General Barnes-Godunova-Levin type inequalities for Sugeno integral

  • Authors:

  • Hamzeh Agahi;H. Román-Flores;A. Flores-Franulič

  • Affiliations:

  • Department of Statistics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424, Hafez Ave., Tehran 15914, Iran and Statistical Research and Training Center, Tehran, ...;Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile;Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

Integral inequalities play important roles in classical probability and measure theory. Non-additive measure is a generalization of additive probability measure. Sugeno's integral is a useful tool in several theoretical and applied statistics which has been built on non-additive measure. For instance, in decision theory, the Sugeno integral is a median, which is indeed a qualitative counterpart to the averaging operation underlying expected utility. In this paper, Barnes-Godunova-Levin type inequalities for the Sugeno integral on abstract spaces are studied in a rather general form and, for this, we introduce some new technics for the treatment of concave functions in the Sugeno integration context. Also, several examples are given to illustrate the validity of this inequality. Moreover, a strengthened version of Barnes-Godunova-Levin type inequality for Sugeno integrals on a real interval based on a binary operation * is presented.