Digital Commons Network^™

Extension Of Soft Set To Hypersoft Set, And Then To Plithogenic Hypersoft Set, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we generalize the soft set tothe hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.

From Big Science To “Deep Science”, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

The Standard Model of particle physics has accomplished a great deal including the discovery of Higgs boson in 2012. However, since the supersymmetric extension of the Standard Model has not been successful so far, some physicists are asking what alternative deeper theory could be beyond the Standard Model? This article discusses the relationship between mathematics and physical reality and explores the ways to go from Big Science to “Deep Science”.

An Approach To Determining Customer Satisfaction In Traditional Serbian Restaurants, Florentin Smarandache, Dragisa Stanujkic, Darjan Karabasevic, Edmundas Kazimieras Zavadskas, Fausto Cavallaro

Branch Mathematics and Statistics Faculty and Staff Publications

The aim of this paper is to make a proposal for an easy–to–use approach to the evaluation of customer satisfaction in restaurants. In order to provide a reliable way to collect respondents’ real attitudes, an approach based on the use of smaller number of evaluation criteria and interactive questionnaire created in a spreadsheet file is proposed in this paper, whereby an easy-to-understand and simple-touse procedure is proposed for determining weights of criteria. In addition to the said, the proposed approach applies the simplified SERVQUAL-based approach, for which reason a simplified version of the Weighted Sum Method based on the decision …

Physics Beyond Catching A Mouse In The Dark: From Big Science To Deep Science, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

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 …

Remark On Creatio Ex Nihilo, Intelligent Design And Emergence Philosophy Approaches To Origin Of The Universe, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

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 …

Nidus Idearum. Scilogs, Iv: Vinculum Vinculorum, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Welcome into my scientific lab! My lab[oratory] is a virtual facility with non-controlled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings "ground", "opinion", "expectation"), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). * In this fourth book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring mostly to topics on NEUTROSOPHY – …

An Approach To Determining Customer Satisfaction In Traditional Serbian Restaurants, Florentin Smarandache, Dragisa Stanujkic, Darjan Karabasevic, Edmundas Kazimieras Zavadskas, F. Cavallaro

Branch Mathematics and Statistics Faculty and Staff Publications

The aim of this paper is to make a proposal for an easy–to–use approach to the evaluation of customer satisfaction in restaurants. In order to provide a reliable way to collect respondents’ real attitudes, an approach based on the use of smaller number of evaluation criteria and interactive questionnaire created in a spreadsheet file is proposed in this paper, whereby an easy-to-understand and simple-touse procedure is proposed for determining weights of criteria. In addition to the said, the proposed approach applies the simplified SERVQUAL-based approach, for which reason a simplified version of the Weighted Sum Method based on the decision …

Nidus Idearum. Scilogs, Vii: Superluminal Physics - Second Edition, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

My lab[oratory] is a virtual facility with non-controlled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings "ground", "opinion", "expectation"), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). * In this seventh book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring to different scientific topics – email messages to research colleagues, or …

Special Issue: New Types Of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/ Off-Set, Neutrosophic Refined Set, And Their Extension To Plithogenic Set/Logic/ Probability, With Applications, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Refined Neutrosophy And Lattices Vs. Pair Structures And Yinyang Bipolar Fuzzy Set, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we present the lattice structures of neutrosophic theories. We prove that Zhang-Zhang’s YinYang bipolar fuzzy set is a subclass of the Single-Valued bipolar neutrosophic set. Then we show that the pair structure is a particular case of refined neutrosophy, and the number of types of neutralities (sub-indeterminacies) may be any finite or infinite number.

The Encyclopedia Of Neutrosophic Researchers - Vol. 3, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This is the third volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. 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: …

Neutrosophic Triplet Structures - Vol. 1, Florentin Smarandache, Memet Sahin

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs, the properties of neutrosophic sets …

On The New Concept Creatio Ex-Rotatione, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

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 discuss the concept of creatio ex nihilo, as well as two other approaches - Intelligent Design and Emergence Theory. 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. We agree with Vaas: [h]ow a conceptual and perhaps physical solution of the temporal aspect of Immanuel Kant’s “first antinomy of pure reason” is possible, i.e., how …

Neutrosophic Set Is A Generalization Of Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set (Picture Fuzzy Set, Ternary Fuzzy Set), Pythagorean Fuzzy Set, Q-Rung Orthopair Fuzzy Set, Spherical Fuzzy Set, And N-Hyperspherical Fuzzy Set, While Neutrosophication Is A Generalization Of Regret Theory, Grey System Theory, And Three-Ways Decision (Revisited), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

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 …

Introduction To Neutrosophic Sociology (Neutrosociology), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Sociology (or Neutrosociology) is the study of sociology using neutrosophic scientific methods.

The huge social data that we face in sociology is full of indeterminacy: it is vague, incomplete, contradictory, hybrid, biased, ignorant, redundant, superfluous, meaningless, ambiguous, unclear, etc.

That’s why the neutrosophic sciences (which deal with indeterminacy), through the process of neutrosophication, are involved, such as: neutrosophy (a new branch of philosophy), neutrosophic set, neutrosophic logic, neutrosophic probability and neutrosophic statistics, neutrosophic analysis, neutrosophic measure, and so on.

Neutrosophy studies only the triads (A, neutA, antiA), where A is an item or a concept, that make sense in …

New Types Of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/ Under-/ Off Set, Neutrosophic Refined Set, And Their Extension To Plithogenic Set/Logic/Probability, With Applications, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This international collective massive book, edited by Florentin Smarandache, has 716 pages, and represents the special issue on neutrosophic environment at SYMMETRY international journal (Scopus, Web of Science, IF: 2.143). The book contains 37 published papers, by 73 authors and coauthors, from 13 countries from around the world, in alphabetical order: China, Cuba, Ecuador, Egypt, India, Jordan, Korea, Malaysia, Pakistan, Romania, Saudi Arabia, United Kingdom, and United States of America.

Advances Of Standard And Nonstandard Neutrosophic Theories, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, we approach different topics related to neutrosophics, such as: Neutrosophic Set, Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set, Picture Fuzzy Set, Ternary Fuzzy Set, Pythagorean Fuzzy Set, Atanassov’s Intuitionistic Fuzzy Set of second type, Spherical Fuzzy Set, n-HyperSpherical Neutrosophic Set, q-Rung Orthopair Fuzzy Set, truth-membership, indeterminacy-membership, falsehood-nonmembership, Regret Theory, Grey System Theory, ThreeWays Decision, n-Ways Decision, Neutrosophy, Neutrosophication, Neutrosophic Probability, Refined Neutrosophy, Refined Neutrosophication, Nonstandard Analysis; Extended Nonstandard Analysis; Open and Closed Monads to the Left/Right; Pierced and Unpierced Binads; MoBiNad Set; infinitesimals; infinities; nonstandard reals; standard reals; Nonstandard Neutrosophic Lattices of First Type (as poset) and …

How To Balance Intuitive And Analytical Functions Of Brain: A Neutrosophic Way Of Scientific Discovery Process, Florentin Smarandache, Victor Christianto, Robert Neil Boyd

Branch Mathematics and Statistics Faculty and Staff Publications

Initially this article stems from our discussion on math and mysticism, inspired by an article by Ralph Abraham. But it becomes a discussion on the role of intuition and inspiration in scientific discovery process. Hopefully this article will help anyone who aspires to be good scientists or engineers.

Nidus Idearum. Scilogs, Vi: Annotations On Neutrosophy, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

My lab[oratory] is a virtual facility with non-controlled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings "ground", "opinion", "expectation"), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). * In this sixth book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring to topics on NEUTROSOPHY – email messages to research colleagues, or …

Nidus Idearum. Scilogs, V: Joining The Dots, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

My lab[oratory] is a virtual facility with noncontrolled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings "ground", "opinion", "expectation"), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). * In this fifth book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, mostly referring to topics on NEUTROSOPHY – email messages to research colleagues, …

A Short Remark On Gödel Incompleteness Theorem And Its Self-Referential Paradox From Neutrosophic Logic Perspective, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

It is known from history of mathematics, that Gödel submitted his two incompleteness theorems, which can be considered as one of hallmarks of modern mathematics in 20th century. Here we argue that Gödel incompleteness theorem and its self-referential paradox have not only put Hilbert’s axiomatic program into question, but he also opened up the problem deep inside the then popular Aristotelian Logic. Although there were some attempts to go beyond Aristotelian binary logic, including by Lukasiewicz’s three-valued logic, here we argue that the problem of self-referential paradox can be seen as reconcilable and solvable from Neutrosophic Logic perspective. Motivation of …

Special Issue: Algebraic Structures Of Neutrosophic Triplets, Neutrosophic Duplets, Or Neutrosophic Multisets, Vol. Ii, Florentin Smarandache, Xiaohong Zhang, Mumtaz Ali

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Plithogenic Fuzzy Whole Hypersoft Set, Construction Of Operators And Their Application In Frequency Matrix Multi Attribute Decision Making Technique, Florentin Smarandache, Shazia Rana, Madiha Qayyum, Muhammad Saeed, Bakhtawar Ali Khan

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, initially a matrix representation of Plithogenic Hypersoft Set (PHSS) is introduced and then with the help of this matrix some local operators for Plithogenic Fuzzy Hypersoft set (PFHSS) are developed. These local operators are used to generalize PFHSS to Plithogenic Fuzzy Whole Hypersoft set (PFWHSS). The generalized PFWHSS set is hybridization of Fuzzy Hypersoft set (which represent multiattributes and their subattributes as a combined whole membership i.e. case of having an exterior view of the event) and the Plithogenic Fuzzy Hypersoft set (in which multi attributes and their subattributes are represented with individual memberships case of having …

On Soft Rough Topology With Multi-Attribute Group Decision Making, Florentin Smarandache, Muhammad Riaz, Atiqa Firdous, Atiqa Fakhar

Branch Mathematics and Statistics Faculty and Staff Publications

Rough set approaches encounter uncertainty by means of boundary regions instead of membership values. In this paper, we develop the topological structure on soft rough set (SR-set) by using pairwise SR-approximations. We define SR-open set, SR-closed sets, SR-closure, SR-interior,SR-neighborhood,SR-bases, product topology onSR-sets, continuous mapping, and compactness in soft rough topological space (SRTS). The developments of the theory onSR-set and SR-topology exhibit not only an important theoretical value but also represent significant applications ofSR-sets. We applied an algorithm based onSR-set to multi-attribute group decision making (MAGDM) to deal with uncertainty.

Improvement Of The Material’S Mechanical Characteristics Using Intelligent Real Time Control Interfaces In Hfc Hardening Process, Florentin Smarandache, Luige Vladareanu, Mihaiela Iliescu, Victor Vladareanu, Alexandru Gal, Octavian Melinte, Adrian Margean

Branch Mathematics and Statistics Faculty and Staff Publications

The paper presents Intelligent Control (IC) Interfaces for real time control of mechatronic systems applied to Hardening Process Control (HPC) in order to improvement of the material’s mechanical characteristics. Implementation of IC laws in the intelligent real time control interfaces depends on the particular circumstances of the models characteristics used and the exact definition of optimization problem. The results led to the development of the IC interfaces in real time through Particle Swarm Optimization (PSO) and neural networks (NN) using off- line the regression methods.

A Bipolar Fuzzy Extension Of The Multimoora Method, Florentin Smarandache, Dragisa Stanujkic, Darjan Karabasevic, Edmundas Kazimieras Zavadskas, Willem Brauer

Branch Mathematics and Statistics Faculty and Staff Publications

The aim of this paper is to make a proposal for a new extension of the MULTIMOORA method extended to deal with bipolar fuzzy sets. Bipolar fuzzy sets are proposed as an extension of classical fuzzy sets in order to enable solving a particular class of decision-making problems. Unlike other extensions of the fuzzy set of theory, bipolar fuzzy sets introduce a positive membership function, which denotes the satisfaction degree of the element x to the property corresponding to the bipolar-valued fuzzy set, and the negative membership function, which denotes the degree of the satisfaction of the element x to …

Tripleta De Estructura Neutrosófica Y Tripleta De Estructura Neutrosófica Extendida, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

En el presente estudio se realiza una revisión de las tripletas de estructura neutrosófica y tripleta de estructura neutrosófica extendida, con el fin de introducir nuevos conceptos a emplear en trabajos futuros.

Separation Axioms On Neutrosophic Soft Topological Spaces, Çi̇ğdem Gündüz, Taha Yasi̇n Öztürk, Sadi Bayramov

Turkish Journal of Mathematics

A neutrosophic set, proposed by Smarandache, considers a truth membership function, an indeterminacy membership function, and a falsity membership function. Neutrosophic soft sets combined by Maji have been utilized successfully to model uncertainty in several areas of application such as control, reasoning, pattern recognition, and computer vision. In the present paper, some basic notions of neutrosophic soft sets have been redefined and the neutrosophic soft point concept has been introduced. Later we give the neutrosophic soft $T_{i}$-space and the relationships between them are discussed in detail.

On Rugina’S System Of Thought, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This article investigates Rugina's orientation table and gives particular examples for several of its seven models. Leon Walras's Economics of Stable Equilibrium and Keynes's Economics of Disequilibrium are combined in Rugina's orientation table in systems which are s percent stable and 100 ÿ s percent unstable, where s may be 100, 95, 65, 50, 35, 5, and 0. Classical logic and modern logic are united in Rugina's integrated logic, and then generalized in neutrosophic logic.

Remark On Vacuum Fluctuation As The Cause Of Universe Creation: Or How Neutrosophic Logic And Material Point Method May Resolve Dispute On The Origin Of The Universe Through Re-Reading Gen. 1:1-2, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

Questions regarding the formation of the Universe and what was there before the existence of Early Universe have been great interest to mankind of all times. In recent decades, the Big Bang as described by the Lambda CDMStandard Model Cosmology has become widely accepted by majority of physics and cosmology communities. Among other things, we can cite A.A. Grib Pavlov who pointed out some problems of heavy particles creation out of vacuum and also other proposal of Creatio ex nihilo theory (CET). But the philosophical problems remain, as Vaas pointed out: Did the universe have a beginning or does it …