Ebook: Fuzzy Relation Equations and Their Applications to Knowledge Engineering
- Tags: Mathematical Logic and Foundations, Artificial Intelligence (incl. Robotics), Computer Science general
- Series: Theory and Decision Library 3
- Year: 1989
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages i-xiii
Introductory Remarks on Fuzzy Sets....Pages 1-5
Fuzzy Relation Equations in Residuated Lattices....Pages 7-22
Lower Solutions of Max-Min Fuzzy Equations....Pages 23-48
Measures of Fuzziness of Solutions of Max-Min Fuzzy Relation Equations on Linear Lattices....Pages 49-57
Boolean Solutions of Max-Min Fuzzy Equations....Pages 59-69
?—Fuzzy Relation Equations and Decomposable Fuzzy Relations....Pages 71-85
Max-Min Decomposition Problem of a Fuzzy Relation in Linear Lattices....Pages 87-103
Fuzzy Relation Equations with Lower and Upper Semicontinuous Triangular Norms....Pages 105-128
Fuzzy Relation Equations with Equality and Difference Composition Operators....Pages 129-144
Approximate Solutions of Fuzzy Relation Equations....Pages 145-174
Handling Fuzziness in Knowledge-Based Systems....Pages 175-185
Construction of Knowledge Base, Its Validation and Optimization....Pages 187-203
Inference Algorithms in Knowledge-Based Systems....Pages 205-223
A Fuzzy Controller and Its Realization....Pages 225-240
Bibliographies....Pages 241-262
Back Matter....Pages 263-279
Content:
Front Matter....Pages i-xiii
Introductory Remarks on Fuzzy Sets....Pages 1-5
Fuzzy Relation Equations in Residuated Lattices....Pages 7-22
Lower Solutions of Max-Min Fuzzy Equations....Pages 23-48
Measures of Fuzziness of Solutions of Max-Min Fuzzy Relation Equations on Linear Lattices....Pages 49-57
Boolean Solutions of Max-Min Fuzzy Equations....Pages 59-69
?—Fuzzy Relation Equations and Decomposable Fuzzy Relations....Pages 71-85
Max-Min Decomposition Problem of a Fuzzy Relation in Linear Lattices....Pages 87-103
Fuzzy Relation Equations with Lower and Upper Semicontinuous Triangular Norms....Pages 105-128
Fuzzy Relation Equations with Equality and Difference Composition Operators....Pages 129-144
Approximate Solutions of Fuzzy Relation Equations....Pages 145-174
Handling Fuzziness in Knowledge-Based Systems....Pages 175-185
Construction of Knowledge Base, Its Validation and Optimization....Pages 187-203
Inference Algorithms in Knowledge-Based Systems....Pages 205-223
A Fuzzy Controller and Its Realization....Pages 225-240
Bibliographies....Pages 241-262
Back Matter....Pages 263-279
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