Fuzzy Preference Modeling

Abstract

We survey of classical and fuzzy relational preference models for single or multiple criteria decision aid (MCDA). After a brief introduction to preference modeling for decision aid (§ 1.1), the chapter is divided in two complementary parts. The first part (§ 1.2) deals with the definition of classical preference structures from a weak preference relation R and with the extension of these structures to the fuzzy case. A particular attention is given to the definition of fuzzy strict preference (P), indifference (I) and incomparability (J) relations from a fuzzy weak preference relation R. The second part (§ 1.3) is devoted to the construction of the preference structures in single or multiple criteria decision problems. After presenting the construction of crisp preference relations from criterion values, we show the specific interest of fuzzy sets in this context. Then we elaborate fuzzy preference structures from criterion values and indicate some extensions of these models when criterion values are imperfectly known.