Abstract
We first describe the basics of fuzzy systems modeling. Fundamental to this is a collection of rules, a rule base, in which the rule antecedents are fuzzy subsets. We first look at issue of the determination of the firing level of a rule for fuzzy set inputs and the subsequent rule base output. We next consider the situation where the system input is uncertain and modeled by a Dempster–Shafer belief structure. Here our input is a collection of fuzzy subsets and the true input fuzzy set is selected based on a probability distribution over these potential input fuzzy sets. We next consider the situation where our input is modeled via a generalized belief structure where the determination of applicable input fuzzy set is modeled via a measure over these potential input fuzzy sets.