This book briefly reviews the basic concepts of type-2 fuzzy systems and then describes the proposed definitions for interval type-3 fuzzy sets and relations, also interval type-3 inference and systems. The use of type-2 fuzzy systems has become widespread in the leading economy sectors, especially in industrial and application areas, such as services, health, defense, and so on. However, recently the use of interval type-3 fuzzy systems has been receiving increasing attention and some successful applications have been developed in the last year. These issues were taken into consideration for this book, as we did realize that there was a need to offer the main theoretical concepts of type-3 fuzzy logic, as well as methods to design, develop and implement the type-3 fuzzy systems. A review of basic concepts and their use in the design and implementation of interval type-3 fuzzy systems, which are relatively new models of uncertainty and imprecision, are presented. The main focus of this work is based on the basic reasons of the need for interval type-3 fuzzy systems in different areas of application. In addition, we describe methods for designing interval type-3 fuzzy systems and illustrate this with some examples and simulations.

In this book four new methods are proposed. In the first method the generalized type-2 fuzzy logic is combined with the morphological gra-dient technique. The second method combines the general type-2 fuzzy systems (GT2 FSs) and the Sobel operator; in the third approach the me-thodology based on Sobel operator and GT2 FSs is improved to be applied on color images. In the fourth approach, we proposed a novel edge detec-tion method where, a digital image is converted a generalized type-2 fuzzy image. In this book it is also included a comparative study of type-1, inter-val type-2 and generalized type-2 fuzzy systems as tools to enhance edge detection in digital images when used in conjunction with the morphologi-cal gradient and the Sobel operator. The proposed generalized type-2 fuzzy edge detection methods were tested with benchmark images and synthetic images, in a grayscale and color format. Another contribution in this book is that the generalized type-2 fuzzy edge detector method is applied in the preprocessing phase of a face rec-ognition system; where the recognition system is based on a monolithic neural network. The aim of this part of the book is to show the advantage of using a generalized type-2 fuzzy edge detector in pattern recognition applications. The main goal of using generalized type-2 fuzzy logic in edge detec-tion applications is to provide them with the ability to handle uncertainty in processing real world images; otherwise, to demonstrate that a GT2 FS has a better performance than the edge detection methods based on type-1 and type-2 fuzzy logic systems.

In this book, a series of granular algorithms are proposed. A nature inspired granular algorithm based on Newtonian gravitational forces is proposed. A series of methods for the formation of higher-type information granules represented by Interval Type-2 Fuzzy Sets are also shown, via multiple approaches, such as Coefficient of Variation, principle of justifiable granularity, uncertainty-based information concept, and numerical evidence based. And a fuzzy granular application comparison is given as to demonstrate the differences in how uncertainty affects the performance of fuzzy information granules.