Fuzzy preference modelling: Fundamentals and recent advances

Abstract

The construction of fuzzy strict preference, indifference and incomparability relations from a fuzzy large preference relation is usually cast into an axiomatic framework based on t-norms. In this contribution, we show that this construction is essentially characterized by the choice of an indifference generator, a symmetrical mapping located between the L ukasiewicz t-norm and the minimum operator. Interesting constructions are obtained by choosing as indifference generator a commutative quasi-copula, an ordinal sum of Frank t-norms or a particular Frank t-norm. © 2008 Springer-Verlag Berlin Heidelberg.