةالنيوتروسوفيكية}عندما بعض مركبات النيوتروسوفيكأصغر من0{، وخلفمجموعة النيوتروسوفيكية}عندمابعض مركبات النيوتروسوفيك خارج المجال[𝟎, 𝟏]،أي:بعض مركبات النيوتروسوفيك أكبر من1، والمركبات الأخرى أصغر من0{.هذا الشيء ليس مفاجئا ً بالنسبة للمجموعة/المنطق الضبابي الكلاسيكي، والمجموعة/المنطق الضبابيالحدسي،أوالاحتمال الكلاسيكي/غير الدقيق،حيثالقيم لايسمح لها أن تكون خارج المجال[𝟎, 𝟏]،حيثعند النظرإلى عالمنا الحقيقي نجد أنَه يحوي الكثير منالأمثلة، والتطبيقات فوق/تحت/خلف مركبات النيوتروسوفيكمثالفي شركة معينةيعتبر العامل يعمل بدوام كامل إذا كانت مدة العمل𝟒𝟎ساعة في الأسبوع،لنعتبر فترةالأسبوع الماضي، حيثعملت هيلين بدوامّجزئي،𝟑𝟎ساعة فقط، وغابت العشر ساعات الأخرى بدون أجر؛،وبالتاليكانت درجة عضويتها𝟑𝟎𝟒𝟎 = 𝟎. 𝟕𝟓 < 𝟏.عمل يوحنا كامل الوقت،أي𝟒𝟎ساعة؛ لذايملك درجة عضوية𝟒𝟎𝟒𝟎 = 𝟏بالنسبة إلى هذه الشركة،لكنجورج عمل𝟓ساعاتإضافية إلى، وقت العمل؛؛ لذاكانت درجة عضويته𝟒𝟎+𝟓𝟒𝟎 = 𝟒𝟓𝟒𝟎 = 𝟏. 𝟏𝟐𝟓 > 𝟏، وبالتالينحتاج إلى التمييز بين العمالالذين يعملون، وقتًاإضافيًا، وأولئكالّذينيعملون كامل الوقت المطلوب، أوجزءًامنالوقت المطلوب، ولهذا السبب نحتاج درجة عضوية مساعدة تكون أكبر من1بشكل أكيد بالنسبة للعمالالّذينيعملون،وًقتا ً إضافيا.الآن عاملةأخرى جين كانت غائبة عن كامل الأسبوع بدون أجر؛لذادرجة عضويتها كانت𝟎𝟒𝟎 = 𝟎، ومعذلك فإن َ ريتشارد الذي تم َ تعيينهًأيضابدوام كامل،لم يأت إلى العملالأسبوعالماضي على الإطلاق (𝟎ساعات العمل)،لكنَهًأيضاتسبب بحدوث حريق مدمر مما تسبب بأضرار جسيمة للشركة، والتي كانت تقدر بنصف راتبه (أي إنه كانسيحصل على العمل𝟐𝟎ساعة في ذلك الأسبوع)؛؛ لذلكدرجة عضويته يجب أن تكون أقل من درجة عضوية جينً(نظراّ؛ لأنجين لم تسبب أضرارًا)، ومن هنا كانت درجة عضوية ريتشارد بالنسبة إلى هذه الشركة كانت−𝟐𝟎𝟒𝟎 =−𝟎. 𝟓 < 𝟎، وبالتالي نحتاج أن نميز بين العمالالّذينيتسببون بأضرار، وأولئكالّذينًيحققون ربحا، وأولئكالّذينلايتسببون في الضرر، ولا يحققون ربحا ً للشركة.وبالتالي درجة العضوية أكبر من1، ودرجة العضوية أصغر من0حقيقية (موجودة) في عالمنا؛ لذا يجبأخذهابعينالاعتبار،ثم َ بشكل مشابه تعميم المنطق/القياس/الاحتمال/الإحصاء النيوتروسوفيك... إلخعلىالتوالي إلىفوق/تحت/خلفالمنطق/القياس/الاحتمال/الإحصاء النيوتروسوفيك]سمارنداش𝟐𝟎𝟎𝟕[.تم َ تقديم العديد من الأمثلة البديهية العملية في هذا الكتاب،من أجل أن نبين أنَه في حياتنا اليومية نتعاملباستمرار مع نظرية فوق/تحت/خلف النيوتروسوفيك، وتطبيقاتها.

(2) (PDF) فوق‬ ‫النيوتروسوفيكية‬ ‫مجموعة‬ ‫تحت‬ ‫النيوتروسوفيكية‬ ‫مجموعة. Available from: https://www.researchgate.net/publication/366446164_fwq_alnywtrwswfykyt_mjmwt_tht_alnywtrwswfykyt_mjmwt [accessed Dec 21 2022].

0(مقدمة)Degree of membership greater than 1 anddegree of membership less than 0(preface)ّعُرف مفهومفوق/تحت/خلفالمجموعة، والمنطق النيوتروسوفيك للمرة الأولىمن قبل المؤلففيعام𝟏𝟗𝟗𝟓، وقّدم في مختلف المؤتمرات، والندوات الوطنية، والدولية[14 -15]بين عامي𝟏𝟗𝟗𝟓 − 𝟐𝟎𝟏𝟔،ونشر للمرةالأولى[1-9,13]في عام𝟐𝟎𝟎𝟕بّحيث إنًها مختلفة تماماعن المجموعات/المنطق/الاحتمالات/الإحصاءات الأخرى، وتم ّ تعميممجموعة النيوتروسوفيكيةعلى التوالي إلىفوقمجموعة النيوتروسوفيكية}عندمابعض مركبات النيوتروسوفيك أكبر من1{، وتحتمجموعةالنيوتروسوفيكية}عندما بعض مركبات النيوتروسوفيكأصغر من0{، وخلفمجموعة النيوتروسوفيكية}عندمابعض مركبات النيوتروسوفيك خارج المجال[𝟎, 𝟏]،أي:بعض مركبات النيوتروسوفيك أكبر من1، والمركبات الأخرى أصغر من0{.هذا الشيء ليس مفاجئا ً بالنسبة للمجموعة/المنطق الضبابي الكلاسيكي، والمجموعة/المنطق الضبابيالحدسي،أوالاحتمال الكلاسيكي/غير الدقيق،حيثالقيم لايسمح لها أن تكون خارج المجال[𝟎, 𝟏]،حيثعند النظرإلى عالمنا الحقيقي نجد أنَه يحوي الكثير منالأمثلة، والتطبيقات فوق/تحت/خلف مركبات النيوتروسوفيكمثالفي شركة معينةيعتبر العامل يعمل بدوام كامل إذا كانت مدة العمل𝟒𝟎ساعة في الأسبوع،لنعتبر فترةالأسبوع الماضي، حيثعملت هيلين بدوامّجزئي،𝟑𝟎ساعة فقط، وغابت العشر ساعات الأخرى بدون أجر؛،وبالتاليكانت درجة عضويتها𝟑𝟎𝟒𝟎 = 𝟎. 𝟕𝟓 < 𝟏.عمل يوحنا كامل الوقت،أي𝟒𝟎ساعة؛ لذايملك درجة عضوية𝟒𝟎𝟒𝟎 = 𝟏بالنسبة إلى هذه الشركة،لكنجورج عمل𝟓ساعاتإضافية إلى، وقت العمل؛؛ لذاكانت درجة عضويته𝟒𝟎+𝟓𝟒𝟎 = 𝟒𝟓𝟒𝟎 = 𝟏. 𝟏𝟐𝟓 > 𝟏، وبالتالينحتاج إلى التمييز بين العمالالذين يعملون، وقتًاإضافيًا، وأولئكالّذينيعملون كامل الوقت المطلوب، أوجزءًامنالوقت المطلوب، ولهذا السبب نحتاج درجة عضوية مساعدة تكون أكبر من1بشكل أكيد بالنسبة للعمالالّذينيعملون،وًقتا ً إضافيا.الآن عاملةأخرى جين كانت غائبة عن كامل الأسبوع بدون أجر؛لذادرجة عضويتها كانت𝟎𝟒𝟎 = 𝟎، ومعذلك فإن َ ريتشارد الذي تم َ تعيينهًأيضابدوام كامل،لم يأت إلى العملالأسبوعالماضي على الإطلاق (𝟎ساعات العمل)،لكنَهًأيضاتسبب بحدوث حريق مدمر مما تسبب بأضرار جسيمة للشركة، والتي كانت تقدر بنصف راتبه (أي إنه كانسيحصل على العمل𝟐𝟎ساعة في ذلك الأسبوع)؛؛ لذلكدرجة عضويته يجب أن تكون أقل من درجة عضوية جينً(نظراّ؛ لأنجين لم تسبب أضرارًا)، ومن هنا كانت درجة عضوية ريتشارد بالنسبة إلى هذه الشركة كانت−𝟐𝟎𝟒𝟎 =−𝟎. 𝟓 < 𝟎، وبالتالي نحتاج أن نميز بين العمالالّذينيتسببون بأضرار، وأولئكالّذينًيحققون ربحا، وأولئكالّذينلايتسببون في الضرر، ولا يحققون ربحا ً للشركة.وبالتالي درجة العضوية أكبر من1، ودرجة العضوية أصغر من0حقيقية (موجودة) في عالمنا؛ لذا يجبأخذهابعينالاعتبار،ثم َ بشكل مشابه تعميم المنطق/القياس/الاحتمال/الإحصاء النيوتروسوفيك... إلخعلىالتوالي إلىفوق/تحت/خلفالمنطق/القياس/الاحتمال/الإحصاء النيوتروسوفيك]سمارنداش𝟐𝟎𝟎𝟕[.تم َ تقديم العديد من الأمثلة البديهية العملية في هذا الكتاب،من أجل أن نبين أنَه في حياتنا اليومية نتعاملباستمرار مع نظرية فوق/تحت/خلف النيوتروسوفيك، وتطبيقاتها

(2) (PDF) فوق‬ ‫النيوتروسوفيكية‬ ‫مجموعة‬ ‫تحت‬ ‫النيوتروسوفيكية‬ ‫مجموعة. Available from: https://www.researchgate.net/publication/366446164_fwq_alnywtrwswfykyt_mjmwt_tht_alnywtrwswfykyt_mjmwt [accessed Dec 21 2022].

This is a photoalbum inspired by a trip in which I ventured almost twenty years ago (2004) in Bahamas, and on which I related at large in my travelog “Frate cu meridianele si paralelele” (Brother of meridians and parallels), tome II, Rm. Valcea, Romania, 2005 (in Romanian).

In addition to images, this album contains short notations on the history of Bahamas or its current real-life, or intents to impart instant perceptions had on the spot, placed retrospectively under the general feeling that Bahamas has the power to penetrate one’s heart, and saccharify it (i.e. literally “to make into sugar”). Consequently, I coined the word Bahama-saccharification to describe that unique word-lacking feeling that I still have twenty years later when images from there come under my eyes or in my mind.

This photo album exhibits photographies from a trip I took in MACAU ten years ago (2012), and on which I related at large in my travelog “EXTENSICA. FOTOJURNAL INSTANTANEU DIN CANTON” (Extenics. Instant photojournal in Canton), Romania, 2012 (in Romanian). In addition to images, this album contains short notations on the history of Macau or its current real-life.

Macau (officially the Macao Special Administrative Region of the People's Republic of China) is a city by the South China Sea, in the western Pearl River Delta, nowadays the most densely populated region in the world.

The first written record of the name "Macau", as "Ya/A Ma Gang“, dates back from 1555. The earliest Portuguese spelling for the place was AMAQUÃO, and many variations were used until Macau became standardized by the new Portuguese orthography.

Scientia Magna is a peer-reviewed, open access journal that publishes original research articles in all areas of mathematics and mathematical sciences. However, papers related to Smarandache’s problems are highly preferred. The papers may be in the format of remarks, conjectures, solved/unsolved or open new proposed problems, notes, articles, miscellaneous, etc.

This fourteenth volume of Collected Papers is an eclectic tome of 87 papers in Neutrosophics and other fields, such as mathematics, fuzzy sets, intuitionistic fuzzy sets, picture fuzzy sets, information fusion, robotics, statistics, or extenics, comprising 936 pages, published between 2008-2022 in different scientific journals or currently in press, by the author alone or in collaboration with the following 99 co-authors (alphabetically ordered) from 26 countries: Ahmed B. Al-Nafee, Adesina Abdul Akeem Agboola, Akbar Rezaei, Shariful Alam, Marina Alonso, Fran Andujar, Toshinori Asai, Assia Bakali, Azmat Hussain, Daniela Baran, Bijan Davvaz, Bilal Hadjadji, Carlos Díaz Bohorquez, Robert N. Boyd, M. Caldas, Cenap Özel, Pankaj Chauhan, Victor Christianto, Salvador Coll, Shyamal Dalapati, Irfan Deli, Balasubramanian Elavarasan, Fahad Alsharari, Yonfei Feng, Daniela Gîfu, Rafael Rojas Gualdrón, Haipeng Wang, Hemant Kumar Gianey, Noel Batista Hernández, Abdel-Nasser Hussein, Ibrahim M. Hezam, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Muthusamy Karthika, Nour Eldeen M. Khalifa, Madad Khan, Kifayat Ullah, Valeri Kroumov, Tapan Kumar Roy, Deepesh Kunwar, Le Thi Nhung, Pedro López, Mai Mohamed, Manh Van Vu, Miguel A. Quiroz-Martínez, Marcel Migdalovici, Kritika Mishra, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohammed Alshumrani, Mohamed Loey, Muhammad Akram, Muhammad Shabir, Mumtaz Ali, Nassim Abbas, Munazza Naz, Ngan Thi Roan, Nguyen Xuan Thao, Rishwanth Mani Parimala, Ion Pătrașcu, Surapati Pramanik, Quek Shio Gai, Qiang Guo, Rajab Ali Borzooei, Nimitha Rajesh, Jesús Estupiñan Ricardo, Juan Miguel Martínez Rubio, Saeed Mirvakili, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, Ahmed A. Salama, Nirmala Sawan, Gheorghe Săvoiu, Ganeshsree Selvachandran, Seok-Zun Song, Shahzaib Ashraf, Jayant Singh, Rajesh Singh, Son Hoang Le, Tahir Mahmood, Kenta Takaya, Mirela Teodorescu, Ramalingam Udhayakumar, Maikel Y. Leyva Vázquez, V. Venkateswara Rao, Luige Vlădăreanu, Victor Vlădăreanu, Gabriela Vlădeanu, Michael Voskoglou, Yaser Saber, Yong Deng, You He, Youcef Chibani, Young Bae Jun, Wadei F. Al-Omeri, Hongbo Wang, Zayen Azzouz Omar.

This thirteenth volume of Collected Papers is an eclectic tome of 88 papers in various fields of sciences, such as astronomy, biology, calculus, economics, education and administration, game theory, geometry, graph theory, information fusion, decision making, instantaneous physics, quantum physics, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, scientific research methods, statistics, and others, structured in 17 chapters (Neutrosophic Theory and Applications; Neutrosophic Algebra; Fuzzy Soft Sets; Neutrosophic Sets; Hypersoft Sets; Neutrosophic Semigroups; Neutrosophic Graphs; Superhypergraphs; Plithogeny; Information Fusion; Statistics; Decision Making; Extenics; Instantaneous Physics; Paradoxism; Mathematica; Miscellanea), comprising 965 pages, published between 2005-2022 in different scientific journals, by the author alone or in collaboration with the following 110 co-authors (alphabetically ordered) from 26 countries: Abduallah Gamal, Sania Afzal, Firoz Ahmad, Muhammad Akram, Sheriful Alam, Ali Hamza, Ali H. M. Al-Obaidi, Madeleine Al-Tahan, Assia Bakali, Atiqe Ur Rahman, Sukanto Bhattacharya, Bilal Hadjadji, Robert N. Boyd, Willem K.M. Brauers, Umit Cali, Youcef Chibani, Victor Christianto, Chunxin Bo, Shyamal Dalapati, Mario Dalcín, Arup Kumar Das, Elham Davneshvar, Bijan Davvaz, Irfan Deli, Muhammet Deveci, Mamouni Dhar, R. Dhavaseelan, Balasubramanian Elavarasan, Sara Farooq, Haipeng Wang, Ugur Halden, Le Hoang Son, Hongnian Yu, Qays Hatem Imran, Mayas Ismail, Saeid Jafari, Jun Ye, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, Abdullah Kargın, Vasilios N. Katsikis, Nour Eldeen M. Khalifa, Madad Khan, M. Khoshnevisan, Tapan Kumar Roy, Pinaki Majumdar, Sreepurna Malakar, Masoud Ghods, Minghao Hu, Mingming Chen, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohamed Loey, Mihnea Alexandru Moisescu, Muhammad Ihsan, Muhammad Saeed, Muhammad Shabir, Mumtaz Ali, Muzzamal Sitara, Nassim Abbas, Munazza Naz, Giorgio Nordo, Mani Parimala, Ion Pătrașcu, Gabrijela Popović, K. Porselvi, Surapati Pramanik, D. Preethi, Qiang Guo, Riad K. Al-Hamido, Zahra Rostami, Said Broumi, Saima Anis, Muzafer Saračević, Ganeshsree Selvachandran, Selvaraj Ganesan, Shammya Shananda Saha, Marayanagaraj Shanmugapriya, Songtao Shao, Sori Tjandrah Simbolon, Florentin Smarandache, Predrag S. Stanimirović, Dragiša Stanujkić, Raman Sundareswaran, Mehmet Șahin, Ovidiu-Ilie Șandru, Abdulkadir Șengür, Mohamed Talea, Ferhat Taș, Selçuk Topal, Alptekin Ulutaș, Ramalingam Udhayakumar, Yunita Umniyati, J. Vimala, Luige Vlădăreanu, Ştefan Vlăduţescu, Yaman Akbulut, Yanhui Guo, Yong Deng, You He, Young Bae Jun, Wangtao Yuan, Rong Xia, Xiaohong Zhang, Edmundas Kazimieras Zavadskas, Zayen Azzouz Omar, Xiaohong Zhang, Zhirou Ma.‬‬‬‬‬‬‬‬

This twelfth volume of Collected Papers includes 86 papers comprising 976 pages on Neutrosophics Theory and Applications, published between 2013-2021 in the international journal and book series “Neutrosophic Sets and Systems” by the author alone or in collaboration with the following 112 co-authors (alphabetically ordered) from 21 countries: Abdel Nasser H. Zaied, Muhammad Akram, Bobin Albert, S. A. Alblowi, S. Anitha, Guennoun Asmae, Assia Bakali, Ayman M. Manie, Abdul Sami Awan, Azeddine Elhassouny, Erick González-Caballero, D. Dafik, Mithun Datta, Arindam Dey, Mamouni Dhar, Christopher Dyer, Nur Ain Ebas, Mohamed Eisa, Ahmed K. Essa, Faruk Karaaslan, João Alcione Sganderla Figueiredo, Jorge Fernando Goyes García, N. Ramila Gandhi, Sudipta Gayen, Gustavo Alvarez Gómez, Sharon Dinarza Álvarez Gómez, Haitham A. El-Ghareeb, Hamiden Abd El-Wahed Khalifa, Masooma Raza Hashmi, Ibrahim M. Hezam, German Acurio Hidalgo, Le Hoang Son, R. Jahir Hussain, S. Satham Hussain, Ali Hussein Mahmood Al-Obaidi, Hays Hatem Imran, Nabeela Ishfaq, Saeid Jafari, R. Jansi, V. Jeyanthi, M. Jeyaraman, Sripati Jha, Jun Ye, W.B. Vasantha Kandasamy, Abdullah Kargın, J. Kavikumar, Kawther Fawzi Hamza Alhasan, Huda E. Khalid, Neha Andalleb Khalid, Mohsin Khalid, Madad Khan, D. Koley, Valeri Kroumov, Manoranjan Kumar Singh, Pavan Kumar, Prem Kumar Singh, Ranjan Kumar, Malayalan Lathamaheswari, A.N. Mangayarkkarasi, Carlos Rosero Martínez, Marvelio Alfaro Matos, Mai Mohamed, Nivetha Martin, Mohamed Abdel-Basset, Mohamed Talea, K. Mohana, Muhammad Irfan Ahamad, Rana Muhammad Zulqarnain, Muhammad Riaz, Muhammad Saeed, Muhammad Saqlain, Muhammad Shabir, Muhammad Zeeshan, Anjan Mukherjee, Mumtaz Ali, Deivanayagampillai Nagarajan, Iqra Nawaz, Munazza Naz, Roan Thi Ngan, Necati Olgun, Rodolfo González Ortega, P. Pandiammal, I. Pradeepa, R. Princy, Marcos David Oviedo Rodríguez, Jesús Estupiñán Ricardo, A. Rohini, Sabu Sebastian, Abhijit Saha, Mehmet Șahin, Said Broumi, Saima Anis, A.A. Salama, Ganeshsree Selvachandran, Seyed Ahmad Edalatpanah, Sajana Shaik, Soufiane Idbrahim, S. Sowndrarajan, Mohamed Talea, Ruipu Tan, Chalapathi Tekuri, Selçuk Topal, S. P. Tiwari, Vakkas Uluçay, Maikel Leyva Vázquez, Chinnadurai Veerappan, M. Venkatachalam, Luige Vlădăreanu, Ştefan Vlăduţescu, Young Bae Jun, Wadei F. Al-Omeri, Xiao Long Xin.‬‬‬‬‬‬

This eleventh volume of Collected Papers includes 90 papers comprising 988 pages on Physics, Artificial Intelligence, Health Issues, Decision Making, Economics, Statistics, written between 2001-2022 by the author alone or in collaboration with the following 84 co-authors (alphabetically ordered) from 19 countries: Abhijit Saha, Abu Sufian, Jack Allen, Shahbaz Ali, Ali Safaa Sadiq, Aliya Fahmi, Atiqa Fakhar, Atiqa Firdous, Sukanto Bhattacharya, Robert N. Boyd, Victor Chang, Victor Christianto, V. Christy, Dao The Son, Debjit Dutta, Azeddine Elhassouny, Fazal Ghani, Fazli Amin, Anirudha Ghosha, Nasruddin Hassan, Hoang Viet Long, Jhulaneswar Baidya, Jin Kim, Jun Ye, Darjan Karabašević, Vasilios N. Katsikis, Ieva Meidutė-Kavaliauskienė, F. Kaymarm, Nour Eldeen M. Khalifa, Madad Khan, Qaisar Khan, M. Khoshnevisan, Kifayat Ullah,, Volodymyr Krasnoholovets, Mukesh Kumar, Le Hoang Son, Luong Thi Hong Lan, Tahir Mahmood, Mahmoud Ismail, Mohamed Abdel-Basset, Siti Nurul Fitriah Mohamad, Mohamed Loey, Mai Mohamed, K. Mohana, Kalyan Mondal, Muhammad Gulfam, Muhammad Khalid Mahmood, Muhammad Jamil, Muhammad Yaqub Khan, Muhammad Riaz, Nguyen Dinh Hoa, Cu Nguyen Giap, Nguyen Tho Thong, Peide Liu, Pham Huy Thong, Gabrijela Popović‬‬‬‬‬‬‬‬‬‬, Surapati Pramanik, Dmitri Rabounski, Roslan Hasni, Rumi Roy, Tapan Kumar Roy, Said Broumi, Saleem Abdullah, Muzafer Saračević, Ganeshsree Selvachandran, Shariful Alam, Shyamal Dalapati, Housila P. Singh, R. Singh, Rajesh Singh, Predrag S. Stanimirović, Kasan Susilo, Dragiša Stanujkić, Alexandra Şandru, Ovidiu Ilie Şandru, Zenonas Turskis, Yunita Umniyati, Alptekin Ulutaș, Maikel Yelandi Leyva Vázquez, Binyamin Yusoff, Edmundas Kazimieras Zavadskas, Zhao Loon Wang.‬‬‬‬

This tenth volume of Collected Papers includes 86 papers in English and Spanish languages comprising 972 pages, written between 2014-2022 by the author alone or in collaboration with the following 105 co-authors (alphabetically ordered) from 26 countries: Abu Sufian, Ali Hassan, Ali Safaa Sadiq, Anirudha Ghosh, Assia Bakali, Atiqe Ur Rahman, Laura Bogdan, Willem K.M. Brauers, Erick González Caballero, Fausto Cavallaro, Gavrilă Calefariu, T. Chalapathi, Victor Christianto, Mihaela Colhon, Sergiu Boris Cononovici, Mamoni Dhar, Irfan Deli, Rebeca Escobar-Jara, Alexandru Gal, N. Gandotra, Sudipta Gayen, Vassilis C. Gerogiannis, Noel Batista Hernández, Hongnian Yu, Hongbo Wang, Mihaiela Iliescu, F. Nirmala Irudayam, Sripati Jha, Darjan Karabašević, T. Katican, Bakhtawar Ali Khan, Hina Khan, Volodymyr Krasnoholovets, R. Kiran Kumar, Manoranjan Kumar Singh, Ranjan Kumar, M. Lathamaheswari, Yasar Mahmood, Nivetha Martin, Adrian Mărgean, Octavian Melinte, Mingcong Deng, Marcel Migdalovici, Monika Moga, Sana Moin, Mohamed Abdel-Basset, Mohamed Elhoseny, Rehab Mohamed, Mohamed Talea, Kalyan Mondal, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Ihsan, Muhammad Naveed Jafar, Muhammad Rayees Ahmad, Muhammad Saeed, Muhammad Saqlain, Muhammad Shabir, Mujahid Abbas, Mumtaz Ali, Radu I. Munteanu, Ghulam Murtaza, Munazza Naz, Tahsin Oner, ‪Gabrijela Popović‬‬‬‬‬, Surapati Pramanik, R. Priya, S.P. Priyadharshini, Midha Qayyum, Quang-Thinh Bui, Shazia Rana, Akbara Rezaei, Jesús Estupiñán Ricardo, Rıdvan Sahin, Saeeda Mirvakili, Said Broumi, A. A. Salama, Flavius Aurelian Sârbu, Ganeshsree Selvachandran, Javid Shabbir, Shio Gai Quek, Son Hoang Le, Florentin Smarandache, Dragiša Stanujkić, S. Sudha, Taha Yasin Ozturk, Zaigham Tahir, The Houw Iong, Ayse Topal, Alptekin Ulutaș, Maikel Yelandi Leyva Vázquez, Rizha Vitania, Luige Vlădăreanu, Victor Vlădăreanu, Ștefan Vlăduțescu, J. Vimala, Dan Valeriu Voinea, Adem Yolcu, Yongfei Feng, Abd El-Nasser H. Zaied, Edmundas Kazimieras Zavadskas.‬‬

In this paper we prove that Neutrosophic Set (NS) is an extension of Intuitionistic Fuzzy Set (IFS) no matter if the sum of single-valued neutrosophic components is < 1, or > 1, or = 1. For the case when the sum of components is 1 (as in IFS), after applying the neutrosophic aggregation operators one gets a different result from that of applying the intuitionistic fuzzy operators, since the intuitionistic fuzzy operators ignore the indeterminacy, while the neutrosophic aggregation operators take into consideration the indeterminacy at the same level as truth-membership and falsehood-nonmembership are taken. NS is also more flexible and effective because it handles, besides independent components, also partially independent and partially dependent components, while IFS cannot deal with these.

This paper presents the importance of Neutrosophy theory in order to find a method that could solve the uncertainties arising on manufacturing process. The aim of this pilot study is to find a procedure to diminish the uncertainties induced by manufacturing, maintenance,
logistics, design, human resources. The study is intended to identify a method to answer uncertainties solving in order to support manufacturing managers, artificial intelligence researchers and businessman in general.

Una nueva rama de la filosofía la cual estudia el origen, naturaleza y alcance de las neutralidades, así como sus interacciones con diferentes espectros ideacionales (1995).
La neutrosófica abrió un nuevo campo de investigación en la metafilosofía.
Etimológicamenteneutron-sofía [Francesneutre<Latinneuter,neutral,ygriegosophia,conocimiento]signif icaconocimientodelospensamientoneutralesycomenzóen1995.

According to the General Theory of Relativity the space is curved around a massive object. Then, after the planet explodes (due to internal forces) or destroyed (because of external forces) does the space around it still remain curved or does it straighten back to flat?

Neutrosophic Logic is a general framework for unification of many existing logics, and its components T (truth), I (indeterminacy), F (falsehood) are standard or non-standard real subsets of ] − 0, 1 + [ with not necessarily any connection between them.

In the macrocosmos, let’s consider an astronomical body (A1), around which orbits another astronomical body (A2), and around (A2) orbits another astronomical body (A3), and again around (A3) orbits another astronomical body (A4), and so on.

Considering the Big Bang Theory, stating that the universe has begun through an explosion of a primeval atom, based on the Christianity believe that the universe was created, the following questions will naturally occur: a) where did this primeval atom come from?

The General Theory of Relativity asserts that it is possible to have a pure gravitational field, without any matter at all, which acts as a source for itself. Then the following questions arise: What does happen to the cosmic travelling small, medium and massive objects and to the atomic and sub-atomic particles in this pure gravitational field?

Generalizing the classical probability and imprecise probability to the notion of " neutrosophic probability " in order to be able to model Heisenberg's Uncertainty Principle of a particle's behavior , Schrödinger's Cat Theory, and the state of bosons which do not obey Pauli's Exclusion Principle (in quantum physics). Neutrosophic probability is close related to neutrosophic logic and neutrosophic set.

In recent years a number of new planetoids have been reported, in particular by M. Brown and his team. While new planet discoveries have been reported from time to time, known as exoplanets, nonetheless discovery of new planetoids in the solar system are very interesting, because they are found after a long period of silence after Pluto finding, around seventy years ago. Therefore, it seems interesting to find out implications of this discovery to our knowledge of solar system, in particular in the context of quantization of celestial system.

There is not a clear frontier between visible matter and invisible matter. An invisible particle does not form a visible object, nor do two invisible particles, three invisible particles, etc. However, at some point, the collection of invisible particles becomes large enough to form a visible object, but there is apparently no definite point where this occurs. A similar paradox is developed in an opposite direction. It is always possible to remove a particle from an object in such a way that what is left is still a visible object. However, repeating and repeating this process, at some point, the visible object is decomposed so that the left part becomes invisible, but there is no definite point where this occurs.

We consider n > 2 identical rockets: R1; R2, . . . , Rn. Each of them moving at constant different velocities respectively v1, v2, . . . , vn on parallel directions in the same sense. In each rocket there is a light clock, the observer on earth also has a light clock.

Neutrosophic Statistical Mechanics is the theory in which, using the neutrosophic statistical behavior of the
constituent particles of a macroscopic system, are predicted the approximate properties of this macroscopic system. Neutrosophic Statistics means statistical analysis of population or sample that has indeterminate (imprecise, ambiguous, vague, incomplete, unknown) data.

In the classical Twin Paradox, according to the Special Theory of Relativity, when the traveling twin blasts off from the Earth to a relative velocity with respect to the Earth, his measuring stick and other physical objects in the direction of relative motion shrink to half their lengths.

In Special Theory of Relativity it looks that the length contraction along the direction of the motion is independent of time, i.e. if a rocket flies one second, or the rocket flies one year the rocket's along-the-motion length contraction is the same, since the contraction
factor depends on the rocket's relativistic speed (v) and on the light speed in vacuum (c) only.

Neutrosophic probability (or likelihood) [1995] is a particular case of the neutrosophic measure. It is an estimation of an event (different from indeterminacy) to occur, together with an estimation that some indeterminacy may occur, and the estimation that the event does not occur. The classical probability deals with fair dice, coins, roulettes, spinners, decks of cards,
random works, while neutrosophic probability deals with unfair, imperfect such objects and processes.

We introduce for the rst time the scienti c notion of neutrosophic measure.The neutrosophic measure is practically a double classical measure: a classical mea-
sure of the determinate part of a neutrosophic object, and another classical measure of the indeterminate part of the same neutrosophic object. Of course, if the inde-
terminate part does not exist (or its measure is zero), the neutrosophic measure is reduced to the classical measure.