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Generally any real-world problem is not always solvable, because in that not only a percentage of uncertainty is present, but also, a certain percentage of indeterminacy is present. The presence of uncertainty has been analyzed using fuzzy…

General Mathematics · Mathematics 2007-05-23 W. B. Vasantha Kandasamy , Florentin Smarandache , K. Ilanthenral

The involvement of uncertainty of varying degrees when the total of the membership degree exceeds one or less than one, then the newer mathematical paradigm shift, Fuzzy Theory proves appropriate. For the past two or more decades, Fuzzy…

General Mathematics · Mathematics 2007-05-23 W. B. Vasantha Kandasamy , Florentin Smarandache

The new concept of fuzzy interval matrices has been introduced in this book for the first time. The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval…

General Mathematics · Mathematics 2007-05-23 W. B. Vasantha Kandasamy , Florentin Smarandache

In this book we study the concepts of Fuzzy Cognitive Maps (FCMs) and their Neutrosophic analogue, the Neutrosophic Cognitive Maps (NCMs).Fuzzy Cognitive Maps are fuzzy structures that strongly resemble neural networks, and they have…

General Mathematics · Mathematics 2007-05-23 Dr. W. B. Vasantha Kandasamy , Florentin Smarandache

This book introduces the concept of fuzzy super matrices and operations on them. This book will be highly useful to social scientists who wish to work with multi-expert models. Super fuzzy models using Fuzzy Cognitive Maps, Fuzzy Relational…

General Mathematics · Mathematics 2008-01-18 W. B. Vasantha Kandasamy , Florentin Smarandache , K. Amal

There are many fuzzy models like Fuzzy matrices, Fuzzy Cognitive Maps, Fuzzy relational Maps, Fuzzy Associative Memories, Bidirectional Associative memories and so on. But almost all these models can give only one sided solution like hidden…

General Mathematics · Mathematics 2007-05-23 Dr. W. B. Vasantha Kandasamy , Dr. Florentin Smarandache

This book presents a comprehensive and systematic survey of graph theory under uncertainty, with particular emphasis on the unifying role of the uncertain graph framework. It reviews fundamental concepts, structural properties, graph…

Artificial Intelligence · Computer Science 2026-05-26 Takaaki Fujita , Florentin Smarandache

In this book, the authors introduce the new notion of superbimatrices and generalize it to supertrimatrices and super n-matrices. Study of these structures is not only interesting and innovative but is also best suited for the computerize…

General Mathematics · Mathematics 2009-06-30 W. B. Vasantha Kandasamy , Florentin Smarandache

This book is organized into seven chapters. Chapter one is introductory in content. The notion of neutrosophic set linear algebras and neutrosophic neutrosophic set linear algebras are introduced and their properties analysed in chapter…

General Mathematics · Mathematics 2010-03-10 W. B. Vasantha Kandasamy , Florentin Smarandache , K. Ilanthenral

The algebraic structure, linear algebra happens to be one of the subjects which yields itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief economic…

General Mathematics · Mathematics 2007-05-23 W. B. Vasantha Kandasamy , Florentin Smarandache , K. Ilanthenral

This book gives the basic notions of fuzzy matrix theory and its applications to simple fuzzy models. The approach is non-traditional in order to attract many students to use this methodology in their research. The traditional approach of…

General Mathematics · Mathematics 2007-05-23 W. B. Vasantha Kandasamy , Florentin Smarandache , K. Ilanthenral

Real-world phenomena often exhibit vagueness, partial truth, and incomplete information. To model such uncertainty in a mathematically rigorous way, many generalized set-theoretic frameworks have been introduced, including Fuzzy Sets [1],…

Artificial Intelligence · Computer Science 2026-03-18 Takaaki Fujita , Florentin Smarandache

This book is organized into four chapters. In Chapter One we just introduce the basic Fuzzy and Neutrosophic tools used in the analysis of the social evil of Untouchability. Since the notion of caste is based on themind, it is appropriate…

General Mathematics · Mathematics 2007-05-23 W. B. Vasantha Kandasamy , Florentin Smarandache , K. Kandasamy

This book introduces special classes of Fuzzy and Neutrosophic matrices. These special classes of matrices are used in the construction of multi-expert special fuzzy models using FCM, FRM and FRE and their Neutorosophic analogues…

General Mathematics · Mathematics 2007-08-01 W. B. Vasantha Kandasamy , Florentin Smarandache , K. Ilanthenral

This book presents the advancements and applications of neutrosophics. Chapter 1 first introduces the interval neutrosophic sets which is an instance of neutrosophic sets. In this chapter, the definition of interval neutrosophic sets and…

Logic in Computer Science · Computer Science 2007-05-23 Haibin Wang , Florentin Smarandache , Yan-Qing Zhang , Rajshekhar Sunderraman

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…

Artificial Intelligence · Computer Science 2016-11-28 Florentin Smarandache , Surapati Pramanik

Combinatorics studies how discrete objects can be counted, arranged, and combined under specified rules. Motivated by uncertainty in real-world data and decisions, modern set-theoretic formalisms such as fuzzy sets, neutrosophic sets, rough…

Artificial Intelligence · Computer Science 2026-02-24 Takaaki Fujita , Florentin Smarandache

This paper presents a Fuzzy Cognitive Map model to quantify implicit bias in structured datasets where features can be numeric or discrete. In our proposal, problem features are mapped to neural concepts that are initially activated by…

Machine Learning · Computer Science 2022-01-14 Gonzalo Nápoles , Isel Grau , Leonardo Concepción , Lisa Koutsoviti Koumeri , João Paulo Papa

In keeping with the definition that biotechnology is really no more than a name given to a set of techniques and processes, the authors apply some set of fuzzy techniques to chemical industry problems such as finding the proper proportion…

General Mathematics · Mathematics 2008-07-15 W. B. Vasantha Kandasamy , Florentin Smarandache

With the advent of computers, one needs algebraic structures that can simultaneously work with bulk data. One such algebraic structure, namely, n-linear algebras of type I are introduced in this book and its applications to n-Markov chains…

General Mathematics · Mathematics 2008-12-11 W. B. Vasantha Kandasamy , Florentin Smarandache
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