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GENERAL RELATED JENSEN TYPE INEQUALITIES FOR FUZZY INTEGRALS

Year 2018, Volume: 8 Issue: 1, 1 - 7, 01.06.2018

- B.daraby

Abstract

In this paper, related inequalities to Jensen type inequality for the semi- normed fuzzy integrals are studied. Several examples are given to illustrate the validity of theorems. Some results on Jensen type inequalities are obtained.

Keywords

Fuzzy measure Jensen's inequality Seminormed fuzzy integral Semiconormed fuzzy integral.

References

  • Daraby, B., Generalization of the Stolarsky type inequality for pseudo-integrals, Fuzzy Sets and Sys- tems 194 (2012) 90-96.
  • Daraby, B., Shafiloo, A. and Rahimi, A., Generalization of the Feng Qi type inequality for pesudo- integral, Gazi University Journal of Science 28 (4) (2015), 695-702.
  • Daraby, B. and Rahimi, A., Jensen type inequality for seminormed fuzzy integrals, Acta Universitatis Apulensis 46 (2016) 1-8.
  • Daraby, B. and Ghazanfary Asll, H. and Sadeqi, I., General related inequalities to Carlson-type inequlity for the Sugeno integral, Applied Mathematics and Computation 305 (2017) 323-329.
  • Kandel, A., Byatt, W.J., Fuzzy sets, fuzzy algebra, and fuzzy statistics, Proceedings of the IEEE 66 (1978) 1619-1639.
  • Klement, E.P., Mesiar, R. and Pap, E., Integration with respect to decomposable measures, based on a conditionally distributive semiring on the unit interval, International Journal of Uncertainty Fuzziness Knowledge-Based Systems 8 (2000) 701-717.
  • Klement, E.P., Mesiar,R. and Pap, E., Triangular norms, in: Trends in Logic, in: Studia Logica Library, Vol. 8, Kluwer Academic Publishers, Dordrecht, 2000.
  • Mesiar, R., Choquet-like integrals, Journal of Mathematical Analysis and Applications 194 (1995) 488.
  • Murofushi, T. and Sugeno, M., Fuzzy t-conorm integral with respect to fuzzy measures: Generalization of Sugeno integral and Choquet integral, Fuzzy Sets and Systems 42 (1991) 57-71.
  • Narukawa, Y., Murofushi, T. and Sugeno, M., Regular fuzzy measure and representation of comono- tonically additive functionals, Fuzzy Sets and Systems 112 (2000) 177-186.
  • Ralescu, D. and Adams, G., The fuzzy integral, Journal of Mathematical Analysis and Application (1980) 562-570.
  • Rom´an-Flores, H., Flores-Franuliˇc, A. and Chalco-Cano, Y., A Jensen type inequality for fuzzy inte- grals, Information Sciences 177 (2007) 3192-3201.
  • Rom´an-Flores, H., Flores-Franuliˇc, A. and Chalco-Cano, Y., A Hardy type inequality for fuzzy inte- grals, Applied Mathematics and Computation 204 (2008) 178-183.
  • Royden, H.L., Real Analysis, Macmillan, New York, 1988.
  • Su´arez Garc´ia, F. and Gil ´Alvarez, P., Two families of fuzzy integrals, Fuzzy Sets and Systems 18 (1986) 67-81.
  • Sugeno, M., Theory of Fuzzy Integrals and Its Applications, Ph.D. Dissertation, Tokyo Institute of Technology, 1974.
  • Wang, Z. and Klir, G.J., Fuzzy Measure Theory, Plenum Press, New York, 1992.
  • Weber, S., Measures of fuzzy sets and measures of fuzziness, Fuzzy Sets and Systems 13 (1984) 247-271.

Year 2018, Volume: 8 Issue: 1, 1 - 7, 01.06.2018

- B.daraby

Abstract

References

  • Daraby, B., Generalization of the Stolarsky type inequality for pseudo-integrals, Fuzzy Sets and Sys- tems 194 (2012) 90-96.
  • Daraby, B., Shafiloo, A. and Rahimi, A., Generalization of the Feng Qi type inequality for pesudo- integral, Gazi University Journal of Science 28 (4) (2015), 695-702.
  • Daraby, B. and Rahimi, A., Jensen type inequality for seminormed fuzzy integrals, Acta Universitatis Apulensis 46 (2016) 1-8.
  • Daraby, B. and Ghazanfary Asll, H. and Sadeqi, I., General related inequalities to Carlson-type inequlity for the Sugeno integral, Applied Mathematics and Computation 305 (2017) 323-329.
  • Kandel, A., Byatt, W.J., Fuzzy sets, fuzzy algebra, and fuzzy statistics, Proceedings of the IEEE 66 (1978) 1619-1639.
  • Klement, E.P., Mesiar, R. and Pap, E., Integration with respect to decomposable measures, based on a conditionally distributive semiring on the unit interval, International Journal of Uncertainty Fuzziness Knowledge-Based Systems 8 (2000) 701-717.
  • Klement, E.P., Mesiar,R. and Pap, E., Triangular norms, in: Trends in Logic, in: Studia Logica Library, Vol. 8, Kluwer Academic Publishers, Dordrecht, 2000.
  • Mesiar, R., Choquet-like integrals, Journal of Mathematical Analysis and Applications 194 (1995) 488.
  • Murofushi, T. and Sugeno, M., Fuzzy t-conorm integral with respect to fuzzy measures: Generalization of Sugeno integral and Choquet integral, Fuzzy Sets and Systems 42 (1991) 57-71.
  • Narukawa, Y., Murofushi, T. and Sugeno, M., Regular fuzzy measure and representation of comono- tonically additive functionals, Fuzzy Sets and Systems 112 (2000) 177-186.
  • Ralescu, D. and Adams, G., The fuzzy integral, Journal of Mathematical Analysis and Application (1980) 562-570.
  • Rom´an-Flores, H., Flores-Franuliˇc, A. and Chalco-Cano, Y., A Jensen type inequality for fuzzy inte- grals, Information Sciences 177 (2007) 3192-3201.
  • Rom´an-Flores, H., Flores-Franuliˇc, A. and Chalco-Cano, Y., A Hardy type inequality for fuzzy inte- grals, Applied Mathematics and Computation 204 (2008) 178-183.
  • Royden, H.L., Real Analysis, Macmillan, New York, 1988.
  • Su´arez Garc´ia, F. and Gil ´Alvarez, P., Two families of fuzzy integrals, Fuzzy Sets and Systems 18 (1986) 67-81.
  • Sugeno, M., Theory of Fuzzy Integrals and Its Applications, Ph.D. Dissertation, Tokyo Institute of Technology, 1974.
  • Wang, Z. and Klir, G.J., Fuzzy Measure Theory, Plenum Press, New York, 1992.
  • Weber, S., Measures of fuzzy sets and measures of fuzziness, Fuzzy Sets and Systems 13 (1984) 247-271.
There are 18 citations in total.

Details

Primary Language English
Authors

- B.daraby This is me

Publication Date June 1, 2018
Published in Issue Year 2018 Volume: 8 Issue: 1

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