Overview

This work presents 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 on 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. The book is intended for researchers, professionals and students working in fuzzy set theory, decision-making and management science.

Full Product Details

Author:   Leonid Kitainik
Publisher:   Springer
Imprint:   Springer
Edition:   1993 ed.
Volume:   13
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   1.270kg
ISBN:  

9780792323679

ISBN 10:   079232367
Pages:   255
Publication Date:   31 August 1993
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Introduction.- 2. Common Notations.- 3. Systematization Of Choice Rules With Binary Relations.- 3.1. Rationality Concept. Multifold Choice.- 3.2. Basic Diohdtomies: Invariant Description.- 3.3. Composition Laws.- 3.4. Synthesis Of Rationality (X)Ncepts.- 4. Fuzzy Decision Procedures.- 4.1. Fuzzy Rationality Concept.- 4.2. Multifold Fuzzy Choice.- 4.3. Families Of Fuzzy Dichotomous Decision Procedures.- 5. Contensiveness Criteria.- 5.1. Motivations And Postulates For Multifold Fuzzy Choice.- 5.2. Dichotomousness And δ-Contensiveness Of Multifold Fuzzy Choice, Procedures, And Relations.- 5.3. Ranking Alternatives Using Multifold Fuzzy Choice.- 6. Fuzzy Inclusions.- 6.1. Motivations, Fuzzy Inclusion And Fuzzy Implication.- 6.2. Axiomatics.- 6.3. Representation Theorem.- 6.4. Properties Of Fuzzy Inclusions.- 6.5. Binary Operations With Fuzzy Inclusions.- 6.6. Characteristic Fuzzy Inclusions (Polynomial And Piecewise-Polynomial Models).- 6.7. Comparative Study Of Fuzzy Inclusions.- 7. Contensiveness Of Fuzzy Dichotomous Decision Procedures In Universal Environment.- 8. Choice With Fuzzy Relations.- 8.1. Basic Technique. Elements Of Multifold Fuzzy Choice.- 8.2. α-Cuts, And Multifold Fuzzy Choice With Basic Dichotomies.- 8.3. The Core Is Unfit.- 8.4. Fuzzy Von Neumann — Morgenstern Solution. Fuzzy Stable Core.- 8.5. Procedures Based On The Dual Composition Law.- 9. Ranking And C-Spectral Properties Of Fuzzy Relations (Fuzzy Von Neumann — Morgenstern — Zadeh Solutions).- 9.1. Basic Characteristics. Ͱ-Mapping.- 9.2. Bounds Of Multifold Fuzzy Choice.- 9.3. Connected Spectrum, And Spectral Properties Of A Fuzzy Relation.- 9.4. Classification Of Multifold Fuzzy Choices.- 9.5. Fuzzy L.Zadeh' Stable Core.- 9.6. Incontensive Procedures BasedOn L.Zadeh' Inclusion.- 10. Invariant, Antiinvariant And Eigen Fuzzy Subsets. Mainsprings Of Cut Technique In Fuzzy Relational Systems.- 11. Contenstveness Of Fuzzy Decision Procedures In Restricted Environment.- 12. Efficiency Of Fuzzy Decision Procedures.- 13. Decision-Making With Special Classes Of Fuzzy Binary Relations.- 13.1. Fuzzy Preorderings.- 13.2. Reciprocal Relations.- 14. Applications To Crisp Choice Rules.- 14.1. Adjusting Crisp Choice.- 14.2. Producing New Choice Rules (Fnmzs And Dipole Decomposition).- 15. Applications To Decision Support Systems And To Multipurpose Decision-Making.- 15.1. General Applications To Decision Support Systems.- 15.2. Applications To Multipurpose Decision-Making.- 15.3. Expert Assistant Ficckas (In Collaboration With S.Orlovski).- Literature.

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