BibTex RIS Cite

GENERAL RELATED JENSEN TYPE INEQUALITIES FOR FUZZY INTEGRALS

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

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.

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

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
Journal Section Research Article
Authors

- B.daraby This is me

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

Cite