Generalization of the Jensen inequality for pseudo-integral

Minkowski type inequality for fuzzy and pseudo-integrals

“…Pseudo-analysis is a generalization of the classical analysis, where instead of the field of real numbers a semiring is taken on a real interval [a, b] ⊂ [−∞, ∞] endowed with pseudo-addition ⊕ and with pseudo-multiplication ( [11,9,8,5,25,6,37]). Based on this structure there where developed the concepts of ⊕-measure (pseudo-additive measure), pseudo-integral, pseudo-convolution, pseudoLaplace transform and etc.…”

Theory and Applications of Non-additive Measures and Corresponding Integrals

“…The inequalities for integrals based on non-additive measures, e.g., Choquet, Sugeno, pseudo-integral have been recently given, see for an overview [28]. Specially, in [3,4,27,28] inequalities with respect to pseudo-integrals were considered. The convergence of decision variables were presented in [8].…”

An approach to pseudo-integration of set-valued functions

“…For the background of this paper we have chosen the field of the pseudo-analysis since it presents a contemporary mathematical theory that is being successfully applied in many different areas of mathematics as well as in various practical problems (see [2,17,18,21,[30][31][32][33][34][35][36]40]). An approach to the problem of integration of set-valued functions from the pseudoanalysis' point of view has been proposed in [10].…”