Probabilistic fuzzy systems, expressions and approaches

In this paper, we aim to provide an overall perspective to the various expressions and approaches regarding probabilistic fuzzy systems. We begin with providing an introduction to the different kinds of uncertainties and associated tools that address them. A general description about the principle of modelling in stochastic environments is then represented. Two different expressions on probabilistic fuzzy sets are subsequently discussed. Moreover three distinct probabilistic fuzzy approaches facing stochastic problems are described and the ad-vantages and disadvantages related to each approach are also illustrated. Several simulations and comparative analysis are also provided to clarify the mentioned concepts.