A generalization of the Chebyshev type inequalities for Sugeno integrals
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In this paper, we give a generalization of the Chebyshev type inequalities for Sugeno integral with respect to non-additive measures. The main results of this paper generalize most of the inequalities for Sugeno integral obtained by many researchers. Also, some conclusions are drawn and some problems for further investigations are given.
KeywordsNonadditive measure Sugeno integral Chebyshev’s inequality Minkowski’s inequality Hölder’s inequality
The work on this paper was partially supported by the Fuzzy Systems and Applications Center of Excellence, Shahid Bahonar University of Kerman, Kerman, Iran. Our thanks go to anonymous referees who helped to improve the original version of our paper.
- Agahi H, Yaghoobi MA (2010) A Minkowski type inequality for fuzzy integrals. J Uncertain Syst 4(3):187–194Google Scholar
- Dubois D, Prade H, Sabbadin R (1998) Qualitative decision theory with Sugeno integrals. In: Proceedings of UAI’98, pp 121–128Google Scholar
- Klement EP, Mesiar R, Pap E (2000) Triangular norms, trends in Logic. Studia Logica Library, vol 8. Kluwer Academic Publishers, DodrechtGoogle Scholar
- Sugeno M (1974) Theory of fuzzy integrals and its applications, PhD thesis. Tokyo Institute of TechnologyGoogle Scholar