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{۱۲}. 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.   

Keywords:

Jensen's inequality , Semiring , pseudo-integral , pseudo-operation , (oplus , otimes)-convex function