Generalized fuzzy integrals of set-valued functions

Abstract

So far, the theory of fuzzy integrals is much wide and complete, but all the integrands are point-valued functions. The paper's purpose is to extend the integrand to set-valued functions, and establish the fuzzy integral of set-valued functions, such that the fuzzy integral of point-valued functions is a special case. The method used here is similar to Aumann's, and the basing fuzzy integral is the generalized fuzzy integral given in [11]. Various kinds of properties and convergence theorems are shown for the fuzzy integral of set-valued functions.