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Steffensen type inequalities for fuzzy integrals

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  • Kaluszka, Marek
  • Boczek, Michal

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.

Suggested Citation

  • Kaluszka, Marek & Boczek, Michal, 2015. "Steffensen type inequalities for fuzzy integrals," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 176-182.
    • Handle: RePEc:eee:apmaco:v:261:y:2015:i:c:p:176-182
    DOI: 10.1016/j.amc.2015.03.102
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    References listed on IDEAS

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    1. N. Balakrishnan & T. Rychlik, 2006. "Evaluating expectations of L-statistics by the Steffensen inequality," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(3), pages 371-384, June.
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