伪积分的Jensen不等式

IF 1.9 4区数学 Q1 MATHEMATICS

Iranian Journal of Fuzzy Systems Pub Date : 2021-06-01 DOI:10.22111/IJFS.2021.6084

Deli Zhang, E. Pap

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引用次数: 2

摘要

本文引入了一个基于半环$([a,b]，oplus, otimes)$的一般$(oplus,otimes)$-凸函数，它具有伪加法$oplus$和伪乘法$otimes。得到了有限ejensen不等式的推广，以及关于(0 +，times)凸函数的伪积分。这也推广了Lebesgue积分的Jensen不等式以及Pap和v{S}trboja引用{12}的结果。同时，我们还证明了半环$([a,b]， sup, otimes)$上关于非降函数的伪积分的Jensen不等式，并给出了广义模糊积分的相应结果。

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Jensen's inequalities for pseudo-integrals

In this paper, we introduce a general$(oplus,otimes)$-convex function based on semirings $([a,b],oplus, otimes)$ with pseudo-addition $oplus$ andpseudo-multiplication $otimes.$ The generalization of the finiteJensen'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 correspondingresults for generalized fuzzy integrals.

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来源期刊

Iranian Journal of Fuzzy Systems 数学-数学

CiteScore

3.50

自引率

16.70%

发文量

期刊介绍： The two-monthly Iranian Journal of Fuzzy Systems (IJFS) aims to provide an international forum for refereed original research works in the theory and applications of fuzzy sets and systems in the areas of foundations, pure mathematics, artificial intelligence, control, robotics, data analysis, data mining, decision making, finance and management, information systems, operations research, pattern recognition and image processing, soft computing and uncertainty modeling. Manuscripts submitted to the IJFS must be original unpublished work and should not be in consideration for publication elsewhere.