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.
Zhang, D. and Pap, E. (2021). Jensen's inequalities for pseudo-integrals. Iranian Journal of Fuzzy Systems, 18(3), 99-109. doi: 10.22111/ijfs.2021.6084
MLA
Zhang, D. , and Pap, E. . "Jensen's inequalities for pseudo-integrals", Iranian Journal of Fuzzy Systems, 18, 3, 2021, 99-109. doi: 10.22111/ijfs.2021.6084
HARVARD
Zhang, D., Pap, E. (2021). 'Jensen's inequalities for pseudo-integrals', Iranian Journal of Fuzzy Systems, 18(3), pp. 99-109. doi: 10.22111/ijfs.2021.6084
CHICAGO
D. Zhang and E. Pap, "Jensen's inequalities for pseudo-integrals," Iranian Journal of Fuzzy Systems, 18 3 (2021): 99-109, doi: 10.22111/ijfs.2021.6084
VANCOUVER
Zhang, D., Pap, E. Jensen's inequalities for pseudo-integrals. Iranian Journal of Fuzzy Systems, 2021; 18(3): 99-109. doi: 10.22111/ijfs.2021.6084
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