Robustness of fuzzy operators in environments with random perturbations

In many applications, such as intelligent decision systems, there are usually random perturbations caused by the constant changing of real situations, thus the analysis of the robustness with respect to random perturbations is practically important. In the side of fuzzy methods, a corresponding problem arises: will a small random perturbation of fuzzy input cause a big variance of fuzzy output? This paper study the robustness of fuzzy schemes in environments with random perturbations. It focuses on fuzzy algebraic operators, and proposes two methods to analyze their robustness in environments with random perturbations. The effectiveness and features of the methods are shown by simulations.