Representations of the fuzzy integral

Several representation formulas of the fuzzy integral have been found, both for general integrand [2,3] and for integrand having suitable continuity properties [2]. In this paper some representations of the fuzzy integral are considered. The case of a topological structure added is treated. Furthermore an expression of the fuzzy integral of a fuzzy variable in terms of a decreasing rearrangement of f is given. © 1989