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Extensions of Chebyshev inequality for fuzzy integral and applications

H. Román-FloresY. Chalco-CanoA. Flores-Franulic

New extensions of Chebyshev type inequalities for the Sugeno integral onabstract spaces are studied. More precisely, necessary andsufficient conditions under which the inequality[int_{A}Phi left( fstar g ight) dmu geq left( int_{A}Phileft( f ight) dmu ight) star left( int_{A}Phi left(g ight) dmu ight)]or its reverse hold for an arbitrary fuzzy measure-based typeSugeno integral $mu $ and a binary operation $star colonlbrack 0,infty )^{2} ightarrow lbrack 0,infty )$ and anonnegative function $Phi :[0,infty )$ $ ightarrow $$[0,infty )$, are given. Also, and as an application, we prove a Milne's type inequality for fuzzy integral.

http://www.lbd.dcc.ufmg.br/colecoes/cbsf/2012/0062.pdf

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