عنوان

Fuzzy Decision Procedures with Binary Relations :

9401119600

9789401119603

b594963

Fuzzy Decision Procedures with Binary Relations :

[Book]

Towards A Unified Theory

by Leonid Kitainik.

Dordrecht

Springer Netherlands

1993

(xxiii, 255 pages)

Theory and decision library., Series D,, System theory, knowledge engineering, and problem solving ;, 13.

Foreword by D. Dubois, H. Prade. Preface. 1. Introduction. 2. Common Notations. 3. Systematization of Choice Rules with Binary Relations. 4. Fuzzy Decision Procedures. 5. Contensiveness Criteria. 6. Fuzzy Inclusions. 7. Contensiveness of Fuzzy Dichotomous Decision Procedures in Universal Environment. 8. Choice with Fuzzy Relations. 9. Ranking and C-Spectral Properties of Fuzzy Relations (Fuzzy Von Neumann--Morgenstern--Zadeh Solutions). 10. Invariant, Antiinvariant and Eigen Fuzzy Subsets. Mainsprings of Cut Technique in Fuzzy Relational Systems. 11. Contensiveness of Fuzzy Decision Procedures in Restricted Environment. 12. Efficiency of Fuzzy Decision Procedures. 13. Decision-Making with Special Classes of Fuzzy Binary Relations. 14. Applications to Crisp Choice Rules. 15. Applications to Decision Support Systems and to Multipurpose Decision-Making. Literature. Index.

This book 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 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 addressed to researchers, professionals and students working in fuzzy set theory, decision-making, management science.

Logic, Symbolic and mathematical.

Mathematics.

Operations research.

by Leonid Kitainik.

Leonid Kitainik

[Book]

Y