Combination Rules of Fuzzy Sets via Random Set Formulation

In this paper, a new angle to establish the combination rules is proposed. Based on the random set formulation of a fuzzy set and the fuzzy set formulation of a random set, various combination rules from stochastic viewpoint can be constructed. Using the concept of independence in probability theory, such combination rules can be derived upon independence and various correlations of the evidence of multiple fuzzy information. Besides, since both fuzzy set and Dempster-Shafer evidence inference can be reformulated to be random sets, applying the method of constructing combination rules via the random set formulation, we can combine multiple fuzzy sets and Dempster-Shafer evidences to be a final fuzzy set or a evidence inference issue