ABSTRACT

A generic type 2 fuzzy set (T2 FS) is a T2 FS whose secondary membership can have a value between [0,1]. Compared to the segment T2 (IT2) FS, where the secondary membership is all 1, the regular T2 FS has more design freedom, and consequently it is receiving more and more attention from T2 FS researchers. An important calculation for a generic T2 FS is central because the centroid provides a measure of the uncertainty of such fuzzy set (FS) and may have to be calculated during type reduction for a generic type 2 fuzzy logic system (T2 FLS). The heart of the regular T2 FS developed by Karnik and Mendel is the sum of the heart of all the built-in T2 FS. The Karnik–Mendel (KM) algorithm or the enhanced Karnik–Mendel (EKM) algorithm is used to calculate the centroid of each α-level T2 FS. The T2 FLS theory and its applications have grown in recent years. One of the main problems with the implementation of such systems is type reduction, which computes the generalized centroid of a T2 FS. The KM algorithm is the most used procedure in interval type 2 fuzzy logic systems (IT2 FLSs). The heart of IT2 FS provides a measure of the uncertainty of IT2 FS. The final stage (FIS) of the system is defuzzification. Differing consists of two stages: type reduction, the procedure of converting a set of type 2 to a set of type 1, and an appropriate diffusing, which provides sharp numbers by diffusing this set of type 1. Type reduction was suggested by Karnik and Mendel and others. This is the “extended version” [“extended version” of the type 1 deferencing method and is called type reduction. This operation is called “type-reduction set” in FLS’s type 2 output set.