Symbolic Neutrosophic Theory

2015-10-14 Florentin Smarandache

Author : Florentin Smarandache
Release : 2015-10-14
Genre : Neutrosophic logic
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Book Rating : 757/5 ( reviews)

Symbolic Neutrosophic Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symbolic Neutrosophic Theory write by Florentin Smarandache. This book was released on 2015-10-14. Symbolic Neutrosophic Theory available in PDF, EPUB and Kindle. 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.

Introduction to Symbolic 2-Plithogenic Probability Theory

2023-01-01 Mohamed Bisher Zeina

Author : Mohamed Bisher Zeina
Release : 2023-01-01
Genre : Mathematics
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Book Rating : /5 ( reviews)

Introduction to Symbolic 2-Plithogenic Probability Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Symbolic 2-Plithogenic Probability Theory write by Mohamed Bisher Zeina. This book was released on 2023-01-01. Introduction to Symbolic 2-Plithogenic Probability Theory available in PDF, EPUB and Kindle. 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.

New Trends in Neutrosophic Theory and Applications

2016-11-05 Florentin Smarandache (editor)

Author : Florentin Smarandache (editor)
Release : 2016-11-05
Genre : Neutrosophic logic
Kind :
Book Rating : 982/5 ( reviews)

New Trends in Neutrosophic Theory and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook New Trends in Neutrosophic Theory and Applications write by Florentin Smarandache (editor). This book was released on 2016-11-05. New Trends in Neutrosophic Theory and Applications available in PDF, EPUB and Kindle. 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.

Interval Neutrosophic Sets and Logic: Theory and Applications in Computing

2005 Haibin Wang

Author : Haibin Wang
Release : 2005
Genre : Mathematics
Kind :
Book Rating : 942/5 ( reviews)

Interval Neutrosophic Sets and Logic: Theory and Applications in Computing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Interval Neutrosophic Sets and Logic: Theory and Applications in Computing write by Haibin Wang. This book was released on 2005. Interval Neutrosophic Sets and Logic: Theory and Applications in Computing available in PDF, EPUB and Kindle. This book presents the advancements and applications of neutrosophics, which are generalizations of fuzzy logic, fuzzy set, and imprecise probability. The neutrosophic logic, neutrosophic set, neutrosophic probability, and neutrosophic statistics are increasingly used in engineering applications (especially for software and information fusion), medicine, military, cybernetics, physics.In the last chapter a soft semantic Web Services agent framework is proposed to facilitate the registration and discovery of high quality semantic Web Services agent. The intelligent inference engine module of soft semantic Web Services agent is implemented using interval neutrosophic logic.

Neutrosophic Sets and Systems, Vol. 40, 2021

Florentin Smarandache

Author : Florentin Smarandache
Release :
Genre : Mathematics
Kind :
Book Rating : /5 ( reviews)

Neutrosophic Sets and Systems, Vol. 40, 2021 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Neutrosophic Sets and Systems, Vol. 40, 2021 write by Florentin Smarandache. This book was released on . Neutrosophic Sets and Systems, Vol. 40, 2021 available in PDF, EPUB and Kindle. “Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

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