Analysis of systems with variable parametric uncertainty using fuzzy functions

Fuzzy functions are used for the modelling and analysis of systems with variable parametric uncertainty. The approach consists of interpreting a fuzzy number as a family of intervals bounding the parameter space, parameterized by the degree of confidence (reliability) in the model. The uncertainty associated with a fuzzy function with non-fuzzy arguments lies in its parameters, which are fuzzy numbers. Interpreting the membership level, a. of these fuzzy numbers as a confidence level in the nominal function (the resulting crisp function for α = 1), an extended function can be viewed as a set of interval functions, each of them with an associated confidence. So, this kind of function allows us to model parametric uncertain systems with variable uncertainty, when the degree of confidence about having the parameter value within a given interval can be estimated. A stability analysis for systems modelled in this way is given¹.