A review on the design and optimization of interval type-2 fuzzy controllers

Abstract

A review of the methods used in the design of interval type-2 fuzzy controllers has been considered in this work. The fundamental focus of the work is based on the basic reasons for optimizing type-2 fuzzy controllers for different areas of application. Recently, bio-inspired methods have emerged as powerful optimization algorithms for solving complex problems. In the case of designing type-2 fuzzy controllers for particular applications, the use of bio-inspired optimization methods have helped in the complex task of finding the appropriate parameter values and structure of the fuzzy systems. In this review, we consider the application of genetic algorithms, particle swarm optimization and ant colony optimization as three different paradigms that help in the design of optimal type-2 fuzzy controllers. We also mention alternative approaches to designing type-2 fuzzy controllers without optimization techniques. We also provide a comparison of the different optimization methods for the case of designing type-2 fuzzy controllers.

Introduction

Uncertainty affects decision-making and emerges in a number of different forms. The concept of information is inherently associated with the concept of uncertainty [49], [53]. The most fundamental aspect of this connection is that the uncertainty involved in any problem-solving situation is a result of some information deficiency, which may be incomplete, imprecise, fragmentary, not fully reliable, vague, contradictory, or deficient in some other way. Uncertainty is an attribute of information [69]. The general framework of fuzzy reasoning allows handling much of this uncertainty and fuzzy systems employ type-1 fuzzy sets, which represent uncertainty by numbers in the range [0, 1]. When an entity is uncertain, like a measurement, it is difficult to determine its exact value, and of course type-1 fuzzy sets make more sense than traditional sets [69]. However, it is not reasonable to use an accurate membership function for something uncertain, so in this case what we need is another type of fuzzy sets, those which are able to handle these uncertainties, the so called type-2 fuzzy sets [13]. The amount of uncertainty in a system can be reduced by using type-2 fuzzy logic because this logic offers better capabilities to handle linguistic uncertainties by modeling vagueness and unreliability of information [61], [68].

Type-2 fuzzy models have emerged as an interesting generalization of fuzzy models based upon type-1 fuzzy sets [13], [30]. There have been a number of claims put forward as to the relevance of type-2 fuzzy sets being regarded as generic building constructs of fuzzy models [26], [59], [64]. Likewise, there is a record of some experimental evidence showing some improvements in terms of accuracy of fuzzy models of type-2 over their type-1 counterparts [20], [27], [44]. Unfortunately, no systematic and comprehensive design framework has been provided and while improvements over type-1 fuzzy models were evidenced, it is not clear whether this effect could always be expected. Furthermore, it is not demonstrated whether the improvement is substantial enough and fully legitimized given the substantial optimization overhead associated with the design of this category of models. There have been a lot of applications of type-2 in intelligent control [9], [14], [30], [31], [50], pattern recognition [54], intelligent manufacturing [27], [52], [71], and others [2], [17], [18], [19]. Similarly, optimization methods have also been applied in the design of optimal type-1 fuzzy systems in diverse areas of application [1], [3], [4], [5], [23], [32], [33], [38], [58]. However, no general design strategy for finding the optimal type-2 fuzzy model has been proposed, and for this reason bio-inspired algorithms have been used to try in find these optimal type-2 models.

In general, the methods for designing a type-2 fuzzy model based on experimental data can be classified into two categories. The first category of methods assumes that an optimal (in some sense) type-1 fuzzy model has already been designed and afterwards a type-2 fuzzy model is constructed through some sound augmentation of the existing model. The second class of design methods is concerned with the construction of the type-2 fuzzy model directly from experimental data. In both cases, an optimization method can help in obtaining the optimal type-2 fuzzy model for the particular application.

Recently, bio-inspired methods have emerged as powerful optimization algorithms for solving complex problems. In the case of designing type-2 fuzzy controllers for particular applications, the use of bio-inspired optimization methods have helped in the complex task of finding the appropriate parameter values and structure of the fuzzy systems. In this review, we consider the application of genetic algorithms, particle swarm optimization and ant colony optimization as three different paradigms that help in the design of optimal type-2 fuzzy controllers. We also mention some hybrid approaches and other optimization methods that have been applied in problem of designing optimal type-2 fuzzy controllers in different domains of application.