Canonical Fuzzy Preference Relations

Abstract

Fuzzy preference matrices are an important tool for group decision making. Often not all group members are willing or able to provide their preferences in the form of fuzzy preference matrices but only in the form of crisp rank orders of options. In this paper we introduce the concepts of reciprocal canonical fuzzy preference matrices and preference weight vectors for additive and multiplicative fuzzy preferences. Consistency is an important property of fuzzy preference matrices, so we present two methods that allow to construct consistent reciprocal canonical additive fuzzy preference matrices and consistent reciprocal canonical multiplicative fuzzy preference matrices from crisp rank orders for arbitrary numbers of elements. These transformations allow to process fuzzy preference matrices and crisp rank orders in the same mathematical framework in group decision making.