Integrating Three Representation Models in Fuzzy Multipurpose Decision Making Based on Preference Relations

The purpose of this paper is to study a fuzzy multipurpose decision making problem, where the information about the alternatives provided by the experts can be of a diverse nature. The information can be represented by means of preference orderings, utility functions and fuzzy preference relations, and our objective is to establish general models which cover all possible representations. Firstly, we must make the information uniform, using fuzzy preference relations. We will present a general procedure to relate preference orderings, utility values and fuzzy preference relations that generalises the procedures normally used where there is a combination of different types of information. We will present generic decision processes based on the concept of fuzzy majority. Fuzzy majority is represented by a fuzzy quantifier, and applied in the aggregation, by means of an OWA operator whose weights are calculated by the fuzzy quantifier. We use two quantifier-guided choice degrees of alternatives. A dominance degree used to quantify the dominance that one alternative has over all the others, in a fuzzy majority sense, and a nondominance degree, that generalises Orlovsky’s non-dominated alternative concept. The application of the two above choice degrees can be carried out according to two different selection processes; a sequential choice process and a conjunction choice process.