Representations of the fuzzy integral (Q1113307)

Several representation formulas of the fuzzy integral have been found, both for general integrand [\textit{D. Ralescu}, J. Math. Anal. Appl. 86, 176-193 (1982; Zbl 0482.60004), \textit{D. Ralescu} and \textit{G. Adams}, ibid. 75, 562-570 (1980; Zbl 0438.28007)] and for integrand having suitable continuity properties (first cited paper). 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 f in terms of a decreasing rearrangement of f is given.