Grades of Monotonicity of Fuzzy Relations and Their Application to Fuzzy Rule Bases

Abstract

In this contribution, we will introduce a notion of monotonicity of a fuzzy relation as a graded property. We will study its behavior w.r.t. fuzzy set operations and show relationship between monotone crisp functions and monotone fuzzy relations. Finally, a connection to special models of a monotone fuzzy rule base system will be provided.