The Construction of a Vague Fuzzy Measure Through L Parameter Optimization

This paper presents a method to construct an aggregation function, reflecting a complex set of initial user preferences, which can be used in the framework of multi-criteria decision making. We consider problems where the decision maker can provide information about the importance and interactions between criteria, as well as a desired portion of criteria to be satisfied. The proposed aggregation process is a vague Choquet integral, whose parameters are constructed in two steps. First, we solve a convex constrained L optimization problem to obtain a fuzzy measure reflecting the importances and interactions between the criteria. Then the measure is transformed by a monotonic mapping to include vague information on what portion of criteria has to be satisfied. The proposed approach provides an automated construction of an aggregation function, which is completely free of data learning and manual processing. In addition, this method provides a novel fuzzy measure that integrates two different classes of information importance/interactions of criteria and vague statements.