Logical foundation of fuzzy preferential systems with application to the electre decision aid methods

Abstract

In this paper we introduce split truth/falseness semantics for a multi-valued logical processing of fuzzy preference modelling. Our approach takes as starting point the standard framework of fuzzy outranking relations as proposed by the French multi-criteria decision aid community. Formal links between a given relational credibility calculus and associated truth polarization techniques will be discussed. The main result is the establishment of a multi-valued logical framework which allows us to naturally postpone any necessary defuzzification step to the end of the decision problem. Scope and purpose In this paper we propose an innovative multi-valued logical framework for processing fuzzy preferential information as is common in the context of multi-criteria preference modelling. Our results concern a methodological and computational enhancement of the Electre decision aid methods as promoted by the French school of decision aid around the work of B. Roy and D. Bouyssou (Roy. Méthodologie Multicritère d'Aide à la Décision. Paris: Economica, 1985; Roy and Bouyssou. Aide Multicritère à la Décision: Methodes et cas. Paris: Economica, 1993). The main achievement concerns the implementation of a logically coherent defuzzification technique in order to make commute logical reasoning and defuzzification of preferential information.