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Fuzzy Relational Systems

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 336/5 ( reviews)

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Book Synopsis Fuzzy Relational Systems by : Radim Belohlávek

Download or read book Fuzzy Relational Systems written by Radim Belohlávek. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, fuzzy sets and fuzzy logic became popular. The reason is that the very idea of fuzzy sets and fuzzy logic attacks an old tradition in science, namely bivalent (black-or-white, all-or-none) judg ment and reasoning and the thus resulting approach to formation of scientific theories and models of reality. The idea of fuzzy logic, briefly speaking, is just the opposite of this tradition: instead of full truth and falsity, our judgment and reasoning also involve intermediate truth values. Application of this idea to various fields has become known under the term fuzzy approach (or graded truth approach). Both prac tice (many successful engineering applications) and theory (interesting nontrivial contributions and broad interest of mathematicians, logicians, and engineers) have proven the usefulness of fuzzy approach. One of the most successful areas of fuzzy methods is the application of fuzzy relational modeling. Fuzzy relations represent formal means for modeling of rather nontrivial phenomena (reasoning, decision, control, knowledge extraction, systems analysis and design, etc. ) in the pres ence of a particular kind of indeterminacy called vagueness. Models and methods based on fuzzy relations are often described by logical formulas (or by natural language statements that can be translated into logical formulas). Therefore, in order to approach these models and methods in an appropriate formal way, it is desirable to have a general theory of fuzzy relational systems with basic connections to (formal) language which enables us to describe relationships in these systems.

Fuzzy Relational Calculus: Theory, Applications And Software (With Cd-rom)

2005-01-06 Computers
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Release : 2005-01-06
Genre : Computers
Kind : eBook
Book Rating : 572/5 ( reviews)

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Book Synopsis Fuzzy Relational Calculus: Theory, Applications And Software (With Cd-rom) by : Yordan Kostadinov Kyosev

Download or read book Fuzzy Relational Calculus: Theory, Applications And Software (With Cd-rom) written by Yordan Kostadinov Kyosev. This book was released on 2005-01-06. Available in PDF, EPUB and Kindle. Book excerpt: This book examines fuzzy relational calculus theory with applications in various engineering subjects. The scope of the text covers unified and exact methods with algorithms for direct and inverse problem resolution in fuzzy relational calculus. Extensive engineering applications of fuzzy relation compositions and fuzzy linear systems (linear, relational and intuitionistic) are discussed. Some examples of such applications include solutions of equivalence, reduction and minimization problems in fuzzy machines, pattern recognition in fuzzy languages, optimization and inference engines in textile and chemical engineering, etc. A comprehensive overview of the authors' original work in fuzzy relational calculus is also provided in each chapter.The attached CD-Rom contains a toolbox with many functions for fuzzy calculations, together with an original algorithm for inverse problem resolution in MATLAB. This book is also suitable for use as a textbook in related courses at advanced undergraduate and graduate levels.

Fuzzy Relation Equations and Their Applications to Knowledge Engineering

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 501/5 ( reviews)

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Book Synopsis Fuzzy Relation Equations and Their Applications to Knowledge Engineering by : Antonio Di Nola

Download or read book Fuzzy Relation Equations and Their Applications to Knowledge Engineering written by Antonio Di Nola. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: It took many decades for Peirce's coneept of a relation to find its way into the microelectronic innards of control systems of eement kilns, subway trains, and tunnel-digging machinery. But what is amazing is that the more we leam about the basically simple coneept of a relation, the more aware we become of its fundamental importanee and wide ranging ramifications. The work by Di Nola, Pedrycz, Sanchez, and Sessa takes us a long distanee in this direction by opening new vistas on both the theory and applications of fuzzy relations - relations which serve to model the imprecise coneepts which pervade the real world. Di Nola, Pedrycz, Sanchez, and Sessa focus their attention on a eentral problem in the theory of fuzzy relations, namely the solution of fuzzy relational equations. The theory of such equations was initiated by Sanchez in 1976, ina seminal paper dealing with the resolution of composite fuzzy relational equations. Sinee then, hundreds of papers have been written on this and related topics, with major contributions originating in France, Italy, Spain, Germany, Poland, Japan, China, the Soviet Union, India, and other countries. The bibliography included in this volume highlights the widespread interest in the theory of fuzzy relational equations and the broad spectrum of its applications.

Toward an Algebraic Theory of Fuzzy Relational Systems

1973 Computer science
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Release : 1973
Genre : Computer science
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Toward an Algebraic Theory of Fuzzy Relational Systems by :

Download or read book Toward an Algebraic Theory of Fuzzy Relational Systems written by . This book was released on 1973. Available in PDF, EPUB and Kindle. Book excerpt: No abstract.

Fuzzy Sets, Fuzzy Logic, And Fuzzy Systems: Selected Papers By Lotfi A Zadeh

1996-05-30 Computers
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Release : 1996-05-30
Genre : Computers
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Book Rating : 811/5 ( reviews)

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Book Synopsis Fuzzy Sets, Fuzzy Logic, And Fuzzy Systems: Selected Papers By Lotfi A Zadeh by : George J Klir

Download or read book Fuzzy Sets, Fuzzy Logic, And Fuzzy Systems: Selected Papers By Lotfi A Zadeh written by George J Klir. This book was released on 1996-05-30. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of selected papers written by the founder of fuzzy set theory, Lotfi A Zadeh. Since Zadeh is not only the founder of this field, but has also been the principal contributor to its development over the last 30 years, the papers contain virtually all the major ideas in fuzzy set theory, fuzzy logic, and fuzzy systems in their historical context. Many of the ideas presented in the papers are still open to further development. The book is thus an important resource for anyone interested in the areas of fuzzy set theory, fuzzy logic, and fuzzy systems, as well as their applications. Moreover, the book is also intended to play a useful role in higher education, as a rich source of supplementary reading in relevant courses and seminars.The book contains a bibliography of all papers published by Zadeh in the period 1949-1995. It also contains an introduction that traces the development of Zadeh's ideas pertaining to fuzzy sets, fuzzy logic, and fuzzy systems via his papers. The ideas range from his 1965 seminal idea of the concept of a fuzzy set to ideas reflecting his current interest in computing with words — a computing in which linguistic expressions are used in place of numbers.Places in the papers, where each idea is presented can easily be found by the reader via the Subject Index.

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