Multi-objective decision making based on fuzzy events and their coherent (fuzzy) measures

Abstract

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 A_i satisfies the objective O_j is a conditional fuzzy event A_i|O_j , represented by a fuzzy set ϕ_ij defined on a partition π_ij of O_j . The elements of π_ij are the particular aspects of the objective O_j considered by A_i; the value assumed by an element x ∈ π_ij is the extent to which A_i 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.