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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.

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.

Pseudo Lattice Graphs and their Applications to Fuzzy and Neutrosophic Models

2014 Mathematics
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Release : 2014
Genre : Mathematics
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Book Rating : 963/5 ( reviews)

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Book Synopsis Pseudo Lattice Graphs and their Applications to Fuzzy and Neutrosophic Models by : W. B. Vasantha Kandasamy

Download or read book Pseudo Lattice Graphs and their Applications to Fuzzy and Neutrosophic Models written by W. B. Vasantha Kandasamy. This book was released on 2014. Available in PDF, EPUB and Kindle. Book excerpt: In this book the authors for the first time have merged vertices and edges of lattices to get a new structure which may or may not be a lattice but is always a graph. This merging is done for graph too which will be used in the merging of fuzzy models. Further merging of graphs leads to the merging of matrices; both these concepts play a vital role in merging the fuzzy and neutrosophic models. Several open conjectures are suggested.

A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences

2002-06-30 Mathematics
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Release : 2002-06-30
Genre : Mathematics
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Book Rating : 170/5 ( reviews)

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Book Synopsis A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences by : K. Glazek

Download or read book A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences written by K. Glazek. This book was released on 2002-06-30. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a guide to the extensive literature on the topic of semirings and includes a complete bibliography. It serves as a complement to the existing monographs and a point of reference to researchers and students on this topic. The literature on semirings has evolved over many years, in a variety of languages, by authors representing different schools of mathematics and working in various related fields. Recently, semiring theory has experienced rapid development, although publications are widely scattered. This survey also covers those newly emerged areas of semiring applications that have not received sufficient treatment in widely accessible monographs, as well as many lesser-known or `forgotten' works. The author has been collecting the bibliographic data for this book since 1985. Over the years, it has proved very useful for specialists. For example, J.S. Golan wrote he owed `... a special debt to Kazimierz Glazek, whose bibliography proved to be an invaluable guide to the bewildering maze of literature on semirings'. U. Hebisch and H.J. Weinert also mentioned his collection of literature had been of great assistance to them. Now updated to include publications up to the beginning of 2002, this work is available to a wide readership. Audience: This volume is the first single reference that can guide the interested scholar or student to the relevant publications in semirings, semifields, algebraic theory of languages and automata, positive matrices and other generalisations, and ordered semigroups and groups.

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