Multi-objective Decision Making Based on Fuzzy Events and Their Coherent (fuzzy) Measures

We propose a reformulation of the problem of making a decision with multiple objectives in terms of fuzzy scores and their consistent defuzzification, with respect to the logical point of view taken into account. The objectives are seen as subsets (or events) of a universal set U and the degree to which an alternative Ai satisfies the objective Oj is a conditional fuzzy event Ai|Oj , represented by a fuzzy set φij defined on a partition πij of Oj . The elements of πij are the particular aspects of the objective Oj considered by Ai; the value assumed by an element x ∈ πij is the extent to which Ai satisfies that particular aspect. Using an appropriate procedure of defuzzification fuzzy scores of alternatives with respect to the objectives are transformed into numerical scores belonging to the interval [0, 1]. We study the conditions of consistency of defuzzified scores taking into account the logical relations among the objectives and the alternatives. Finally, we develop criteria for the aggregation of scores of each alternative.