New Methodology to Approximate Type-Reduction Based on a Continuous Root-Finding Karnik Mendel Algorithm

Abstract

Interval Type-2 fuzzy systems allow the possibility of considering uncertainty in models based on fuzzy systems, and enable an increase of robustness in solutions to applications, but also increase the complexity of the fuzzy system design. Several attempts have been previously proposed to reduce the computational cost of the type-reduction stage, as this process requires a lot of computing time because it is basically a numerical approximation based on sampling, and the computational cost is proportional to the number of samples, but also the error is inversely proportional to the number of samples. Several works have focused on reducing the computational cost of type-reduction by developing strategies to reduce the number of operations. The first type-reduction method was proposed by Karnik and Mendel (KM), and then was followed by its enhanced version called EKM. Then continuous versions were called CKM and CEKM, and there were variations of this and also other types of variations that eliminate the type-reduction process reducing the computational cost to a Type-1 defuzzification, such as the Nie-Tan versions and similar enhancements. In this work we analyzed and proposed a variant of CEKM by viewing this process as solving a root-finding problem, in this way taking advantage of existing numerical methods to solve the type-reduction problem, the main objective being eliminating the type-reduction process and also providing a continuous solution of the defuzzification.

High-Speed Interval Type-2 Fuzzy Systems for Dynamic Parameter Adaptation in Harmony Search for Optimal Design of Fuzzy Controllers

“…The theoretical constructs of interval type-2 fuzzy logic are described in this section. The objective of this work is to implement an approximation method that was recently published by [26] in parameter adaptation for HS, where it is possible to demonstrate the reduction of the computational cost when carrying out experimentation in various case studies. In this article, this approximate method for type reduction was implemented with the main goal of efficiently finding good results for HS.…”

Review and Investigation of Simplified Rules Fuzzy Logic Speed Controller of High Performance Induction Motor Drives

“…Recently type-2 fuzzy sets have gained a lot of interest-s in motor drives application due to their adaptive nature in handling fuzzy rules [54], [57]. Despite the appealing features of type-2 fuzzy sets, they are not preferred for cost-sensitive real-time applications due to their extra high computational cost compared to type-1 fuzzy sets which require high capabilities processors, thus increasing the cost of application [58], [60]. In summary, the development of fuzzy logic systems has led to great advancement in control system applications.…”

A Comprehensive Study of the Efficiency of Type-Reduction Algorithms

“…There have been a lot of type-reduction approaches proposed in the literature [9,10,11,12,13,14,15,16,17,18,19,20,21]. While some of the recent work on type-reduction approaches is based on continuous algorithms or general type-2 fuzzy systems [22,23], this paper focuses on discrete type-reduction approaches which are based on computing the centroid of an interval type-2 fuzzy set. The Karnik-Mendel (KM) algorithm is an iterative approach to determine the switch points when computing the centroids of IT2 fuzzy sets [9].…”