Maximum Entropy Functions of Discrete Random Fuzzy Variables and Genetic Algorithm

Abstract

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

Keywords: Random fuzzy variables; Chance measure; Entropy; Genetic algorithm