Krassimir T. Atanassov's Books

Index Matrices: Towards an Augmented Matrix Calculus

By: Krassimir T. Atanassov

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Index Matrices: Towards an Augmented Matrix Calculus

By: Krassimir T. Atanassov

This book presents the very concept of an index matrix and its related augmented matrix calculus in a comprehensive form. It mostly illustrates the exposition with examples related to the generalized nets and intuitionistic fuzzy sets which are examples of an extremely wide array of possible application areas. The present book contains the basic results of the author over index matrices and some of its open problems with the aim to stimulating more researchers to start working in this area.

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Page Count

116

Publisher

Springer

Published Date

ISBN 10

3319109456

ISBN 13

9783319109459

On Intuitionistic Fuzzy Sets Theory

By: Krassimir T. Atanassov

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On Intuitionistic Fuzzy Sets Theory

By: Krassimir T. Atanassov

This book aims to be a comprehensive and accurate survey of state-of-art research on intuitionistic fuzzy sets theory and could be considered a continuation and extension of the author ́s previous book on Intuitionistic Fuzzy Sets, published by Springer in 1999 (Atanassov, Krassimir T., Intuitionistic Fuzzy Sets, Studies in Fuzziness and soft computing, ISBN 978-3-7908-1228-2, 1999). Since the aforementioned book has appeared, the research activity of the author within the area of intuitionistic fuzzy sets has been expanding into many directions. The results of the author ́s most recent work covering the past 12 years as well as the newest general ideas and open problems in this field have been therefore collected in this new book.

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328

Publisher

Springer

Published Date

ISBN 10

3642291279

ISBN 13

9783642291272

Intuitionistic Fuzzy Sets

Theory and Applications

By: Krassimir T. Atanassov

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Intuitionistic Fuzzy Sets

Theory and Applications

By: Krassimir T. Atanassov

In the beginning of 1983, I came across A. Kaufmann's book "Introduction to the theory of fuzzy sets" (Academic Press, New York, 1975). This was my first acquaintance with the fuzzy set theory. Then I tried to introduce a new component (which determines the degree of non-membership) in the definition of these sets and to study the properties of the new objects so defined. I defined ordinary operations as "n", "U", "+" and "." over the new sets, but I had began to look more seriously at them since April 1983, when I defined operators analogous to the modal operators of "necessity" and "possibility". The late George Gargov (7 April 1947 - 9 November 1996) is the "god father" of the sets I introduced - in fact, he has invented the name "intu itionistic fuzzy", motivated by the fact that the law of the excluded middle does not hold for them. Presently, intuitionistic fuzzy sets are an object of intensive research by scholars and scientists from over ten countries. This book is the first attempt for a more comprehensive and complete report on the intuitionistic fuzzy set theory and its more relevant applications in a variety of diverse fields. In this sense, it has also a referential character.

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Page Count

336

Publisher

Physica

Published Date

ISBN 10

3790818704

ISBN 13

9783790818703

Interval-Valued Intuitionistic Fuzzy Sets

By: Krassimir T. Atanassov

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Interval-Valued Intuitionistic Fuzzy Sets

By: Krassimir T. Atanassov

The book offers a comprehensive survey of interval-valued intuitionistic fuzzy sets. It reports on cutting-edge research carried out by the founder of the intuitionistic fuzzy sets, Prof. Krassimir Atanassov, giving a special emphasis to the practical applications of this extension. A few interesting case studies, such as in the area of data mining, decision making and pattern recognition, among others, are discussed in detail. The book offers the first comprehensive guide on interval-valued intuitionistic fuzzy sets. By providing the readers with a thorough survey and important practical details, it is expected to support them in carrying out applied research and to encourage them to test the theory behind the sets for new advanced applications. The book is a valuable reference resource for graduate students and researchers alike.

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205

Publisher

Springer Nature

Published Date

ISBN 10

3030320901

ISBN 13

9783030320904

Intuitionistic Fuzzy Logics

By: Krassimir T. Atanassov

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Intuitionistic Fuzzy Logics

By: Krassimir T. Atanassov

The book offers a comprehensive survey of intuitionistic fuzzy logics. By reporting on both the author’s research and others’ findings, it provides readers with a complete overview of the field and highlights key issues and open problems, thus suggesting new research directions. Starting with an introduction to the basic elements of intuitionistic fuzzy propositional calculus, it then provides a guide to the use of intuitionistic fuzzy operators and quantifiers, and lastly presents state-of-the-art applications of intuitionistic fuzzy sets. The book is a valuable reference resource for graduate students and researchers alike.

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Page Count

144

Publisher

Springer

Published Date

ISBN 10

3319489534

ISBN 13

9783319489537

Generalized Nets

By: Krassimir T Atanassov

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Generalized Nets

By: Krassimir T Atanassov

The Generalized Nets (GNs) are extensions of Petri nets and of different Petri nets modifications, introduced by the author (1982). In the book, definitions and the basic properties of GNs are given. The GNs extensions and reductions are discussed. GNs, which describe the functioning and results of the work of different types of petri nets, different types of finite automata and of Turing machines, are given. Over the GNs are defined different operations, relations and operators. They can also be transferred onto other nets. Many open problems in the GNs theory are given.

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Page Count

396

Publisher

World Scientific

Published Date

ISBN 10

9814506311

ISBN 13

9789814506311

New Visual Perspectives on Fibonacci Numbers

By: Krassimir T. Atanassov

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New Visual Perspectives on Fibonacci Numbers

By: Krassimir T. Atanassov

Discusses new ground on Fibonacci sequences and the well-known Fibonacci numbers. There is a continuing emphasis on diagrams, both geometric and combinatorial, which helps to tie disparate topics together, weaving around the unifying themes of the golden mean and various generalizations of the Fibonacci recurrence relation.

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334

Publisher

World Scientific

Published Date

ISBN 10

9812381341

ISBN 13

9789812381347

On Some of the Smarandache Problems, Vol. II

By: Mladen V. Vassilev-Missana,Krassimir T. Atanassov

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On Some of the Smarandache Problems, Vol. II

By: Mladen V. Vassilev-Missana,Krassimir T. Atanassov

Five years after having published the first volume, the authors obtained many new results related to Smarandaches Problems. They are collected in this book and deal with Smarandache sequences, infinite numbers, functions, formulas, conjunctures in Number Theory.

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Publisher

Infinite Study

Published Date

ISBN 10

1931233896

ISBN 13

9781931233897

Interval-Valued Intuitionistic Fuzzy Sets

By: Krassimir T. Atanassov

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Interval-Valued Intuitionistic Fuzzy Sets

By: Krassimir T. Atanassov

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Page Count

205

Publisher

Springer Nature

Published Date

ISBN 10

3030320901

ISBN 13

9783030320904

On Intuitionistic Fuzzy Sets Theory

By: Krassimir T. Atanassov

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On Intuitionistic Fuzzy Sets Theory

By: Krassimir T. Atanassov

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Page Count

328

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Springer

Published Date

ISBN 10

3642291279

ISBN 13

9783642291272

Book's by Krassimir T. Atanassov

Index Matrices: Towards an Augmented Matrix Calculus

Index Matrices: Towards an Augmented Matrix Calculus

On Intuitionistic Fuzzy Sets Theory

On Intuitionistic Fuzzy Sets Theory

Intuitionistic Fuzzy Sets

Intuitionistic Fuzzy Sets

Interval-Valued Intuitionistic Fuzzy Sets

Interval-Valued Intuitionistic Fuzzy Sets

Intuitionistic Fuzzy Logics

Intuitionistic Fuzzy Logics

Generalized Nets

Generalized Nets

New Visual Perspectives on Fibonacci Numbers

New Visual Perspectives on Fibonacci Numbers

On Some of the Smarandache Problems, Vol. II

On Some of the Smarandache Problems, Vol. II

Interval-Valued Intuitionistic Fuzzy Sets

Interval-Valued Intuitionistic Fuzzy Sets

On Intuitionistic Fuzzy Sets Theory

On Intuitionistic Fuzzy Sets Theory

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