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In recent years, there are a number of proposals to consider collision-based soliton computer based on certain chemical reactions, namely Belousov-Zhabotinsky reaction, which leads to soliton solutions of coupled Nonlinear Schroedinger equations. They are called Manakov System. But it seems to us that such a soliton computer model can also be based on solitary wave solution of Maxwell-Dirac equation, which reduces to Choquard equation. And soliton solution of Choquard equation has been investigated by many researchers, therefore it seems more profound from physics perspective. However, we consider both schemes of soliton computer are equally possible. More researches are needed to verify our proposition. [ABSTRACT FROM AUTHOR]

The Vehicle Routing Problem (VRP) has been extensively studied by different researchers from all over the world in recent years. Multiple solutions have been proposed for different variations of the problem, such as Capacitive Vehicle Routing Problem (CVRP), Vehicle Routing Problem with Time Windows (VRP-TW), Vehicle Routing Problem with Pickup and Delivery (VRPPD), among others, all of them with deterministic times. In the last years, researchers have been interested in including in their different models the variations that travel times may experience when exposed to all kind of phenomena, mainly vehicle traffic. This article addresses the VRP from this perspective, proposing the design and implementation of a genetic algorithm based on neutrosophic theory for calculating the fitness function of each route, considering the variability and uncertainty present in travel times. A deterministic genetic algorithm is also implemented with the average travel times to compare it with the neutrosophic algorithm using simulation. As conclusion, a deterministic algorithm does not necessarily generate the best solution in the real world, full of uncertainty. Also, the quantification of uncertainty using neutrosophic theory can be used in route planning, opening a broad and interesting field of research for future investigations. [ABSTRACT FROM AUTHOR]

The IndetermSoft Set is as an extension of the Soft Set, because the data, or the function, or the sets involved in the definition of the soft set have indeterminacy - as in our everyday life, and we still need to deal with such situations. And similarly, IndetermHyperSoft Set as extension of the HyperSoft Set, when there is indeterminate data, or indeterminate functions, or indeterminate sets. Herein, 'Indeterm' stands for 'Indeterminate' (uncertain, conflicting, incomplete, not unique outcome). We now introduce for the first time the TreeSoft Set as extension of the MultiSoft Set. Several applications are presented for each type of soft set. [ABSTRACT FROM AUTHOR]

In the fifth version of our response-paper [26] to Imamura's criticism, we recall that NonStandard Neutrosophic Logic was never used by neutrosophic community in no application, that the quarter of century old neutrosophic operators (1995-1998) criticized by Imamura were never utilized since they were improved shortly after but he omits to tell their development, and that in real world applications we need to convert/approximate the NonStandard Analysis hyperreals, monads and binads to tiny intervals with the desired accuracy - otherwise they would be inapplicable. We point out several errors and false statements by Imamura [21] with respect to the inf/sup of nonstandard subsets, also Imamura's "rigorous definition of neutrosophic logic" is wrong and the same for his definition of nonstandard unit interval, and we prove that there is not a total order on the set of hyperreals (because of the newly introduced Neutrosophic Hyperreals that are indeterminate), whence the Transfer Principle from R to R* is questionable. After his criticism, several response publications on theoretical nonstandard neutrosophics followed in the period 2018-2022. As such, I extended the NonStandard Analysis by adding the left monad closed to the right, right monad closed to the left, pierced binad (we introduced in 1998), and unpierced binad - all these in order to close the newly extended nonstandard space (R*) under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations [23, 24]. Improved definitions of NonStandard Unit Interval and NonStandard Neutrosophic Logic, together with NonStandard Neutrosophic Operators are presented. [ABSTRACT FROM AUTHOR]

In an earlier paper published in a neutrosophic math journal (IJNS), we discussed a new approach to technology, which may be called as 'opti-realism' or 'pess-optimism' as alternative to utopianism based on technocracy, which may lead the world into global technototalitarianism. In this article, we submit a new approach to Nature and technology, which is more modest and humble, rather than a techno-utopianism version of reality that most futurists argue for. Our proposed approach resembles more to Myer-Briggs 16 types of personality, including IJNS, IFNS etc. In our scheme, there are 8 characters of approach toward technology which can lead to many variations or we call it 'Permutation." Of course, if the readers ask one variation that we prefer, we would answer: Small Tech, High Touch. [ABSTRACT FROM AUTHOR]

In recent years, it becomes clear that ITER project in France, as one of the largest experimental fusion reactors underway, is far away from achieving net energy production. In this review article, we presented a short communication this week with Robert Neil Boyd, a senior physicist who happens to have his own working design of fusion reactor in the past. We hope that this transcript of our communication with him (as per 15-17th Nov. 2021) may be found useful for younger scientists. [ABSTRACT FROM AUTHOR]

In our initial paper discussing plausible steps toward workable warp drive machines. The following article express our view on this debate. While there are still objections toward existing warp drive proposals, such as by G. Landis, Harold White etc., because they are all based on GTR, nonetheless we think it is possible by starting to see if it is possible to deviate from Newton's third law. And we discuss possible a propulsion method based on negative masses, and discuss how optical diameter drive can be first step for realistic lab-scale version of negative mass propulsion. [ABSTRACT FROM AUTHOR]

In this paper we prove that Neutrosophic Statistics is an extension of the Interval Statistics, since it may deal with all types of indeterminacies (with respect to the data, inferential procedures, probability distributions, graphical representations, etc.), it allows the reduction of indeterminacy, and it uses the neutrosophic probability that is more general than imprecise and classical probabilities, andhas more detailed corresponding probability density functions. While Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to the arguments by Woodall et al. [1]. We show that not all indeterminacies (uncertainties) may be represented by intervals. Also, in some applications, we should better use hesitant sets (that have less indeterminacy) instead of intervals. We redirect the authors to the Plithogenic Probability and Plithogenic Statistics that are the most general forms of MultiVariate Probability and MultiVariate Statistics respectively (including, of course, the Imprecise Probability and Interval Statistics as subclasses). [ABSTRACT FROM AUTHOR]

On the third version of this response-paper to Imamura's criticism, we recall that Non Standard Neutrosophic Logic was never used by neutrosophic community in no application, that the quarter of century oldneutrosophic operators (1995-1998) criticized by Imamura were never utilized since they were improved shortly after but he omits to tell their development, and that in real world applications we need to convert/approximate the Non Standard Analysis hyperreals, monads and binads to tiny intervals with the desired accuracy - otherwise they would be inapplicable. We point out several errors and false statements by Imamura [21] with respect to the inf/sup of nonstandard subsets, also Imamura's "rigorous definition of neutrosophic logic" is wrong and the same for his definition of nonstandard unit interval, and we prove that there is not a total order on the set of hyperreals (because of the newly introduced Neutrosophic Hyperreals that are indeterminate), whence the transfer principle is questionable. After his criticism, several response publications on theoretical nonstandard neutrosophics followed in the period 2018-2022. As such, Iextended the Non Standard Analysis by adding the left monad closed to the right, right monad closed to the left, pierced binad (we introduced in 1998), and unpierced binad-all these in order to close the newly extended nonstandard space (R) under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations [23, 24]. Improved definitions of Non Standard Unit Interval and Non Standard Neutrosophic Logic are presented. [ABSTRACT FROM AUTHOR]

In this paper one introduces for the first time the IndetermSoft Set, as extension of the classical (determinate) Soft Set, that deals with indeterminate data, and similarly the HyperSoft Set extended to IndetermHyperSoft Set, where 'Indeterm' stands for 'Indeterminate' (uncertain, conflicting, not unique outcome). They are built on an IndetermSoft Algebra that is an algebra dealing with IndetermSoft Operators resulted from our real world. Afterwards, the corresponding Fuzzy / Intuitionistic Fuzzy / Neutrosophic / and other fuzzy-extension IndetermSoft Set & IndetermHyperSoft Set are presented together with their applications. [ABSTRACT FROM AUTHOR]

In this paper, one recalls the general definition of the SuperHyperAlgebra with its SuperHyperOperations and SuperHyperAxioms [2, 6]. Then one introduces for the first time the SuperHyperTopology and especially the SuperHyperFunction and Neutrosophic SuperHyperFunction. One gives a numerical example of a SuperHyperGroup. [ABSTRACT FROM AUTHOR]

In this paper, we extend the notion of Hv-semigroups to neutro-Hv-semigroups and anti-Hv-semigroups and investigate many of their properties. We show that these new concepts are different from the classical concept of Hv-semigroups by presenting several examples. In general, the neutro-algebras and anti-algebras are generalizations and alternatives of classical algebras. The goal and benefits of our proposed extension of this study is to explore not only the hyperoperations and axioms that are totally true as in previous algebraic hyperstructures, but also the cases when they have degrees of truth, indeterminacy and falsehood. Therefore, we enlarge the field of research. [ABSTRACT FROM AUTHOR]

Nowadays, great effort has been focused on various kinds of batteries commonly referred to as electric energy storage systems (EESS), such as lithium-related batteries, sodium-related batteries, zinc-related batteries, aluminum-related batteries and so on. Some cathodes can be used for these batteries, such as sulfur, oxygen, layered compounds. In the present article, let us consider the basic battery configuration, i.e. they are mostly composed of cathode and anode metals. Such a classic System can be considered as "Two elements" model. Based on Neutrosophic Logic as developed by one of us (FS), we consider in this paper that actually we can extend it further to become a Neutrosophic battery system, consists of three-elements (or may be more), i.e. cathode-anode-catalyst system. The catalytic electrolyte method is found to be significant to achieve high-performance battery. [ABSTRACT FROM AUTHOR]

There is a persistence interest among physicists, to investigate on possibility of FTL (faster than light) travels, even if those fields related to FTL are most likely categorized to fringe research. Especially after Alcubierre introduces a new notion call because (one of us : anything; by generalizing implications of EPR paradox, which is known in most QM experiments. But the question remains unsolved: how to make it possible? This short article reviews several progress in such a FTL drive, while it does not necessarily mean that we agree with Alcubierre nor GTR-based approaches. We will argue in terms of possible realization of trajectory in complex plane (i.e. Argand plane.). [ABSTRACT FROM AUTHOR]

The newly introduced theories, proposed as extensions of the fuzzy theory, such as the Neutrosophic, Pythagorean, Spherical, Picture, Cubic theories, and their numerous hybrid forms, are criticized by the authors of [1]. In this paper we respond to their critics with respect to the neutrosophic theories and show that the DST, that they want to replace the A-IFS with, has many flaws. Their misunderstanding, with respect to the partial and total independence of the neutrosophic components, is that in the framework of the neutrosophic theories we deal with a MultiVariate Truth-Value (truth upon many independent random variables) as in our real-life world, not with a UniVariate Truth-Value (truth upon only one random variable) as they believe. About the membership degrees outside of the interval [0, 1], which are now in the arXiv and HAL mainstream, it is normal that somebody who over-works (works overtime) to have an over-membership (i.e., membership degree above 1) to be distinguished from those who do not work overtime (whose membership degree is between 0 and 1). And, similarly, a negative employee (that who does only damages to the company) to have a negative membership (i.e., membership degree below 0) in order to distinguish him from the positive employees (those whose membership degree is above 0). There are elementary practical applications in this paper that allow us to think out of box (in this case the box is the interval [0, 1]). [ABSTRACT FROM AUTHOR]

In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric space, by founding the NeutroGeometry & AntiGeometry. While the Non-Euclidean Geometries resulted from the total negation of only one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom and even of more axioms from any geometric axiomatic system (Euclid’s, Hilbert’s, etc.), and the NeutroAxiom results from the partial negation of one or more axioms [and no total negation of no axiom] from any geometric axiomatic system. Therefore, the NeutroGeometry and AntiGeometry are respectively alternatives and generalizations of the Non-Euclidean Geometries. In the second part, we recall the evolution from Paradoxism to Neutrosophy, then to NeutroAlgebra & AntiAlgebra, afterwards to NeutroGeometry & AntiGeometry, and in general to NeutroStructure & AntiStructure that naturally arise in any field of knowledge. At the end, we present applications of many NeutroStructures in our real world. [ABSTRACT FROM AUTHOR]

A single-valued neutrosophic set is one of the advanced fuzzy sets that is capable of handling complex real-world information satisfactorily. A development of single-valued neutrosophic set and fuzzy bipolar set, called a bipolar neutrosophic set, was introduced. Distance measures between fuzzy sets and advanced fuzzy sets are important tools in diagnostics and prediction problems. Sometimes they are defined without considering the condition of the inclusion relation on sets. In decision-making applications, this condition should be required (here it is called the inference of the measure). Moreover, in many cases, a distance measure capable of discriminating between two nearly identical objects is considered an effective measure. Motivated by these observations, in this paper, a new distance measure is proposed in a bipolar neutrosophic environment. Furthermore, an entropy measure is also developed by the similarity between two sets of mutual negation. Finally, an application to medical diagnosis is presented to illustrate the effective applicability of the proposed distance measure, where entropy values are used to characterize noises of different attributes. [ABSTRACT FROM AUTHOR]

A Plithogenic Logical proposition P is a proposition that is characterized by many degrees of truth-values with respect to many corresponding attribute-values (or random variables) that characterize P. Each degree of truth-value may be classical, fuzzy, intuitionistic fuzzy, neutrosophic, or other fuzzy extension type logic. At the end, a cumulative truth of P is computed. [ABSTRACT FROM AUTHOR]

In this paper we exemplify the types of Plithogenic Probability and respectively Plithogenic Statistics. Several applications are given. The Plithogenic Probability of an event to occur is composed from the chances that the event occurs with respect to all random variables (parameters) that determine it. Each such a variable is described by a Probability Distribution (Density) Function, which may be a classical, (T,I,F)-neutrosophic, I-neutrosophic, (T,F)-intuitionistic fuzzy, (T,N,F)-picture fuzzy, (T,N,F)-spherical fuzzy, or (other fuzzy extension) distribution function. The Plithogenic Probability is a generalization of the classical MultiVariate Probability. The analysis of the events described by the plithogenic probability is the Plithogenic Statistics. [ABSTRACT FROM AUTHOR]

In the current paper, particular acheivments of single-valued neutrosophic continuity on a singlevalued neutrosophic topological space (𝔗 ̃, 𝜏̃𝛾̃, 𝜏̃𝜂̃, 𝜏̃𝜇̃) are introduced. Some necessary implications between them are illustrated. The theories of r-single-valued neutrosophic compact, r-single-valued neutrosophic ideal compact, r-single-valued neutrosophic quasi H-closed and r-single-valued neutrosophic compact modulo an single-valued neutrosophic ideal I~ are presented and investigated. [ABSTRACT FROM AUTHOR]

While several reviews on potential applications of electroculture are available, in this survey we discuss these issues from history, starting from earliest experiments by Ross. And in the last section, we discuss possible application of laserculture, another form of potential improvement. It is our hope that what we present here may be found useful for improving agricultural performance in many countries, as well as reducing dependence on fertilizer. [ABSTRACT FROM AUTHOR]

In this paper, a new environment namely, intuitionistic fuzzy hypersoft set (IFHSS) is defined. We introduce some fundamental operators of intuitionistic fuzzy hypersoft sets such as subset, null set, absolute set, complement, union, intersection, equal set etc. Validity and application are presented with appropriate examples. For greater precision and accuracy, in the future, proposed operations in decision making processes such as personal selection, management issues and others will play a vital role. [ABSTRACT FROM AUTHOR]

We recall and improve our 2019 and 2020 concepts of n-SuperHyperGraph, Plithogenic n-SuperHyperGraph, n-Power Set of a Set, and we present some application from the real world. The n-SuperHyperGraph is the most general form of graph today and it is able to describe the complex reality we live in, by using n-SuperVertices (groups of groups of groups etc.) and n-SuperHyperEdges (edges connecting groups of groups of groups etc.). [ABSTRACT FROM AUTHOR]

This short article pairs the realms of "Mathematics", "Philosophy", and "Poetry", presenting some comers of intersection of this type of scientocreativity. Poetry have long been following mathematical patterns expressed by stern formal restrictions, as the strong metrical structure of ancient Greekheroic epic, or the consistent meter with standardized rhyme scheme and a "volta" of Italian sonnets. Poetry was always connected to Philosophy, and further on, notable mathematicians, like the inventor of quaternions, William Rowan Hamilton, or Ion Barbu, the creator of the Barbilian spaces, have written appreciated poems. We will focus here on an avant-garde movement in literature, art, philosophy, and science, called Paradoxism, founded in Romania in 1980 by a mathematician, philosopher and poet, and on the laboured writing exercises of the Oulipo group, founded in Paris in 1960 by mathematicians and poets, both of them still in act. [ABSTRACT FROM AUTHOR]

In this paper we prove that the Single-Valued (and respectively Interval-Valued, as well as Subset-Valued) Score, Accuracy, and Certainty Functions determine a total order on the set of neutrosophic triplets (T, I, F). This total order is needed in the neutrosophic decision-making applications. [ABSTRACT FROM AUTHOR]

The rare earth industry is a crucial strategic industry that is related to the national economy and national security. In the context of economic globalization, international competition is becoming increasingly fierce, and the rare earth industry is facing a more severe survival and development environment than ever before. Although China is the greatest world's rare earth country in rare earth reserves, production, consumption and export volume, it is not a rare earth power. The rare earth industry has no right to speak in the international market. The comparative advantage is weakening and the security of rare earth industry appears. Therefore, studying the rare earth industry security has important theoretical and practical significance. When measuring the China's rare earth industry security, the primary problem involves tremendous uncertainty. Neutrosophic soft set (NSS), depicted by the parameterized form of truth membership, falsity membership and indeterminacy membership, is a more serviceable pattern for capturing uncertainty. In this paper, five dimensions of rare earth industry security are identified and then prioritized against twelve different criteria relevant to structure, organization, layout, policy and ecological aspects of industry security. Then, the objective weight is computed by CRITIC (Criteria Importance Through Inter-criteria Correlation) method while the integrated weight is determined by concurrently revealing subjective weight and objective weight. Later, neutrosophic soft decision making method based CoCoSo (Combined Compromise Solution) is explored for settling the issue of low discrimination. Lastly, the feasibility and validity of the developed algorithm is verified by the issue of China's rare earth industry security evaluation. [ABSTRACT FROM AUTHOR]

The primary goal of this article is to establish and investigate the idea of interval-valued neutrosophic soft subring. Again, we have introduced function under interval-valued neutrosophic soft environment and investigated some of its homomorphic attributes. Additionally, we have established product of two intervalvalued neutrosophic soft subrings and analyzed some of its fundamental attributes. Furthermore, we have presented the notion of interval-valued neutrosophic normal soft subring and investigated some of its algebraic properties and homomorphic attributes. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to develop and study the notion of interval-valued neutrosophic subring. Also, we have studied some homomorphic characteristics of interval-valued neutrosophic subring. Again, we have defined the concept of product of two interval-valued neutrosophic subrings and analyzed some of its important properties. Furthermore, we have developed the notion of interval-valued neutrosophic normal subring and studied some of its basic characteristics and homomorphic properties. [ABSTRACT FROM AUTHOR]