فهرست نشریات علمی دسترسی آزاد ایران

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.