Representations of the fuzzy integral
type: Item
instance of: scholarly article
title: Representations of the fuzzy integral
zbMATH Open document ID: 0662.28014
DOI: 10.1016/0165-0114(89)90190-5
author: Massimo Squillante
author: Aldo G. S. Ventre
published in: Fuzzy Sets and Systems
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 28E10
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 4081889
zbMATH Keywords: representation formulas of the fuzzy integral
zbMATH Keywords: fuzzy variable
zbMATH Keywords: decreasing rearrangement
MaRDI profile type: Publication
full work available at URL: 0165-0114(89)90190-5
OpenAlex ID: W2024642616
cites work: Q4039929
cites work: Toward a general theory of fuzzy variables
cites work: The fuzzy integral
cites work: A Yosida-Hewitt like theorem for \(\perp\)-decomposable measures
cites work: \(\perp\)-decomposable measures and integrals for Archimedean t-conorms \(\perp\)
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description: scientific article; zbMATH DE number 4081889