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... training of both men and women for mutual negotiation. Unless these support systems are in place, women in relationship with HIV- infected men may ... ...e adaptable in case of data when we are not in a position to inter-relate two systems but we know they are inter- related indirectly. Such study is p... ...te calculus reasoning techniques used in artificial intelligence (AI) expert systems. It allows us to reason with sets instead of propositions. The... ... months. She has two children, one is married and the other is studying some computer course in Tiruppur. She says that after her husband died the... ...asamy and daughters Meena and Kama. Her current interests include Smarandache algebraic structures, fuzzy theory, coding/ communication theory. In t... ...e has guided eight Ph.D. scholars in the different fields of non- associative algebras, algebraic coding theory, transportation theory, fuzzy groups... ...d a Book Series, consisting of ten research books on the topic of Smarandache Algebraic Structures which were published by the American Research Pr...

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...2 Lukasiewicz Multi-Valued-logic: History and Introduction to Multi- Valued Algebra 2.1 Introduction to trivalent logic and plurivalent logic We all have heard of typical binary logic, Yes or No. Or in a famous phrase by Shakespeare: “To be or not to be.” In the same way all computer hardwares ...

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...Foreword 6 1 Introduction: Paradoxes, Lukasiewicz, Multi-Valued logic 7 2 Lukasiewicz Multi-Valued Logic: History and Introduction to Multi-Valued Algebra 10 2.1. Introduction to trivalent logic and plurivalent logic 10 2.2. History of Lukasiewicz and Multi-Valued Logic 12 2.3. Introduction to Multi-Valued Algebra, Chang’s Notation 15 2.4. Linkage between Multi-Valu...

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...As someone who works heavily in both math and computers, I can truly appreciate the role that logic plays in our modern world. One cannot understand the foundations of mathematics while lacking knowledge of the basics of logic and how proofs are constructed. Two of the f...

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...ica 3 Foreword As someone who works heavily in both math and computers, I can truly appreciate the role that logic plays in our modern ... ...c from those courses. Logic is also a fundamental component of advanced computer classes. I am currently teaching advanced courses in assembly lan... ... currently teaching advanced courses in assembly language programming and computer organization. Reference is constantly being made to how the rules... ...ogic Section 2 Logical Connectives in Neutrosophic Logic Section 3 Algebraic Properties of Neutrosophic Logics Section 4 Defining Other Co... ...ion for logically equivalent. The statements in theorem 1.3.1 are all algebraic properties of propositions, where the equals sign is used in pla... ...l logic, they do possess natural limitations. When more general reasoning systems are constructed, it is impractical or impossible to use truth tabl... ...valued logic. Fuzzy logic has found many uses in areas such as control systems, expert systems, inference engines and artificial intelligence. Ma... ...ifier in PNL1 is ( t max , i max , f min ). Section 3 Algebraic Properties of Neutrosophic Logics Definition 4.3.1: A semigrou...

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...ief conditioning rules . . . . . 66 1.10 Conclusion . . . . . . . . . . 68 1.11 References . . . . . . . . . . . 68 Chapter 2 DSm field and linear algebra of refined labels 75 by F. Smarandache, J. Dezert and X. Li 2.1 Introduction . . . . . . . . . . 76 2.2 DSm field and linear algebra of refined labels . . . . 77 2.2.1 Qualitative operators on DSm-LARL . . . . . ...

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...completeness, inconsistency, redundancy, contradiction. It is a non-classical logic. Eksioglu (1999) explains some of them: “Imprecision of the human systems is due to the imperfection of knowledge that humain receives (observation) from the external world. Imperfection leads to a doubt about the value of a variable, a decision to be taken or a conclusion to be drawn for t...

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...rets the uninterpretable; - regards, from many different angles, old concepts, systems: showing that an idea, which is true in a given referential s... ... and to make war in the peaceful ideas; - measures the stability of unstable systems, and instability of stable systems. Let's note by <A> an id... ...sical logic. Eksioglu (1999) explains some of them: “Imprecision of the human systems is due to the imperfection of knowledge that humain receives ... ...ey (1993-1999) present the evolutionary algorithms which are used “to describe computer-based problem solving systems which employ computational mo... ...e should be strict rules, and rules with exceptions. Recursivity is seen as a computer program that learns from itself. The statistical regression... ...ves/fuzzy-mail99/0819.html. [13] Girard, Jean-Yves, Linear logic, Theoretical Computer Science, 50:1-102, 1987. [14] Guinnessy, Paul; Gilbert, Joh... ...versity of Texas at Arlington, Vol. XIX, 143-154, 1999. [42] Stoyanova, D., Algebraic structures of intuitionistic fuzzy sets, Third Sci. Sessio... ...ork of A. Kolmogorov in 1933, the axiomatic of the probability theory based on algebras and measure theory has been definitely adopted. We remind now ... .... (54) The last constraint in (54) can also be written as (55) Now with basic algebraic manipulation, the optimal global bpa we are searching for, c...

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... as follows b σ g αβ ∇ α ∇ β F σ =0, h i σ g αβ ∇ α ∇ β F σ =0. After some algebra we obtain the chr.inv.-d’Alembert equations for the feld of the gra... ...hys. A: Math. Gen., v. 37, 2004, 931. 4. Nottale L. Computing Anticipatory Systems. CASYS’03 — Sixth International Conference, Li` ege, Belgique, 11–1... ...fed Newtonian Dynamics Carlos Castro Center for Theor. Studies of Physical Systems, Clark Atlanta University, Atlanta, USA E-mail: czarlosromanov@yaho... ... modifed Newtonian dynamics induced by the Yang’s Noncommutative Spacetime algebra involving a lower and upper scale in Nature. 1 Introduction In rece... ... include a theory with all topologies as well. It turned out that Clifford algebras contained the appropriate algebro-geometric features to im- plemen... ...os Castro and Matej Pavˇ siˇ c † Center for Theor. Studies of Physical Systems, Clark Atlanta University, Atlanta, USA E-mail: czarlosromanov@yaho... .... 30, 2000, 139. 95. Gottesman D. The Heisenberg representation of Quantum Computers. arXiv: quant-ph/9807006. 96. Baugh J., Finkelstein D., Galiautdi... ... the decay registered by the detector in 1-second intervals, are stored in computer archive. Depending on specifc targets, a time sequence of 1- secon... ...ils see in [8, 9]). Comparison of histograms was performed using auxiliary computer program by Edwin Pozharski [8]. A mechanical device designed by on...

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... movements; it reveals that the world is full of indeterminacy; it interprets the uninterpretable; regards, from many different angles, old concepts, systems and proves that an idea which is true in a given referential system, may be false in another, and vice versa; attempts to make peace in the war of ideas, and to make war in the peaceful ideas! The main principle of ne...

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...s the uninterpretable; regards, from many different angles, old concepts, systems and proves that an idea which is true in a given referential syste... ...and far-reaching consequences as a mathematical tool for modeling complex systems. Prof. Bart Kosko, the guru of fuzzy logic, introduced the Fuzzy C... ... has been explained by us, in this book, include: modeling of supervisory systems; design of hybrid models for complex systems; mobile robots and in ... ...CM for Decision Support in an Intelligent Intrusion Detection System As computer technology advances and the threats of computer crime increase, th... ...ver the years, intrusion detection has become a major area of research in computer science. Intrusion detection systems are often characterized based... ...ed as part of an intrusion detection research effort in the Department of Computer Science at Mississippi State University. The following unique fea... ...eutrosophic structures In this section we define some new neutrosophic algebraic structures like neutrosophic fields, neutrosophic spaces and neu... ...asantha Kandasamy, W.B., N.R. Neelakantan and S.R. Kannan. Replacement of Algebraic Linear Equations by Fuzzy Relation Equations in Chemical Enginee... ...y and daughters Meena and Kama. Her current interests include Smarandache algebraic structures, fuzzy theory, coding / communication theory. In the p...

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.... Metaphors of the Net VII. The Solow Paradox VIII. Decision Support Systems Author: Sam Vaknin Contact Info: palma@unet.com.mk; samvaknin... ...n since March 2000. From an open, somewhat anarchic, web of networked computers - it has evolved into a territorial, commercial, corporate exten... ... reviewers. The Internet was suppose to change all that. Originally, a computer network for the exchange of (restricted and open) research result... ...s Suite101) use the Dewey decimal system. Others invented and implemented systems of their making. Additionally, one click publishing technology (su... ...-alone, instant self-publishing and self-assembly system. Self-publishing systems do exist (for instance, Purdue University's) - but they incorporat... ...m this phase which ended only a few years ago. It started with a complete computer anarchy manifested in ad hoc networks, local networks, networks of... ... step by step instructions and hints for solving math problems (including algebra and geometry). The program addresses most math textbooks and more ...

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... Using this model one can study the effect of any pair of attributes of the systems which are given as resultant neutrosophic bivector. Thus the r... ...nodes are in the off state. Now the effect of A on the neutrosophic dynamical systems N(E B ) is as follows. AN(E B ) = (A 1 ∪ A 2 ) (N (E 1 )... ...nd their extensions to these models. 1. Abraham, R. Linear and Multilinear Algebra, W. A. Benjamin Inc., 1966. 2. Adams, E.S., and D.A. Farber. ... ...p://law.vanderbilt.edu/lawreview/vol525/adams.pdf 3. Albert, A. Structure of Algebras, Colloq. Pub., 24, Amer. Math. Soc., 1939. 4. Allen, J., S.... ...in/32/3271/A327183.php 11. Birkhoff, G., and MacLane, S. A Survey of Modern Algebra, Macmillan Publ. Company, 1977. 12. Birkhoff, G. On the struc... .... Cognitive Maps and Hyper-knowledge: A Blueprint for Active Decision Support Systems. In Cognitive Maps and Strategic Thinking, Carlsson, C. ed., ... ... Maps, IEICE Transactions in Fundamentals of Electronics, Communications and Computer Sciences (JTC-CSCC '95), Sept. 18-21 1996, v E79-A, no. 6, 92... ... S.H. Kim. Fuzzy Cognitive Maps Considering Time Relationships, Int. J. Human Computer Studies, 42, 157-162, 1995. 101. Pelaez, C.E., and J.B. Bow...

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...n particular. I was also inspired and informed by colleagues and students in computer science, English, history, and political science. But the work I... ...a colleague—helped in more ways than I can count. A number of scientists and computer scientists made me see things I other- wise would not have—Drew ... ...le of thought. Today, though, I am viewing his letter over the Internet on a computer screen. (You can too. The details are at the back of the book.) ... ...nt copyright law regime, it largely holds for their patent and trademark law systems, and utilitarian strands suffuse even “the sacred rights of autho... ... of other countries, including Britain, concluded that their national patent systems were doomed. Various proposals were made to replace patents, with... ...nstitute any kind of survey of crit- ical reactions to intellectual property systems, but I believe that nevertheless they give us some sense of typic... ...free to the autodidact.) We can imagine language, scientific knowledge, basic algebra, the tonic scale, or the classics of four-hundred-year-old litera... ...e more abstractly these are described, the more they come to resemble simple algebraic expressions, replete with “if, then” statements and instruc- ti... ...e article goes on to describe some of the key elements of so-called “Boolean algebra”— “or,” “and,” “not,” and so on—implemented in living mammalian c...

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...uctures are a very nice tool as this answers a major problem faced by all algebraic structures – groups, semigroups, loops, groupoids etc. that is th... ... two subgroups, or two subrings, or two subsemigroups etc. do not form any algebraic structure but all of them find a nice bialgebraic structure as b... ...is bialgebraic structure these would remain only as sets without any nice algebraic structure on them. Further when these bialgebraic structures are... ...loops, birings … , we felt it very essential to define and describe these systems and illustrate them with examples. To the best of the authors know... ...l Society, Providence, R.I., (1967). 5. BRUCK, R. H., A survey of binary systems, Springer-Verlag, (1958). 6. BRUCK, R.H, Some theorems on Moufang ... ..., Esik, Free De Morgan Bisemigroups and Bisemilattices, Basic Research in Computer Science (BRICS) http://www.brics.dk 126. The Near-ring online...

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... Militaria, Bucharest, Romania. Dr. B.S. Kirangi, Department of Mathematics and Computer Science, University of Mysore, Karnataka, India. Co... ...ol and fuzzy control based on FRE 108 4 1.19 A FRE in dynamic fuzzy systems 113 1.20 Solving FRE with a linear objective function 117... ... a characterization of t-norms for fuzzy sets 146 1.26 Solvability criteria for systems of FRE 156 1.27 Infinite FRE to a complete browerian lattice... ... These functions are useful for performing various kinds of simplifications of systems that preserve desirable properties in sets such as ordering ... ...lem of unique solvability of a fuzzy relation equation in an arbitrary max-min algebra. By a max-min fuzzy algebra B we mean any linearly ordered ... ...and the relation X ∈ B (n, p) is unknown. An important special case of max-min algebra is Godel algebra, in which the underlying set is the closed ... ...is the closed unit interval with natural ordering of real numbers. This max-min algebra will be denoted by B G . An implication operator in B G is ... ...uzzy relational equation algorithm to perform threat analysis in the context of computer Generated Forces Systems such Mod SAF (Modular semi automa... ...aw, Y.K., New Algorithms for Solving Fuzzy Relation Equations, Mathematics and Computers in Simulation, 59 (2002) 329-333. [85-86] 289 64. Mic...

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... Militaria, Bucharest, Romania. Dr. B.S. Kirangi, Department of Mathematics and Computer Science, University of Mysore, Karnataka, India. Co... ...ol and fuzzy control based on FRE 108 4 1.19 A FRE in dynamic fuzzy systems 113 1.20 Solving FRE with a linear objective function 117... ... a characterization of t-norms for fuzzy sets 146 1.26 Solvability criteria for systems of FRE 156 1.27 Infinite FRE to a complete browerian lattice... ... These functions are useful for performing various kinds of simplifications of systems that preserve desirable properties in sets such as ordering ... ...lem of unique solvability of a fuzzy relation equation in an arbitrary max-min algebra. By a max-min fuzzy algebra B we mean any linearly ordered ... ...and the relation X ∈ B (n, p) is unknown. An important special case of max-min algebra is Godel algebra, in which the underlying set is the closed ... ...is the closed unit interval with natural ordering of real numbers. This max-min algebra will be denoted by B G . An implication operator in B G is ... ...uzzy relational equation algorithm to perform threat analysis in the context of computer Generated Forces Systems such Mod SAF (Modular semi automa... ...aw, Y.K., New Algorithms for Solving Fuzzy Relation Equations, Mathematics and Computers in Simulation, 59 (2002) 329-333. [85-86] 289 64. Mic...

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...owe. A well-documented and large dictionary, dealing with terms needed in Computer Science, The Free Online Dictionary of Computing, is edited by D... ...lligence, neural networks, evolutionary programming, neutrosophic dynamic systems, and quantum mechanics. Especially in quantum theory there i... ...the uninterpretable; - regards, from many different angles, old concepts, systems: showing that an idea, which is true in a given referential system... ...d to make war in the peaceful ideas; - measures the stability of unstable systems, and instability of stable systems. D) Methods of Neutrosophic S... ...paradoxist intuition is a high level of awareness; - postmodernist; - an algebraic, physical and chemical philosophy; - consistent with its inconsi... ...rough the objects and see the essence. What could be a philosophical algebra? But a philosophical vector space? And how should we introduce a p... ...anical Philosophy? Devices of producing presuppositions on running belt (computer programming) - futile philosophy. 47 A priori thought à l... ...zarre ideas. g) Futurist Philosophy: ideas created by machines, robots, computers using artificial intelligence; this is the philosophy of tomorr... ..., Õ), where NL is the set of neutrosophic logical propositions, is not an algebra. Nor ( c(. 0, 1 + 0), 3, 4, C), where c(. 0, 1 + 0) is the set o...

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...on the Smarandache notions in the theory of numbers; in 1997 (at the Chair in Algebra of the State University from Moldova) he obtained the title of ... ...ma acra? -Ai sa intelegi, copile, numai cand o sa ai soacra.) or -With the computer even an idiot can calculate! -Please, let me try. I think tha... ...aradoxism, the relation between the smarandachian literature, mathematics and computers, and not finally, his avatars of an emigrant to America and .... ...the frequent calls for the events foreground ( happenings). The literature on computer recommended by author aims the same thing- receiver’s 45 i... ...use the inner contradictions of the objects, phenomena, ideas, communication systems aso., will exist practically for ever, even though in a perman...

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...bipartite graphs plays the role of representing the neutrosophic models. Thus to construct the neutrosophic graphs one needs some of the neutrosophic algebraic structures viz. neutrosophic fields, neutrosophic vector spaces and neutrosophic matrices. So we for the first time introduce and study these concepts. As our analysis in this book is application of neutrosophic alg...

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... 1 Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Mo... ...itaria, Bucharest, Romania. Dr. B.S. Kirangi, Department of Mathematics and Computer Science, University of Mysore, Karnataka, India. Copyri... ... f a c e 5 Chapter One INTRODUCTION TO SOME NEUTROSOPHIC ALGEBRAIC STRUCTURES 1.1 Neutrosophic Fields 7 1.2 Neutrosophic Vect... ... ABOUT THE AUTHORS 149 5 Preface Study of neutrosophic algebraic structures is very recent. The introduction of neutrosophic th... ...y related to the currently fashionable field of graph theory. Although the computer oriented proof of [2, 29] settled the conjecture in 1976 and ha... ... SERVICES NEW PRODUCT INTER- ORGANISATIONAL EFFICIENCY INFORMATION SYSTEMS EVALUATION INTERNAL EFFICIENCY NEW ENTRANTS BUSINESS COMP... ... Baets, B., and Kerre, E.E., Fuzzy Relational Compositions, Fuzzy sets and Systems, 60, (1993), 109- 120. 15. Dirac, G.A., Some Theorems on Abstrac... ...s by consensus concept and fuzzy relational equations, Intern. J of General Systems, 10, (1984), 47-56. 25. Holton, D.A., and Sheehan, J., The P...

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...tachment, self-control, etc., characteristic of the Oriental philosophical systems, that out of conservatism and suspicion we prefer not to understan... ...an geometries due to I.Bolyai, Lobacevski or Gauss, or the so-called Bool algebras – speculative modeling with dramatic theoretical and practical ap... ...f his method: <… I understand not so much a critique of books (ideas) and systems, but of the reason′s capability…> and <… I call transcendental any... ...by the magazine of prestige ″The Sword of the Lord″, in 1970, the I.B.M. computers of the American space program would allegedly have discovered a ... ...st a whole day>. According to the news in the ″Evening World″, the I.B.M. computers would allegedly have found a first period of time lapse of 23 ho... ...e where it had descended on the Ahaz sun dial...> According to the I.B.M. computers, the ten steps of the above mentioned sun dial represent exactly... ...lace, but it is equally true that this also means a drawing-apart of the systems one from another – the universal expansion. Contrary to the appare... ...atician could have brought more contributions to the present level of the algebraic functions, even though this one is based on his own theory of so...

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... the fight against AIDS. The picture at the bottom of the back-cover is a computer generated image of the human immunodeficiency virus (HIV). Pictur... ...iveristy, Australia. Dr. G. Lakshma Reddy, Department of Mathematics and Computer Science, University of Hyderabad, Andhra Pradesh, India Copy... ...ference in status between men and women, supported by social and cultural systems make it difficult for women to take preventive and safe-sex measur... ... are Maximum Infected, Using Fuzzy Matrices In this section we give an algebraic approach to the problem of studying the psychological aspects an... ...cludes the graph-search techniques used in artificial- intelligence expert systems. FCMs feedback allows experts to freely draw causal pictures of th... ...ngs, neural networks architecture cover a wide range. In one sense every computer is a neural net, because we can view traditional digital logic as... ... structure of the world embed so deeply in both neural networks and fuzzy systems, it is very appropriate to study the psychological effects of HIV/... ...y and daughters Meena and Kama. Her current interests include Smarandache algebraic structures, fuzzy theory, coding/ communication theory. In the p... ...s guided eight Ph.D. scholars in the different fields of non- associative algebras, algebraic coding theory, transportation theory, fuzzy groups, an...

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...METRIES American Research Press Rehoboth, NM 2005 Linfan MAO Institute of Systems Science Academy of Mathematics and Systems Chinese Academy of Scien... ...search/basic Peer Reviewers: F.Tian and X.D.Hu, Academy of Mathematics and Systems, Chinese Academy of Sciences, Beijing 100080, P.R.China. Y.P.Liu an... ... Alaska Pacific University, AK, USA. H.Iseri, Department of Mathematics and Computer Information Science, Mansfield University, Mansfield, PA 16933, USA.... ...Chapter 2 On the automorphisms of a Klein Surface and a s-manifold31 §1 An algebraic definition of a voltage map.....................................31... .....................................104 5.3 Combinatorial construction of an algebraic curve of genus .................105 5.4 Classification of s-manifo... ...face is introduced by Alling and Greenleaf [2] in 1971 concerned with real algebraic curves, correspondence with that of Riemann surface concerned wit... ...m of the graph Γ is defined to be ρ(Γ) ={̺(v)|v∈V(Γ)} and all pure rotation systems of the graph Γ is denoted by ̺(Γ). Thefirst characteristic forembedd...

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...00 =F 00 =0, as for any anti- symmetric tensor of the 2nd rank, after some algebra we obtain the other components of the feld tensor F αβ F 0i = 1 c 2... ...ccount that the Lorentz condition for the feld b α is D=0 (48), after some algebra we obtain the chr.inv.-d’Alembert equations for the time density fe... ...y (Scotland) [9] and other laboratories around the world. The experimental systems used in these attempts were more sensitive than those of the Weber ... ...onsiderations, the theory of gravitational waves is directly linked to the algebraical classi- fcation of spaces given by Petrov [37] ( Petrov classif... ...in which numerous variables are linked by relationships (6.13) and (6.14). Systems such as this cannot be solved analytically in general, but we can o... ...undergo changes through the action of a wave of the space curvature. These systems are described by the world-lines deviation equation — the Synge equ... ...McCabe argues the hypothesis, for instance, that our universe is part of a computer simulation implementation generates empirical predictions and it i... ...bservable substance. I argued that the soundness of the virtual reality or computer simulation hypothesis depends on how Universe is defned. The fact ... ... 19th Biennial Meeting, PSA2004 2004. 15. McCabe G. Universe creation on a computer, 2004. e-print, Pittsburgh Archives/00001891. E. Harokopos. Power ...

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...ng neutrosophic aggregations); — Neutrosophic Triplet Loop; — Neutrosophic Triplet Function; — Neutrosophic Modal Logic; — and Neutrosophic Hedge Algebras. The Refined Neutrosophic Set / Logic / Probability were introduced in 2013 by F. Smarandache. Since year 2016 a new interest has been manifested by researchers for the Neutrosophic Triplets and their corresponding ...