(Max,⊕)-transforms and genetic algorithms for fuzzy measure identification

Fuzzy measures generalize additive measures and probabilities. Their advantage with respect to additive ones is that they permit to model interactions between objects. Mesiar introduced in 1999 k-order Pan-additive fuzzy measures that generalize k-order additive and k-maxitive ones. They are related to the Möbius transform and related generalizations. In this paper we introduce some other transforms that we call and that permit to represent fuzzy measures in a convenient way when we use genetic algorithms in fuzzy measure identification problems. We illustrate its use identifying a measure for a subjective evaluation problem using a Choquet integral and a Sugeno integral.