A convolution type inequality for fuzzy integrals

Some inequalities and convergence theorems for Choquet integrals

“…Some integral inequalities, such as Markov's inequality, Jensen's inequality, Hölder's inequality and Minkowski inequality, play important roles in classic probability and integral theory. Recently, Román-Flores et al studied several counterpart inequalities for Sugeno fuzzy integrals [10][11][12], which further enrich non-additive integral theory.…”

A generalization of the Chebyshev type inequalities for Sugeno integrals

“…Sugeno integral is analogous to Lebesgue integral which has been studied by many authors, including Pap (1995), Ralescu and Adams (1980), and Wang and Klir (1992), among others. Román-Flores et al (2007, 2008a started the studies of inequalities for Sugeno integral, and then followed by the authors (Agahi and Yaghoobi 2010;Mesiar and Ouyang 2009;Ouyang et al , 2010 or its reverse hold for an arbitrary fuzzy measure-based type fuzzy integral l and a binary operation H: ½0; 1Þ 2 ! ½0; 1Þ?…”

On the special form of integral convolution type inequality due to Walter and Weckesser

“…where d ∈ (0, 1], p ≥ 1 and f : [0, d] → [0, ∞) is an arbitrary continuous increasing (throughout the paper we use terms increasing and decreasing in the weak sense) function, is called the classical Bushell-Okrasiński inequality (the non-classical forms of (1.1) include its generalizations to various kinds of integrals-for instance, fuzzy integrals like the Sugeno integral [8] or the universal integral [1]). It was proved in [3] as an auxiliary result in the study of the existence of solutions of some class of Volterra integral equations and almost immediately questions about an extension of (1.1) arose [9].…”