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

Fuzzy measures and convergence

Several theorems have been proved, e.g. by Ralescu, Ralescu and Adams, Puri and Ralescu, and Klement, in order to unify the approach to uncertainty of both statistical and fuzzy origin. The present paper is motivated by the same instances and deals with some extensions of the measure-theoretical bases of fuzzy measures and convergence properties, e.g. a B. Levi-like theorem. © 1988