Fuzzy Decision Procedures with Binary Relations

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.