Jensen's inequalities for pseudo-integrals

	Jensen's inequalities for pseudo-integrals
Iranian Journal of Fuzzy Systems
مقاله 9، دوره 18، شماره 3، مرداد و شهریور 2021، صفحه 99-109 اصل مقاله (359.71 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2021.6084
نویسندگان
D. Zhang^* ¹؛ E. Pap²
¹College of Mathematics, Changchun Normal University, Changchun 130032, Jilin, PR China
²Singidunum University, 11000 Belgrade, Serbia
چکیده
In this paper, we introduce a general $(\oplus,\otimes)$-convex function based on semirings $([a,b], \oplus, \otimes)$ with pseudo-addition $\oplus$ and pseudo-multiplication $\otimes.$ The generalization of the finite Jensen's inequality, as well as pseudo-integral with respect to $(\oplus,\otimes)$-convex functions, is obtained. This also generalizes Jensen's inequalities for Lebesgue integral and the results of Pap and \v{S}trboja \cite{12}. Meanwhile, we also prove Jensen's inequalities for pseudo-integrals on semirings $([a,b], \sup, \otimes)$ with respect to nondecreasing functions and present corresponding results for generalized fuzzy integrals.
کلیدواژه‌ها
Jensen's inequality؛ semiring؛ pseudo-integral؛ pseudo-operation؛ $(oplus؛ otimes)$-convex function

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