# Review of Recent Type-2 Fuzzy Controller Applications
## 1 Introduction  
Fuzzy logic sets were first introduced by [PERSON] [1]. Developments in fuzzy logic then stimulated the creation of fuzzy logic systems (FLSs), which emerged in many applications in systems modeling and control. [PERSON] and Baaklini are the ones that presented the first fuzzy logic controller (FLC) [2]. Earlier FLS designs were generally categorized as Type-1 fuzzy logic systems (T1 FLSs). T1 FLSs were used by Japanese companies who adopted the FLSs and implemented them in a water treatment plant by Fuji Electric in 1983 and in a subway system by Hitachi in 1987.  
One of the main challenges in the design of T1 FLSs is the shape of a membership function (MF) that is used. To incorporate uncertainty in fuzzy systems, [PERSON] introduced Type-2 fuzzy sets (T2 FSs). These are an extension of T1 FSs, which adds an extra degree of freedom to entitle an uncertainty factor in the systems [3]. T2 FSs have membership grades, which are also fuzzy [4]. According to [PERSON] in [5], \"increased fuzziness in a description means increased ability to handle inexact information in a logically correct manner\". This extra uncertainly gives the T2 FLS an extra degree of freedom (DOF) and increases the complexity in most T2 FLS applications [3].  
Due to the mathematical complexity of T2 FLSs, a simpler form of them was proposed, called interval Type-2 fuzzy logic systems (IT2 FLS). In an IT2 FLS, the uncertainty is mapped into a thirddimension where the value of the MF is also mapped for each point on a two-dimensional domain. This special IT2 FLS is a simpler form of T2 FLS and also relies on the mathematics of T1 FLS [6]. The major difference is that the defuzzifier block of a T1 FLS is replaced by an output processing block in a T2 FLS. This block consists of a type reduction (TR) followed by defuzzification, meaning that the TR is the function that maps a T2 FS to a T1 FS. This enables mapping the uncertainty to an interval between the upper membership function (UMF) and the lower membership function (LMF).  
T2 FLSs, including IT2 FLSs, are a more recent approach to solving problems that in many cases a T1 FLS cannot properly accomplish. The robustness of both T1 and IT2 FLSs is investigated in [7]. It was determined that the IT2 FLS outputs have small approximation errors; however, choosing to design a T1 or IT2 FLS is relatively application dependent. Furthermore, in [8], it has been shown that increasing the number of rules and the number of MFs beyond a certain limit is impractical. This increases the complexity of the FLC with almost no effect on the output. Regardless of this, IT2 FLSs are used in many applications, such as robot control, bandwidth control, industrial systems control, electrical control and aircraft control.  
In this paper, we present the new applications of T2 FLC and introduce the vital and key areas where they have been successfully implemented and used. While the intent of this paper is not focusing on theory or how to design these systems, we 'briefly' review different T2 FLC systems and their structures, so interested readers have a better understanding of them. Consequently, we focus mainly on the applications, present challenges and future directions in this field, which are of interest to engineers, practitioners and researchers who would like to use T2 FLC in their applications.  
The remainder of the paper is organized as follows: in Section 2 of this paper, we briefly discuss the most well-known IT2 algorithms; in Section 3, we present a literature review of IT2 FLCs along with their applications; and finally, in Section 4, we draw conclusions and future directions.