Leonid Kitainik – författare

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.

In decision theory there are basically two appr~hes to the modeling of individual choice: one is based on an absolute representation of preferences leading to a ntDnerical expression of preference intensity. This is utility theory. Another approach is based on binary relations that encode pairwise preference. While the former has mainly blossomed in the Anglo-Saxon academic world, the latter is mostly advocated in continental Europe, including Russia. The advantage of the utility theory approach is that it integrates uncertainty about the state of nature, that may affect the consequences of decision. Then, the problems of choice and ranking from the knowledge of preferences become trivial once the utility function is known. In the case of the relational approach, the model does not explicitly accounts for uncertainty, hence it looks less sophisticated. On the other hand it is more descriptive than normative in the first stand because it takes the pairwise preference pattern expressed by the decision-maker as it is and tries to make the best out of it. Especially the preference relation is not supposed to have any property. The main problem with the utility theory approach is the gap between what decision-makers are and can express, and what the theory would like them to be and to be capable of expressing. With the relational approach this gap does not exist, but the main difficulty is now to build up convincing choice rules and ranking rules that may help the decision process.