Jensen's inequalities for pseudo-integral

Časopis: Iranian Journal of Fuzzy Systems

Volume, no: 18 , 3

ISSN: 1735-0654

DOI: 10.22111/IJFS.2021.5893

Stranice: 99-109


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 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 Štrboja [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.
Ključne reči: Jensen's inequality, semiring, pseudo-integral, pseudo-operation, (oplus,otimes)-convex function.