Fuzzy Relation Equations and Their Applications to Knowledge Engineering / Edition 1

by Antonio Di Nola, S. Sessa, Witold Pedrycz, E. Sanchez

Overview

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.

Product Details

ISBN-13:	9780792303077
Publisher:	Springer Netherlands
Publication date:	07/31/1989
Series:	Theory and Decision Library D: , #3
Edition description:	1989
Pages:	280
Product dimensions:	6.14(w) x 9.21(h) x 0.36(d)

Table of Contents

1: Introductory Remarks on Fuzzy Sets.- 2: Fuzzy Relation Equations in Residuated Lattices.- 3: Lower Solutions of Max-Min Fuzzy Equations.- 4: Measures of Fuzziness of Solutions of Max-Min Fuzzy Relation Equations on Linear Lattices.- 5: Boolean Solutions of Max-Min Fuzzy Equations.- 6:—-Fuzzy Relation Equations and Decomposable Fuzzy Relations.- 7: Max-Min Decomposition Problem of a Fuzzy Relation in Linear Lattices.- 8: Fuzzy Relation Equations with Lower and Upper Semicontinuous Triangular Norms.- 9: Fuzzy Relation Equations with Equality and Difference Composition Operators.- 10: Approximate Solutions of Fuzzy Relation Equations.- 11: Handling Fuzziness in Knowledge-Based Systems.- 12: Construction of Knowledge Base, Its Validation and Optimization.- 13: Inference Algorithms in Knowledge-Based Systems.- 14: A Fuzzy Controller and Its Realization.- 15: Bibliographies.- Author Index.

Editorial Reviews

Explores equations for mathematical sets with borders that are not sharply defined, first from the perspective of fundamental theory, emphasizing lattice structures, in accordance with the symbolic computations peculiar to artificial intelligence. Then fuzzy sets and fuzzy relations are expressed in the real unit interval in order to apply the theory to general fields and contexts, like knowledge acquisition and expert systems, the handling of fuzzy information in knowledge-based systems, and the design of fuzzy controllers. Includes two extensive overall bibliographies. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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