Fixpoints of fuzzy closure operators via ordinary algorithms

Abstract

We present a way to compute the set of fixpoints of a given fuzzy closure operator via algorithms for computing sets of fixpoints of ordinary closure operators. We assume that the fuzzy closure operator is given by a set of fuzzy sets generating this operator. The proposed way is based on certain reduction theorems which we provide and which relate fuzzy and ordinary closure operators and the sets of their fixpoints. We also present explicit description of selected algorithms which result using the presented approach.