Representation, optimization and generation of fuzzy measures

Abstract

We review recent literature on three aspects of fuzzy measures: their representations, learning optimal fuzzy measures and random generation of various types of fuzzy measures. These three aspects are interdependent: methods of learning fuzzy measures depend on their representation, and may also include random generation as one of the steps, on the other hand different representations also affect generation methods, while random generation plays an important role in simulation studies for post-hoc analysis of sets of measures learned from data and problem-specific constraints. Explicit modelling of interactions between the decision variables is a distinctive feature of integrals based on fuzzy measures, but its price is high computational complexity. To extend their range of applicability efficient representations and computational techniques are required. All three mentioned aspects provide mathematical and computational tools for novel applications of fuzzy measures and integrals in decision making and information fusion, allow scaling up significantly the domain of applicability and reduce their complexity.