This paper propose a Berwald type inequality and a Favard type inequality for Sugeno integrals. That is, we first show that ((s)∫01f(x)pdμ)1p ≤ Hp,q ((s)∫01f(x)qdμ)1q holds for some constant Hp,q,0<q<p where f is a monotone and concave function on [0, 1] and μ 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 ((s)∫01f (x)pdμ)1p ≤ (p11−p−pp1−p+1) (s)∫01f(x)du 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.
['Dug Hun Hong']
Berwald and Favard Type Inequalities for Fuzzy Integrals