Some Revised Aspects of Type-2 Fuzzy Sets Use

Abstract

In this work we revise some less investigated aspects of a type-2 fuzzy logic system ( FLS ), which can handle rule uncertainties. The specificity of this type-2 FLS usually comprises the operations of fuzzification, inference, and output processing. We focus on “inference”, which in our opinion should be based on an operation of fuzzy implication, rather than on commonly used t-norm one. This paper also investigates some original properties of fuzzy grades under the operations of join ⊔ , meet ⊓ and implication ⟶ , which are defined by using the extension principal L. A. Zadeh, and shows that convex fuzzy grades form normal convex fuzzy grades , which in their turn form a distributive lattice under ⊔ and ⊓ . In this article we present much more effective implementation of such operations. We also explore an important feature of IF-THEN rules for type-2 fuzzy sets . This study introduces the notion of semantic similarity measure of these rules and their importance for logical inference in type-2 FLS . All theoretical concepts presented in this work are thoroughly illustrated by relevant examples.