Some Properties of Membership Functions Composed of Triangle Functions and Piecewise Linear Functions

Summary . IF-THEN rules in fuzzy inference is composed of multiple sets (membership functions). can therefore be considered as a pair membership functions [7]. The evaluation function control composite with approximate reasoning and functional on the set functions. We obtained continuity compactness [12]. Therefore, we proved existence functions, which maximizes (minimizes) rules, by using extreme value theorem. (fuzzy sets) defined this article to verifier our proofs before Mizar [9], [10], [4]. Membership triangle function, piecewise linear Gaussian used practice are formalized existing On other hand, not only curve mentioned above but also straight lines (piecewise function) like triangular trapezoidal formalized. Moreover, different from definition [3] formalizations two lines, minimum maximum proposed. prove, [2], [1] formalism, some properties such periodicity [13], [8].