Maximum entropy membership functions for discrete fuzzy variables

Due to the deficiency of information, the membership function of a fuzzy variable cannot be obtained explicitly. It is a challenging work to find an appropriate membership function when certain partial information about a fuzzy variable is given, such as expected value or moments. This paper solves such problems for discrete fuzzy variables via maximum entropy principle and proves some maximum entropy theorems with certain constraints. A genetic algorithm is designed to solve the general maximum entropy model for discrete fuzzy variables, which is illustrated by some numerical experiments.