Investigation on the influence of a new trapezoidal-triangular membership function in IT2FLS with type-reductions for a manufacturing application

Abstract

The performance of Interval type-2 fuzzy logic system (IT2FLS) can be affected by many factors including the type of reduction methodology followed and the kind of membership function applied. Further, a particular membership function is influenced by its construction, the type of optimisation and adaptiveness applied, and the learning scheme adopted. The available literature lags in providing detailed information about such factors affecting the performance of IT2FLS. In this work, an attempt has been made to comprehensively study the factors affecting the performance of IT2FLS by introducing a new trapezoidal-triangular membership function (TTMF). A real-time application of drilling operation has been considered as an example for predicting temperature of the job, which is considered as one of the key state variables to evaluate. A detailed comparison based on membership functions (MFs) such as triangular membership function (TrMF), trapezoidal membership function (TMF), the newly introduced trapezoidal-triangular membership function (TTMF), semi-elliptic membership function (SEMF), and Gaussian membership function (GMF) has been performed and presented. Further, the average error rate obtained with two “type-reduction” methods such as “Wu-Mendel” uncertainty bounds and Center of sets type reduction (COS TR) has also been discussed. This study provides information for selecting a particular MF and “type reduction” scheme for the implementation of IT2FLS. Also, concludes that MF having fewer parameters such as GMF and SEMF possess significant advantages in terms of computation complexity compared to others.