On the Change of the Distribution Shape of Randomized Fuzzy Variables by Filtering over Compatibility Degrees

Abstract

A fuzzy output of a fuzzy controller is usually determined by a deterministic procedure e.g. by the center-of-gravity method. A fuzzy controller is a special case of a fuzzy-rule based system. If a fuzzy-rule based system should be used to simulate a real system, some indeterminacy and uncertainty about the system output may be desirable. The output can be generated as follows: first a λ-level set is randomly generated according to some rules, then an element of the generated λ-level set is chosen according to the uniform distribution over the chosen λ-level set. The result of this procedure is a probability distribution over the output set. We can influence this process in various ways e.g. we can “filter out” some undesirable compatibility degrees λ.We study the impact of such a “filtering” on the shape of the resulting probability density function over the output space.