Steffensen type inequalities for fuzzy integrals

Marek Kaluszka and Michal Boczek

Applied Mathematics and Computation, 2015, vol. 261, issue C, 176-182

Abstract: We provide several Steffensen type inequalities for the Sugeno integral. The inequalities are of the form −∫abfgdμ⩽A−∫aa+λfdμ+Bor−∫abfgdμ⩽A−∫b−λbfdμ+B,where A, B are constants, μ is a fuzzy measure on R,g: [a, b] → [0, 1], f:[a,b]→R+ is nonincreasing or nondecreasing and λ=(b−a)∧−∫abgdμ. We show that some of our sufficient conditions are also necessary.

Keywords: Fuzzy measure; Sugeno integral; Steffensen's inequality (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:261:y:2015:i:c:p:176-182

DOI: 10.1016/j.amc.2015.03.102

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