Pseudo-analysis and nonlinear equations

Abstract

 There are presented some recent results and applications of pseudo-analysis. There is presented an integration theory based on pseudo-additive measures and operations: triangular norms (and also uni-norms) and triangular conorms related by conditionally distributive equation forming conditionally distributive semiring on the unit interval [0, 1]. There is given an extension of the classical von Neumann–Morgenstern utility theory, where the solutions of the system of nonlinear equations with corresponding triangular norms and triangular norms give the decomposition of hybrid probabilistic-possibilistic measures. This enables to calculate the utility function. Related to the fixed point theory on probabilistic metric spaces and fuzzy metric spaces general theorems are obtained.