Download or read book Symbolic Neutrosophic Theory written by Florentin Smarandache and published by Infinite Study. This book was released on 2015-10-14 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symbolic (or Literal) Neutrosophic Theory is referring to the use of abstract symbols (i.e. the letters T, I, F, or their refined indexed letters Tj, Ik, Fl) in neutrosophics. In the first chapter we extend the dialectical triad thesis-antithesis-synthesis (dynamics of and , to get a synthesis) to the neutrosophic tetrad thesis-antithesis-neutrothesis-neutrosynthesis (dynamics of , , and , in order to get a neutrosynthesis). In the second chapter we introduce the neutrosophic system and neutrosophic dynamic system. A neutrosophic system is a quasi- or (t,i,f)–classical system, in the sense that the neutrosophic system deals with quasi-terms/concepts/attributes, etc. [or (t,i,f)-terms/concepts/attributes], which are approximations of the classical terms/concepts/attributes, i.e. they are partially true/membership/probable (t), partially indeterminate (i), and partially false/nonmembership/improbable (f), where t, i, f are subsets of the unitary interval [0, 1]. In the third chapter we introduce for the first time the notions of Neutrosophic Axiom, Neutrosophic Deducibility, Neutrosophic Axiomatic System, Degree of Contradiction (Dissimilarity) of Two Neutrosophic Axioms, etc. The fourth chapter we introduced for the first time a new type of structures, called (t, i, f)-Neutrosophic Structures, presented from a neutrosophic logic perspective, and we showed particular cases of such structures in geometry and in algebra. In any field of knowledge, each structure is composed from two parts: a space, and a set of axioms (or laws) acting (governing) on it. If the space, or at least one of its axioms (laws), has some indeterminacy of the form (t, i, f) ≠ (1, 0, 0), that structure is a (t, i, f)-Neutrosophic Structure. In the fifth chapter we make a short history of: the neutrosophic set, neutrosophic numerical components and neutrosophic literal components, neutrosophic numbers, etc. The aim of this chapter is to construct examples of splitting the literal indeterminacy (I) into literal sub-indeterminacies (I1,I2,…,Ir), and to define a multiplication law of these literal sub-indeterminacies in order to be able to build refined I-neutrosophic algebraic structures. In the sixth chapter we define for the first time three neutrosophic actions and their properties. We then introduce the prevalence order on (T, I, F) with respect to a given neutrosophic operator "o", which may be subjective - as defined by the neutrosophic experts. And the refinement of neutrosophic entities , , and . Then we extend the classical logical operators to neutrosophic literal (symbolic) logical operators and to refined literal (symbolic) logical operators, and we define the refinement neutrosophic literal (symbolic) space. In the seventh chapter we introduce for the first time the neutrosophic quadruple numbers (of the form a+bT+cI+dF) and the refined neutrosophic quadruple numbers. Then we define an absorbance law, based on a prevalence order, both of them in order to multiply the neutrosophic components T, I, F or their sub-components T_j, I_k, F_l and thus to construct the multiplication of neutrosophic quadruple numbers.

Download or read book New Trends in Neutrosophic Theory and Applications written by Florentin Smarandache (editor) and published by Infinite Study. This book was released on 2016-11-05 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic theory and applications have been expanding in all directions at an astonishing rate especially after the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structure such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been a very important tool in all various areas of data mining, decision making, e-learning, engineering, medicine, social science, and some more. The book “New Trends in Neutrosophic Theories and Applications” focuses on theories, methods, algorithms for decision making and also applications involving neutrosophic information. Some topics deal with data mining, decision making, e-learning, graph theory, medical diagnosis, probability theory, topology, and some more. 30 papers by 39 authors and coauthors.

Download or read book New Trends in Neutrosophic Theory and Applications Volume II written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic theory and applications have been expanding in all directions at an astonishing rate especially after the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc.

Download or read book Degrees of Membership 1 and written by Florentin Smarandache and published by Infinite Study. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We have defined the Neutrosophic Over- /Under-/Off-Set and -Logic for the first time in 1995 and published in 2007. During 1995-2016 we presented them to various national and international conferences and seminars and did more publishing during 2007-2016. These new notions are totally different from other sets/logics/probabilities. We extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, to Neutrosophic Underset {when some neutrosophic component is < 0}, and to Neutrosophic Offset {when some neutrosophic components are off the interval [0, 1], i.e. some neutrosophic component > 1 and other neutrosophic component < 0}. This is no surprise since our real- world has numerous examples and applications of over-/under-/off-neutrosophic components.

Download or read book An Overview of Neutrosophic and Plithogenic Theories and Applications written by Florentin Smarandache and published by Infinite Study. This book was released on 2023-01-01 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present this research to all researchers and scholars who have realized the existence of indeterminacy in all data, through the results they obtain and the values that are not accurate enough and that may cause loss to the systems and facilities under study, and we will present through it the emergence, foundations and development of Neutrosophic theories and their applications for more than two decades (1995- 2023) since it was defined and studied, along with its applications, in order to be able to present new studies and research that keep pace with the great scientific development that our contemporary world is witnessing, through the use of research that has been published by the professionals and found on the attached open links.

Download or read book Advances of Standard and Nonstandard Neutrosophic Theories written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, Three-Ways 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; and so on.

Download or read book Neutrosophic Perspectives Triplets Duplets Multisets Hybrid Operators Modal Logic Hedge Algebras And Applications 2nd edition written by Florentin Smarandache and published by Infinite Study. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is part of the book-series dedicated to the advances of neutrosophic theories and their applications, started by the author in 1998. Its aim is to present the last developments in the field. This is the second extended and improved edition of Neutrosophic Perspectives (September 2017; first edition was published in June 2017). For the first time, we now introduce: — Neutrosophic Duplets and the Neutrosophic Duplet Structures; — Neutrosophic Multisets (as an extension of the classical multisets); — Neutrosophic Spherical Numbers; — Neutrosophic Overnumbers / Undernumbers / Offnumbers; — Neutrosophic Indeterminacy of Second Type; — Neutrosophic Hybrid Operators (where the heterogeneous t-norms and t-conorms may be used in designing neutrosophic aggregations); — Neutrosophic Triplet Weak Set (and con-sequently we have renamed the previous Neutros-ophic Triplet Set (2014-2016) as Neutrosophic Triplet Strong Set in order to distinguish them); — Neutrosophic Perfect Triplet; — Neutrosophic Imperfect Triplet; — Neutrosophic triplet relation of equivalence; — Two Neutrosophic Friends; — n Neutrosophic Friends; — 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 Neutros-ophic Triplet Algebraic Structures (introduced by F. Smarandache & M. Ali). Subtraction and Division of Neutrosophic Numbers were introduced by F. Smarandache - 2016, and Jun Ye – 2017. We also present various new applications in: neutrosophic multi-criteria decision-making, neutrosophic psychology, neutrosophic geographical function (the equatorial virtual line), neutrosophic probability in target identification, neutrosophic dynamic systems, neutrosophic quantum computers, neutrosophic theory of evolution, and neutrosophic triplet structures in our everyday life. Keywords: neutrosophy, neutrosophic duplets, neutrosophic duplet structures, neutrosophic multisets, neutrosophic hedge algebras, neutrosophic multi-criteria decision-making, neutrosophic psychology, neutrosophic geographical function, neutrosophic probability in target identification,

Download or read book New Challenges in Neutrosophic Theory and Applications written by Stefan Vladutescu and published by . This book was released on 2020 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrosophic theory has representatives on all continent sand, therefore, it can be said to be a universal theory. On the other hand, according to the two volumes of “The Encyclopedia of Neutrosophic Researchers” (2016, 2018) about 150 researchers from 37 countries apply the idea and the neutrosophic method. Neutrosophic theory was founded by Professor Florentin Smarandache in 1998; it constitutes further generalization of fuzzy and intuitionistic fuzzy theories. The key distinction between the neutrosophic set/logic and other types of sets/logics consists of the introduction of the degree of indeterminacy/neutrality (I) as independent component in the neutrosophic set. Thus, neutrosophic theory involves the degree of membership-truth (T), the degree of indeterminacy (I), and the degree of non-membership-falsehood (F). In recent years, the field of neutrosophic set, logic, measure, probability and statistics, precalculus and calculus etc. and their applications in multiple fields have been extended and applied in various fields, such as communication, management and information technology. The present volume gathers the latest neutrosophic techniques, methodologies or mixed approaches, being thus a barometer of the neutrosophic research in 2020.

Download or read book On Clean and Nil clean Symbolic 2 Plithogenic Rings written by P. Prabakaran and published by Infinite Study. This book was released on 2023-01-01 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ring is said to be clean if every element of the ring can be written as a sum of an idempotent element and a unit element of the ring and a ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a nilpotent element of the ring. In this paper, we generalize these arguments to symbolic 2-plithogenic structure. We introduce the structure of clean and nil-clean symbolic 2-plithogenic rings and some of its elementary properties are presented. Also, we have found the equivalence between classical clean(nil-clean) ring R and the corresponding symbolic 2-plithogenic ring 2-SPR.

Download or read book An Introduction to The Symbolic 3 Plithogenic Vector Spaces written by Rozina Ali and published by Infinite Study. This book was released on 2023-01-01 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this paper is to define and study for the first time the concept of symbolic 3-plithogenic vector spaces based on symbolic 3-plithogenic sets and classical vector spaces.Also, many related substructures will be defined and handled such as AH-functions, AH-spaces, and symbolic 3-plithogenic basis.

Download or read book Introduction to Symbolic 2 Plithogenic Probability Theory written by Mohamed Bisher Zeina and published by Infinite Study. This book was released on 2023-01-01 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we present for the first time the concept of symbolic plithogenic random variables and study its properties including expected value and variance. We build the plithogenic formal form of two important distributions that are exponential and uniform distributions. We find its probability density function and cumulative distribution function in its plithogenic form. We also derived its expected values and variance and the formulas of its random numbers generating. We finally present the fundamental form of plithogenic probability density and cumulative distribution functions. All the theorems were proved depending on algebraic approach using isomorphisms. This paper can be considered the base of symbolic plithogenic probability theory.

Download or read book On Neutrosophic Offuninorms written by Erick González Caballero and published by Infinite Study. This book was released on with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uninorms comprise an important kind of operator in fuzzy theory. They are obtained from the generalization of the t-norm and t-conorm axiomatic. Uninorms are theoretically remarkable, and furthermore, they have a wide range of applications. For that reason, when fuzzy sets have been generalized to others—e.g., intuitionistic fuzzy sets, interval-valued fuzzy sets, interval-valued intuitionistic fuzzy sets, or neutrosophic sets—then uninorm generalizations have emerged in those novel frameworks.

Download or read book Introduction to Symbolic 2 Plithogenic Probability Theory written by Mohamed Bisher Zeina and published by Infinite Study. This book was released on 2023-01-01 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we present for the first time the concept of symbolic plithogenic random variables and study its properties including expected value and variance. We build the plithogenic formal form of two important distributions that are exponential and uniform distributions. We find its probability density function and cumulative distribution function in its plithogenic form. We also derived its expected values and variance and the formulas of its random numbers generating. We finally present the fundamental form of plithogenic probability density and cumulative distribution functions. All the theorems were proved depending on algebraic approach using isomorphisms. This paper can be considered the base of symbolic plithogenic probability theory.

Download or read book An Overview of Plithogenic Set and Symbolic Plithogenic Algebraic Structures written by Florentin Smarandache and published by Infinite Study. This book was released on 2023-04-01 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is devoted to Plithogeny, Plithogenic Set, and its extensions. These concepts are branches of uncertainty and indeterminacy instruments of practical and theoretical interest. Starting with some examples, we proceed towards general structures. Then we present definitions and applications of the principal concepts derived from plithogeny, and relate them to complex problems.

Download or read book Neutrosophic Systems with Applications NSWA Vol 1 2023 written by Florentin Smarandache and published by Infinite Study. This book was released on 2023-09-23 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on neutrosophic and plithogenic sets, logics, probabilities and statistics.

Download or read book A few little steps beyond Knuth s Boolean Logic Table with Neutrosophic Logic A Paradigm Shift in Uncertain Computation written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. This article amalgamates insights from over twelve key references encompassing seminal works in boolean logic, neutrosophic logic, and their applications in diverse scientific and computational domains, aiming to pave the way for a more robust and adaptable logic framework in computation.

Download or read book On the Concept of Symbolic 7 Plithogenic Real Matrices written by Khadija Ben Othman and published by Infinite Study. This book was released on 2023-01-01 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this paper is to study the properties of symbolic 7-plithogenic matrices with real entries, where an algebraic view of their properties and relations will be presented and discussed. Also, we present many theorems that concern the computing of their eigenvalues and eigenvectors and their connection with classical ordinary matrices. Many related examples will be provided to clarify the validity of our work.