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Fuzzy Decision Procedures with Binary Relations : Towards A Unified Theory - Leonid Kitainik

Fuzzy Decision Procedures with Binary Relations

Towards A Unified Theory

Hardcover Published: 31st August 1993
ISBN: 9780792323679
Number Of Pages: 255

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Fuzzy Decision Procedures with Binary Relations: Towards a Unified Theory presents new ideas in the synthesis, analysis, and quality estimating of choice and ranking rules with crisp and valued preference relations of arbitrary type (non-transitive, non-antisymmetric, etc.). A regular structure of rationality concepts underlying conventional and modern choice rules is discovered, giving rise to a notion of a "Fuzzy Decision Procedure." Quality estimates for decision procedures (contensiveness and efficiency criteria) differ from the paradigm of Choice Theory; they are derived from the conjectures of continuous preferences, and of acceptability of multifold choice. This method results in an "extended choice logic," with uncertainty being organically absorbed by decision rules. Paradoxically, in this "softer" logic, the list of well-defined decision rules is considerably reduced, and revision of acknowledged rules is motivated.
Applications to Decision Support Systems and Multicriteria Decision-Making are discussed and explained. Two relatively independent topics of the book are the axiomatic study of fuzzy implications and inclusions, and the general technique for fuzzy relational systems. Fuzzy Decision Procedures with Binary Relations: Towards a Unified Theory is addressed to researchers, professionals and students working in fuzzy set theory, decision making, and management science.

Foreword
Preface
Acknowledgments
Introductionp. 1
Common Notationsp. 7
Systematization of Choice Rules with Binary Relationsp. 11
Fuzzy Decision Proceduresp. 31
Contensiveness Criteriap. 37
Fuzzy Inclusionsp. 47
Contensiveness of Fuzzy Dichotomous Decision Procedures in Universal Environmentp. 103
Choice with Fuzzy Relationsp. 109
Ranking and C-Spectral Properties of Fuzzy Relations (Fuzzy von Neumann - Morgenstern - Zadeh Solutions)p. 137
Invariant, Antiinvariant and Eigen Fuzzy Subsets. Mainsprings of Cut Technique in Fuzzy Relational Systemsp. 165
Contensiveness of Fuzzy Decision Procedures in Restricted Environmentp. 183
Efficiency of Fuzzy Decision Proceduresp. 199
Decision-Making with Special Classes of Fuzzy Binary Relationsp. 207
Applications to Crisp Choice Rulesp. 217
Applications to Decision Support Systems and to Multipurpose Decision-Makingp. 225
Literaturep. 240
Indexp. 250
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792323679
ISBN-10: 079232367X
Series: THEORY AND DECISION LIBRARY SERIES D, SYSTEM THEORY, KNOWLEDGE ENGINEERING, AND PROBLEM SOLVING
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 255
Published: 31st August 1993
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.15  x 2.54
Weight (kg): 0.68