The non-singleton fuzzification operation for general forms of interval type-2 fuzzy logic systems

Abstract

Recently, the theory regarding interval type-2 fuzzy sets and fuzzy logic systems has been further developed. In the first instance, the concepts of interval type-2 fuzzy sets were broadened, proving that this class of sets include some which are different from interval-valued sets. In a later work, the set theoretic operations of union and intersection on these sets were studied and presented under the framework of general type-2 fuzzy sets. This stimulated and motivated the further study of fuzzy logic systems using these new sets, which have been referred to as the general forms of interval type-2 fuzzy sets. However, as usual when a new fuzzy logic framework is presented, only the singleton version of these systems was introduced. In this work we aim to generalise that work, introducing the non-singleton general forms of interval type-2 fuzzy logic systems. We will present a real example on how to use these non-singleton fuzzy logic systems in real world applications.