Hölder Type Inequality and Jensen Type Inequality for Choquet Integral
The integral inequalities play important roles in classic measure theory. With the development of fuzzy measure theory, experts want to seek for the integral inequalities of fuzzy integral. We concern on the inequalities of Choquet integral. In this paper, Hölder type inequality and Jensen type inequality for Choquet integral are presented. As the fuzzy measure are not additive, thus what is the other conditions for integral inequalities are discussed. Besides, examples are given to show that the conditions can’t be omitted.
KeywordsType Inequality Integral Inequality Fuzzy Measure Classic Measure Hardy Type Inequality
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