On some optimisation models in a fuzzy-stochastic environment

This paper is on fuzzy stochastic optimisation, an area that is quickly coming to the forefront of mathematical programming under uncertainty. An even stronger motivating factor for the growing interest in this area can be found in the ubiquitous nature of decision problems involving hybrid imprecision. More precisely, we consider a range of situations in which random factors and fuzzy information co-occur in an optimisation setting. Related hybrid optimisation models are discussed and converted into deterministic terms through appropriate tools like probabilistic set, uncertain probability, and fuzzy random variable, making good use of uncertainty principles. We also discuss ways to deal with the resulting problems. Numerical examples carried out using class optimisation software demonstrate the efficiency of the proposed approaches. We shall end this article by pointing out some of the challenges that currently occupy researchers in this emerging field.