The problem of possibilistic-probabilistic optimization

Abstract

This paper studies the models and methods for solving optimization problems with hybrid possibilistic-probabilistic uncertainty. The models under consideration have a peculiarity that the interaction of fuzzy parameters is described by the weakest t-norm. We propose solution methods that are based on the integration of indirect optimization methods (the design of equivalent problems) and direct (stochastic quasi-gradient) optimization methods. We establish the results for the models that were not considered in the previous publications on the subject. The resulting models and methods allow us to construct the generalized portfolio analysis models that are intended for managing combined (hybrid) uncertainty.