On fuzzy integral inequalities and fuzzy expectation
type: Item
instance of: scholarly article
title: On fuzzy integral inequalities and fuzzy expectation
zbMATH Open document ID: 0654.28014
DOI: 10.1016/0022-247X(87)90108-9
author: Aldo G. S. Ventre
author: Antonio Di Nola
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: The authors consider some inequalities and some equalities for Sugeno's fuzzy integrals taking values in the positive extended reals. They may be regarded as extensions of the following theorem: \(\int h d\mu =k\quad \Leftrightarrow \quad \mu (\{h\geq k\})\geq k\geq \mu (\{h>k\}).\) Furthermore, the authors give a kind of fuzzy equation and its solution. Finally, an energy of a fuzzy set is defined as a nonnegative functional.
Mathematics Subject Classification ID: 28E10
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 4067287
zbMATH Keywords: inequalities
zbMATH Keywords: Sugeno's fuzzy integrals
zbMATH Keywords: fuzzy equation
MaRDI profile type: Publication
cites work: On the analytic formalism of the theory of fuzzy sets
cites work: Q4191975
cites work: L-fuzzy sets
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cites work: Toward a general theory of fuzzy variables
cites work: The fuzzy integral
cites work: Q4405392
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full work available at URL: 0022-247x(87)90108-9
OpenAlex ID: W1983977679
description: scientific article; zbMATH DE number 4067287