Type-2 fuzzy sets let us model and minimize the effects of uncertainties in rule-base fuzzy logic systems. However, they are difficult to understand for a variety of reasons which we enunciate. In this paper, we strive to overcome the difficulties by: (1) establishing a small set of terms that let us easily communicate about type-2 fuzzy sets and also let us define such sets very precisely, (2) presenting a new representation for type-2 fuzzy sets, and (3) using this new representation to derive formulas for union, intersection and complement of type-2 fuzzy sets without having to use the Extension Principle.

/pdf/type-2-fuzzy-sets-made-simple-3iyg95vkei.pdf

Type-2 fuzzy sets made simple

We present the theory and design of interval type-2 fuzzy logic systems (FLSs). We propose an efficient and simplified method to compute the input and antecedent operations for interval type-2 FLSs: one that is based on a general inference formula for them. We introduce the concept of upper and lower membership functions (MFs) and illustrate our efficient inference method for the case of Gaussian primary MFs. We also propose a method for designing an interval type-2 FLS in which we tune its parameters. Finally, we design type-2 FLSs to perform time-series forecasting when a nonstationary time-series is corrupted by additive noise where SNR is uncertain and demonstrate an improved performance over type-1 FLSs.

https://sipi.usc.edu/~mendel/publications/Liang%26Mendel%20TFS%2010-00%20%232.pdf

Interval type-2 fuzzy logic systems: theory and design

We introduce a type-2 fuzzy logic system (FLS), which can handle rule uncertainties. The implementation of this type-2 FLS involves the operations of fuzzification, inference, and output processing. We focus on "output processing," which consists of type reduction and defuzzification. Type-reduction methods are extended versions of type-1 defuzzification methods. Type reduction captures more information about rule uncertainties than does the defuzzified value (a crisp number), however, it is computationally intensive, except for interval type-2 fuzzy sets for which we provide a simple type-reduction computation procedure. We also apply a type-2 FLS to time-varying channel equalization and demonstrate that it provides better performance than a type-1 FLS and nearest neighbor classifier.

/pdf/type-2-fuzzy-logic-systems-20ss17tkqw.pdf

Type-2 fuzzy logic systems

Autonomous mobile robots navigating in changing and dynamic unstructured environments like the outdoor environments need to cope with large amounts of uncertainties that are inherent of natural environments. The traditional type-1 fuzzy logic controller (FLC) using precise type-1 fuzzy sets cannot fully handle such uncertainties. A type-2 FLC using type-2 fuzzy sets can handle such uncertainties to produce a better performance. In this paper, we present a novel reactive control architecture for autonomous mobile robots that is based on type-2 FLC to implement the basic navigation behaviors and the coordination between these behaviors to produce a type-2 hierarchical FLC. In our experiments, we implemented this type-2 architecture in different types of mobile robots navigating in indoor and outdoor unstructured and challenging environments. The type-2-based control system dealt with the uncertainties facing mobile robots in unstructured environments and resulted in a very good performance that outperformed the type-1-based control system while achieving a significant rule reduction compared to the type-1 system.

A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots

Although the notion is a relatively recent one, the notions and principles of Granular Computing (GrC) have appeared in a different guise in many related fields including granularity in Artificial Intelligence, interval computing, cluster analysis, quotient space theory and many others. Recent years have witnessed a renewed and expanding interest in the topic as it begins to play a key role in bioinformatics, e-commerce, machine learning, security, data mining and wireless mobile computing when it comes to the issues of effectiveness, robustness and uncertainty. The Handbook of Granular Computing offers a comprehensive reference source for the granular computing community, edited by and with contributions from leading experts in the field. Includes chapters covering the foundations of granular computing, interval analysis and fuzzy set theory; hybrid methods and models of granular computing; and applications and case studies. Divided into 5 sections: Preliminaries, Fundamentals, Methodology and Algorithms, Development of Hybrid Models and Applications and Case Studies. Presents the flow of ideas in a systematic, well-organized manner, starting with the concepts and motivation and proceeding to detailed design that materializes in specific algorithms, applications and case studies. Provides the reader with a self-contained reference that includes all pre-requisite knowledge, augmented with step-by-step explanations of more advanced concepts. The Handbook of Granular Computing represents a significant and valuable contribution to the literature and will appeal to a broad audience including researchers, students and practitioners in the fields of Computational Intelligence, pattern recognition, fuzzy sets and neural networks, system modelling, operations research and bioinformatics.

/pdf/handbook-of-granular-computing-4lcg97a60f.pdf

Kung Chris Wu

Papers

Fuzzy interval control of mobile robots