Hölder Type Inequality and Jensen Type Inequality for Choquet Integral

  • Xuan Zhao
  • Qiang Zhang
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 123)


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.


Type Inequality Integral Inequality Fuzzy Measure Classic Measure Hardy Type Inequality 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Xuan Zhao
    • 1
  • Qiang Zhang
    • 1
  1. 1.School of Management and EconomicsBeijing Institute of TechnologyBeijingChina

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