Berwald and Favard Type Inequalities for Fuzzy Integrals

This paper propose a Berwald type inequality and a Favard type inequality for Sugeno integrals. That is, we first show that

holds for some constant $H_{p,q},0<q<p$ where f is a monotone and concave function on [0, 1] and $\mu$ is the Lebesgue measure on $ℝ$. If q = 1, then as a special case of the Berwald type inequality, we show that the following Favard type inequality holds for Sugeno integrals A deeper discussion for Favard type inequality for Sugeno integrals using Berwald type inequality is also considered. Some examples are provided to illustrate the optimality of the proposed inequality.