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Journals / Gazi University Journal of Science / 2015 / Volume: 28 Issue: 4

generalizations of the Feng Qi Type Inequality for Pseudo-Integral

Bayaz Daraby
Amir Shafiloo
Asghar Rahimi
Pages
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Publication Date
2015-12-16
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

There are considered two cases of the real semiring with pseudo-operations: One, when pseudo-operations are defined by monotone and continuous function $g$ (then the pseudo-integrals reduces $g$-integral), and the second with a semiring $([a, b],\max,\odot)$, where the pseudo-multiplication $\odot$ is generated.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, generalizations of the Feng Qi type integral inequalities for pseudo-integrals are proved.
📊
Key Findings & Data:In this paper, generalizations of the Feng Qi type integral inequalities for pseudo-integrals are proved.
💡
Conclusion & Impact:There are considered two cases of the real semiring with pseudo-operations: One, when pseudo-operations are defined by monotone and continuous function $g$ (then the pseudo-integrals reduces $g$-integral), and the second with a semiring $([a, b],\max,\odot)$, where the pseudo-multiplication $\odot$ is generated.
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:Sugeno integrals · integral inequality · Feng Qi inequality

Abstract

In this paper, generalizations of the Feng Qi type integral inequalities for pseudo-integrals are proved. There are considered two cases of the real semiring with pseudo-operations: One, when pseudo-operations are defined by monotone and continuous function $g$ (then the pseudo-integrals reduces $g$-integral), and the second with a semiring $([a, b],\max,\odot)$, where the pseudo-multiplication $\odot$ is generated.

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Cite This Article

Daraby, B., Shafiloo, A., Rahimi, A. (2015). generalizations of the Feng Qi Type Inequality for Pseudo-Integral. Gazi University Journal of Science, Volume: 28 Issue: 4. https://ajindex.com/articles/1269570

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References (53)

  1. bibitem{ham}
  2. H. Agahi, M. A. Yaghoobi, A Feng Qi type inequality for Sugeno integral, Fuzzy Inf. Eng. (2010) 3: 293-304.
  3. bibitem{Ana}
  4. G. Anastassiou, Chebyshev-Gr$overset{.}u$ss type inequalities via Euler type and Fink identities, Mathematics Computing and Modelling 45 (2007) 1189-1200.
  5. bibitem{bou}
  6. L. Bougoffa, On Minkowski and Hardy integral inequalities, Journal of Inequalities in Pure and Applied Mathematics 7(2) (2006) article 60.
  7. bibitem{cab}
  8. J. Caballero, K. Sadarangani, Hermite-Hadamard inequality for fuzzy integrals. Applied Mathematics and Computation
  9. bibitem{che}
  10. T. Y. Chen, H. L. Chang, G. H. Tzeng, Using fuzzy measures and habitual domains to analyze the public attitude and apply to the gas taxi policy, European Journal of Operational Research 137 (2002) 145-161.
  11. bibitem{Dar}
  12. B. Daraby, Generalization of the Stolarsky type
  13. inequality for pseudo-integrals, Fuzzy Sets and Systems 194 (2012) 90-96.
  14. bibitem{dar}
  15. B. Daraby, L. Arabi, Related Fritz Carlson type inequality for Sugeno integrals, Soft Computing 17 (2013) 1745-1750.
  16. bibitem{flo}
  17. A. Flores-Franuli$check{c}$, H. Rom$acute{a}$n-Flores, A Chebyshev type inequality for fuzzy integrals, Applied Mathematics and Computation 190 (2007) 1178-1184.
  18. bibitem{flor}
  19. A. Flores-Franuliv{c}, H. Rom$acute{a}$n-Flores, Y. Chalco-Cano, A convolution type inequality for fuzzy integrals, Applied Mathematics and Computation 195 (2008) 94-99.
  20. bibitem{Flo}
  21. A. Flores-Franuliv{c}, H. Rom$acute{a}$n-Flores, Y. Chalco-Cano, Markov type inequalities
  22. for fuzzy integrals, Applied Mathematics and Computation 207 (2009) 242-247.
  23. bibitem{Flor}
  24. A. Flores-Franuliv{c}, H. Rom$acute{a}$n-Flores, Y. Chalco-Cano, A note on fuzzy integral inequality of Stolarsky type, Applied Mathematics and Computation 196 (2008) 55-59.
  25. bibitem{hon}
  26. D. H. Hong, A sharp Hardy-type inequality of Sugeno integrals, Applied Mathematics and Computation 217 (2010) 437-440.
  27. bibitem{kra}
  28. S. G. Krantz, Jensen's Inequality, $sharp$ 9.1.3 in Handbook of Complex Variables, Boston, MA: Birkh$overset{.}a$user, 119, 1999.
  29. bibitem{luj}
  30. J.-Y. Lu, K.-S. Wu, J.-C. Lin, Fast full search in motion estimation by hierarchical use of Minkowski's
  31. inequality, Pattern Recognition 31 (1998) 945-952.
  32. bibitem{mes1}
  33. R. Mesiar, E. Pap, Idempotent integral as limit of $g-$integrals, Fuzzy Sets and Systems 102 (1999) 385-392.
  34. bibitem{mes}
  35. R. Mesiar, Y. Ouyang, General Chebyshev type inequalities for Sugeno integrals, Fuzzy Sets and Systems 160 (2009) 58-64.
  36. bibitem{Mes}
  37. R. Mesiar, E. Pap, Idempotent integral as limit of $g$-integrals, Fuzzy Sets and Systems 102 (1999) 385-392.
  38. bibitem{min}
  39. H. Minkowski, Geometrie der Zahlen, Teubner, Leipzig, 1910.
  40. bibitem{ozk}
  41. U. M, $overset{.}O$zkan, M. Z. Sarikaya, H. Yildirim, Extensions of certain integral inequalities on time scales, Applied
  42. Mathematics Letters 21 (2008) 993-1000.
  43. bibitem{Pap6}
  44. E. Pap, An integral generated by decomposable measure, Univ. Novom
  45. Sadu Zb. Rad. Prirod. -Mat. Fak. Ser. Mat. 20 (1) (1990)
  46. bibitem{feng}
  47. F. Qi, Several integral inequalities. J. Inequal. Pure Appl. Math. 1(2) Art 19.
  48. bibitem{wan}
  49. Z. Wang, G. Klir, Fuzzy Measure Theory, Plenum Press, New York, 1992.
  50. G. Anastassiou, Chebyshev-Gr$overset{.}u$ss type inequalities via Euler type and Fink identities, Mathematics Computing and Modelling 45 (2007) 1189-1200.
  51. S. G. Krantz, Jensen's Inequality, $sharp$ 9.1.3 in Handbook of Complex Variables, Boston, MA: Birkh$overset{.}a$user, 119, 1999.
  52. J.-Y. Lu, K.-S. Wu, J.-C. Lin, Fast full search in motion estimation by hierarchical use of Minkowski's
  53. U. M, $overset{.}O$zkan, M. Z. Sarikaya, H. Yildirim, Extensions of certain integral inequalities on time scales, Applied