A Generalized Type-2 Fuzzy Controller (GT2FC) was developed.Simulation of a GT2FC for a mobile robot is presented.Experiments support the notion that GT2FC handles more uncertainty. The aim of this paper is to show that a Generalized Type-2 Fuzzy Control System can outperform Type-1 and Interval Type-2 Fuzzy Control Systems when external perturbations are present. A Generalized Type-2 Fuzzy System can handle better uncertainty because of the nature of its membership functions, and as such, they are better tailored for situations where external noise is present. To test the noise resilience of Fuzzy Controllers, the design of a Fuzzy Controller for a mobile robot is presented in this paper, in conjunction with three types of external perturbations: band-limited white noise, pulse noise, and uniform random number noise. Noise resilience is measured through different performance indices, such as ITAE, ITSE, IAE, and ISE. Simulation results show that Generalized Type-2 Fuzzy Controllers outperform their Type-1 and Interval Type-2 Fuzzy Controller counterparts in the presence of external perturbations.

Generalized Type-2 Fuzzy Systems for controlling a mobile robot and a performance comparison with Interval Type-2 and Type-1 Fuzzy Systems

The purpose of this tutorial paper is to make general type-2 fuzzy logic systems (GT2 FLSs) more accessible to fuzzy logic researchers and practitioners, and to expedite their research, designs, and use. To accomplish this, the paper 1) explains four different mathematical representations for general type-2 fuzzy sets (GT2 FSs); 2) demonstrates that for the optimal design of a GT2 FLS, one should use the vertical-slice representation of its GT2 FSs because it is the only one of the four mathematical representations that is parsimonious; 3) shows how to obtain set theoretic and other operations for GT2 FSs using type-1 (T1) FS mathematics (α- cuts play a central role); 4) reviews Mamdani and TSK interval type-2 (IT2) FLSs so that their mathematical operations can be easily used in a GT2 FLS; 5) provides all of the formulas that describe both Mamdani and TSK GT2 FLSs; 6) explains why center-of sets type-reduction should be favored for a GT2 FLS over centroid type-reduction; 7) provides three simplified GT2 FLSs (two are for Mamdani GT2 FLSs and one is for a TSK GT2 FLS), all of which bypass type reduction and are generalizations from their IT2 FLS counterparts to GT2 FLSs; 8) explains why gradient-based optimization should not be used to optimally design a GT2 FLS; 9) explains how derivative-free optimization algorithms can be used to optimally design a GT2 FLS; and 10) provides a three-step approach for optimally designing FLSs in a progressive manner, from T1 to IT2 to GT2, each of which uses a quantum particle swarm optimization algorithm, by virtue of which the performance for the IT2 FLS cannot be worse than that of the T1 FLS, and the performance for the GT2 FLS cannot be worse than that of the IT2 FLS.

General Type-2 Fuzzy Logic Systems Made Simple: A Tutorial

An integrated approach to green supplier selection based on the interval type-2 fuzzy best-worst and extended VIKOR methods

This article compares three methods [Interval Approach (IA), Enhanced Interval Approach (EIA) and Hao–Mendel Approach (HMA)] for estimating (synthesizing) an interval type-2 fuzzy set (IT2 FS) model for a word, beginning with data that are collected from a group of subjects, or from a single subject. It summarizes the stages for each of the methods in tables so it is possible to compare the steps of each stage side-by-side. It also demonstrates, by means of an example of three words, that using more information contained in the collected data intervals is equivalent to reducing the uncertainty in the IT2 FS model. It recommends the HMA because it uses more information contained in the collected data intervals than does the IA or the EIA, and because it is the only method to-date that leads to normal IT2 FSs. Such fuzzy sets are easier to compute with than are non-normal IT2 FSs.

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A comparison of three approaches for estimating (synthesizing) an interval type-2 fuzzy set model of a linguistic term for computing with words

Multi-attribute group decision making using combined ranking value under interval type-2 fuzzy environment

This paper focuses on an approach, called the HM Approach (HMA), to determine (for the first time) a normal interval type-2 fuzzy set model for a word that uses interval data about a word that are collected either from a group of subjects or from one subject. The HMA has two parts: 1) Data part, which is the same as the Data Part of the enhanced interval approach (EIA) [44] , and 2) Fuzzy Set Part, which is very different from the second part of the EIA, the most notable difference being that in the HMA, the common overlap of subject data intervals is interpreted to indicate agreement by all of the subjects for that overlap, and therefore, a membership grade of 1 is assigned to the common overlap. Another difference between the HMA and EIA is the way in which data intervals are collectively classified into either a Left-shoulder, Interior, or Right-shoulder footprint of uncertainty. The HMA does this more simply than does the EIA, and requires fewer probability assumptions about the intervals than does the EIA.

Encoding Words Into Normal Interval Type-2 Fuzzy Sets: HM Approach

Similarity measures for general type-2 fuzzy sets based on the α-plane representation

Removing Mixed Gaussian and Impulse Noise (MGIN) is considered to be one of the most essential topics in the domain of image restoration, and it is much more challenging than to remove pure Gaussian or impulse noise separately. Therefore, relatively fewer works have been published in this area. This paper proposes a new integrated approach for MGIN removal that is based on a Non-Singleton Interval Type-2 (NS-IT2) Fuzzy Logic System (FLS), and explains how to design such a NS-IT2 FLS using a Quantum-behaved Particle Swarm Optimization (QPSO) algorithm. Then the paper goes on to introduce two supplementary components, a Block-Matching 3-Dimensional Discrete Cosine Transformation (BM3D DCT) filter and a contrast scaling filter, which augment the overall performance of the NS-IT2 FLS. Finally, the paper shows that this proposed approach indeed provides both quantitatively and visually much better results compared to other often-used non-fuzzy techniques as well as its Type-1 (T1) and singleton IT2 (S-IT2) counterparts.

Universal image noise removal filter based on type-2 fuzzy logic system and qpso

Removing Mixed Gaussian and Impulse Noise (MGIN) is considered to be very important in the domain of image restoration, but it is a somewhat more challenging topic than removing pure Gaussian or impulse noise. Therefore, relatively fewer works have been published in this area. This paper pro poses a Non-Singleton Interval Type-2 (IT2) Fuzzy Logic System (FLS) for MGIN removal, explains how it can be designed based on a Quantum-behaved Particle Swarm Optimization algorithm, and shows that it provides both quantitatively and visually much better results compared to other often-used non-fuzzy techniques as well as its Type-1 and singleton IT2 counterparts.

A Non-Singleton Interval Type-2 Fuzzy Logic System for universal image noise removal using Quantum-behaved Particle Swarm Optimization

The Perceptual Computer (Per-C) is an application of Zadeh's theory of computing with words (CWW) in the field of assisting people to make subjective judgments. This paper describes an application of the Per-C to evaluate Learning Outcomes (LOs) in an outcome-based education (OBE) system. The evaluation problem in this paper is viewed as a hierarchical decision making problem. In the first level of the hierarchy, the crisp score of each assessment is mapped into an interval type-2 fuzzy set (IT2 FS) for each student. The assessments are then aggregated to obtain the performance of each LO. The linguistic weighted power mean (LWPM) is used as the CWW engine, so that some mandatory requirements can be implemented. Finally, by aggregating the performance of all LOs, the final performance is obtained. We also present an example of our proposed Per-C using a fictitious course.

Minshen Hao

Papers

Encoding Words Into Normal Interval Type-2 Fuzzy Sets: HM Approach

Similarity measures for general type-2 fuzzy sets based on the α-plane representation

Universal image noise removal filter based on type-2 fuzzy logic system and qpso

A Non-Singleton Interval Type-2 Fuzzy Logic System for universal image noise removal using Quantum-behaved Particle Swarm Optimization

Perceptual Computer application in Learning Outcome evaluation