Document Type : Research Paper
Authors
Department of Mathematics, University of Maragheh, P. O. Box 55136-553, Maragheh, Iran.
Abstract
In this paper, we have proved and stated the Sitaru-Schweitzer type inequality for fuzzy integrals and also we state this inequality for pseudo-integrals in two classes. The first one is for pseudo-integrals where pseudo-addition and pseudo-multiplication are constructed by a monotone continuous function $g:[0, \infty ]\to[0, \infty]$. Another one is given by the semiring $([a, b], \max, \odot)$ where an increasing function generates pseudo-multiplication.
Keywords
Main Subjects
[1] H. Agahi, R. Mesiar and Y. Ouyang, General Minkowski type inequality for Sugeno integral, Fuzzy Sets Syst., 161 (2010), pp. 708-715.
[2] H. Agahi, R. Mesiar and Y. Ouyang, New general extensions of Chebyshev type inequality for Sugeno integrals, International Jornal of Approxinate Reasoning, 51 (2002), pp. 135-140.
[3] B. Daraby, A review on some fuzzy integral inequalities, Sahand Commun. Math. Anal., 18 (3) (2021), pp. 153-185.
[4] B. Daraby, Generalizations of related Fritz Carlson type inequalities for fuzzy integrals, Sahand Commun. Math. Anal., 18, (4) (2021), pp. 131-153.
[5] B. Daraby, Generalization of the Stolarsky type inequality for pseudo-integrals, Fuzzy Sets Syst., 194 (2012), pp. 90-96.
[5] B. Daraby, Generalization of the Stolarsky type inequality for pseudo-integrals, Fuzzy Sets Syst., 194 (2012), pp. 90-96.
[6] B. Daraby and L. Arabi, Related Fritz Carlson type inequalities for Sugeno integrals, Soft Comput., 17 (10) (2013), pp. 1745-1750.
[7] B. Daraby and F. Ghadimi, General Minkowski type and related inequalities for seminormed fuzzy integrals, Sahand Commun. Math. Anal., 1 (1) (2014), pp. 9-20.
[8] B. Daraby, H. G. Asll and I. Sadeqi, General related inequalities to Carlson-type inequality for the Sugeno integral, Appl. Math. Comput., 305 (2017), pp. 323-329.
[9] B. Daraby, A. Rahimi and M. Tahmouresi,
Generalization of a two-dimensional Hardy type inequality for pseudo-integrals, Advances in Mathematical Sciencs and Applications, 32 (1) (2023), pp. 225-236.
Generalization of a two-dimensional Hardy type inequality for pseudo-integrals, Advances in Mathematical Sciencs and Applications, 32 (1) (2023), pp. 225-236.
[10] B. Daraby, A. Shafiloo and A. Rahimi, Generalizations of the Feng Qi type inequality for pseudo-integral, Gazi University Journal of Science, 28 (4) (2015), pp. 695-702.
[11] B. Daraby, R. Mesiar, F. Rostampour and A. Rahimi, Related Thunsdorff type and Frank-Pick type inequalities for Sugeno integral, Appl. Math. Comput., 414 (2022), 126683.
[12] S. Ezghari, A. Zahi and K. Zenkouar, A new nearest neighbor classification method based on fuzzy set theory and aggregation operators, Expert Systems with Applications, 80 (2017), pp. 58-74.
[13] A. Flores-Franulic and H. Roman-Flores, A Chebyshev type inequality for fuzzy integrals, Appl. Math. Comput., 190 (2007), pp. 1178-1184.
[14] A. Flores-Franulic, H. Roman-Flores and Y. Chalco-Cano, Markov type inequalities for fuzzy integrals, Appl. Math. Comput., 207 (2009), pp. 242-247.
[15] M.R. Karimzadeh, B. Daraby and A. Rahimi, Diaz-Metcalf type inequality for Sugeno and pseudo-integrals, Iran. J. Fuzzy Syst., 20 (2023), pp. 31-41.
[16] R. Mesiar and E. Pap, Idempotent integral as limit of g-integrals, Fuzzy Sets Syst., 102 (3) (1999), pp. 385-392.
[17] E. Pap, g-Calculus, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat., 23 (1) (1993), pp. 145-156.
[18] E. Pap, Null-Additive Set Functions, Kluwer Academic Publishers, Mathematics and
Its Applications 337, Dordrecht Boston London, 1995.
Its Applications 337, Dordrecht Boston London, 1995.
[19] E. Pap, Pseudo-additive measures and their applications, In Handbook of measure theory (pp. 1403-1468). North-Holland, 2002.
[20] E. Pap and M. Štrboja, Generalization of the Jensen inequality for pseudo-integral, Information Sciences, 180 (2010), pp. 543-548.
[20] E. Pap and M. Štrboja, Generalization of the Jensen inequality for pseudo-integral, Information Sciences, 180 (2010), pp. 543-548.
[21] D. Ralescu, G. Adams, The fuzzy integral, Journal of Mathematical Analysis and Applications, 75(2) (1980), 562-570.
[22] H. Roman-Flores, A. Flores-Franulič and Y. Chalco-Cano, A Hardy-type inequality for fuzzy integrals, Appl. Math. Comput., 204 (1) (2008), pp. 178-183.
[23] D. Sitaru, Math Phenomenon, Pitești: Editura Paralela, 45 (168) (2016).
[24] Z. Wang and G.J. Klir, Fuzzy Measure Theory, Springer Science & Business Media, (1992).
[25] D. Zhang and E. Pap, Jensen's inequalities for pseudo-integrals, Iran. J. Fuzzy Syst., 18 (3) (2021), pp. 99-109.
)