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Smarandache Fuzzy Algebra
The author studies the Smarandache Fuzzy Algebra, which, like its predecessor Fuzzy Algebra, arose from the need to define structures that were more compatible with the real world where the grey areas mattered, not only black or white.In any human field, a Smarandache n-structure on a set S means a weak structure {w(0)} on S such that there exists a chain of proper subsets P(n-1) in P(n-2) in?in P(2) in P(1) in S whose corresponding structures verify the chain {w(n-1)} includes {w(n-2)} includes? includes {w(2)} includes {w(1)} includes {w(0)}, where 'includes' signifies 'strictly stronger' (i.e., structure satisfying more axioms).This book is referring to a Smarandache 2-algebraic structure...
Complex Valued Graphs for Soft Computing
In this book the authors define, describe, and develop the notion of complex valued graphs, complex neutrosophic valued graphs, and mod complex valued graphs in a systematic way. However complex neural networks have been analyzed and studied as early as 2003. This book gives several applications of them in medical diagnosis, soft computing, and so on.
Super Linear Algebra
Super Linear Algebras are built using super matrices. These new structures can be applied to all fields in which linear algebras are used. Super characteristic values exist only when the related super matrices are super square diagonal super matrices.Super diagonalization, analogous to diagonalization is obtained. These newly introduced structures can be applied to Computer Sciences, Markov Chains, and Fuzzy Models.
Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps
In a world of chaotic alignments, traditional logic with its strict boundaries of truth and falsity has not imbued itself with the capability of reflecting the reality. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that could infuse into itself a representation of the real world. Out of this need arose the system of Neutrosophy (the philosophy of neutralities, introduced by FLORENTIN SMARANDACHE), and its connected logic Neutrosophic Logic, which is a further generalization of the theory of Fuzzy Logic. In this book we study the concepts of Fuzzy Cognitive Maps (FCMs) and their Neutrosophic analogue, the Neutrosophic Cognitive Maps...
The Encyclopedia of Neutrosophic Researchers, 1st volume
This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The 78 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: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements.
Smarandache Non-Associative Rings
Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B in A which is embedded with a stronger structure S. These types of structures occur in our everyday's life, that's why we study them in this book. Thus, as a particular case: A Non-associative ring is a non-empty set R together with two binary operations '+' and '.' such that (R, +) is an additive abelian group and (R, .) is a groupoid. For all a, b, c in R we have (a + b) . c = a . c + b . c and c . (a + b) = c . a + c . b. A Smarandache non-associative ring is a non-associative ring (R, +, .) which has a proper subset P in R, that is an associative ring (with respect to the same binary operations on R).
Dual Numbers
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n-Linear Algebra of Type II
n-Linear Algebra of type II is constructed over n-fields, n-eigen values and n-eigen vectors and it will find applications in finite element analysis of civil and mechanical structures with uncertain parameters
Fuzzy Interval Matrices, Neutrosophic Interval Matrices and their Applications
This book introduces for the first time the notion of fuzzy interval matrices, fuzzy interval bimatrices, fuzzy interval n-matrices, neutrosophic interval matrices, neutrosophic interval bimatrices, neutrosophic interval n-matrices, fuzzy neutrosophic interval matrices and fuzzy neutrosophic interval n-matrices, where n >= 2.These new notions find their applications in FCInM, FRInM, FBAItM, NCInM, NCRInM and NRInM models, where n>=1.It is important to mention that these Fuzzy interval n-matrices and Fuzzy neutrosophic interval n-matrices will find their usage in Leontief economic models and Markov chains that have lots of industrial applications.
