Advances In Type 2 Fuzzy Sets And Systems

This book explores recent developments in the theoretical foundations and novel applications of general and interval type-2 fuzzy sets and systems, including: algebraic properties of type-2 fuzzy sets, geometric-based definition of type-2 fuzzy set operators, generalizations of the continuous KM algorithm, adaptiveness and novelty of interval type-2 fuzzy logic controllers, relations between conceptual spaces and type-2 fuzzy sets, type-2 fuzzy logic systems versus perceptual computers; modeling human perception of real world concepts with type-2 fuzzy sets, different methods for generating membership functions of interval and general type-2 fuzzy sets, and applications of interval type-2 fuzzy sets to control, machine tooling, image processing and diet. The applications demonstrate the appropriateness of using type-2 fuzzy sets and systems in real world problems that are characterized by different degrees of uncertainty.

This book reviews current state of the art methods for building intelligent systems using type-2 fuzzy logic and bio-inspired optimization techniques. Combining type-2 fuzzy logic with optimization algorithms, powerful hybrid intelligent systems have been built using the advantages that each technique offers. This book is intended to be a reference for scientists and engineers interested in applying type-2 fuzzy logic for solving problems in pattern recognition, intelligent control, intelligent manufacturing, robotics and automation. This book can also be used as a reference for graduate courses like the following: soft computing, intelligent pattern recognition, computer vision, applied artificial intelligence, and similar ones. We consider that this book can also be used to get novel ideas for new lines of re-search, or to continue the lines of research proposed by the authors.

This book generalizes fuzzy logic systems for different types of uncertainty, including - semantic ambiguity resulting from limited perception or lack of knowledge about exact membership functions - lack of attributes or granularity arising from discretization of real data - imprecise description of membership functions - vagueness perceived as fuzzification of conditional attributes. Consequently, the membership uncertainty can be modeled by combining methods of conventional and type-2 fuzzy logic, rough set theory and possibility theory. In particular, this book provides a number of formulae for implementing the operation extended on fuzzy-valued fuzzy sets and presents some basic structures of generalized uncertain fuzzy logic systems, as well as introduces several of methods to generate fuzzy membership uncertainty. It is desirable as a reference book for under-graduates in higher education, master and doctor graduates in the courses of computer science, computational intelligence, or fuzzy control and classification, and is especially dedicated to researchers and practitioners in industry.

Fuzzy logic systems have been a hot topic in the scientific and academic community for more than half a century. The idea of making machines behave and make decisions like humans do is astounding. The development and implementation of fuzzy logic systems can be seen in various real physical applications in daily human life. The methods employed using fuzzy logic have resulted in innovative technologies. This book provides insights into understanding the principles and concepts behind the advances of fuzzy logic systems. It presents ideas concerning fuzzy logic systems and their technological applications. The book is arranged into two sections on theories and foundations of fuzzy logic systems and implementations of fuzzy logic systems in service to the community.

This book focuses on the fields of fuzzy logic and metaheuristic algorithms, particularly the harmony search algorithm and fuzzy control. There are currently several types of metaheuristics used to solve a range of real-world of problems, and these metaheuristics contain parameters that are usually fixed throughout the iterations. However, a number of techniques are also available that dynamically adjust the parameters of an algorithm, such as probabilistic fuzzy logic. This book proposes a method of addressing the problem of parameter adaptation in the original harmony search algorithm using type-1, interval type-2 and generalized type-2 fuzzy logic. The authors applied this methodology to the resolution of problems of classical benchmark mathematical functions, CEC 2015, CEC2017 functions and to the optimization of various fuzzy logic control cases, and tested the method using six benchmark control problems – four of the Mamdani type: the problem of filling a water tank, the problem of controlling the temperature of a shower, the problem of controlling the trajectory of an autonomous mobile robot and the problem of controlling the speed of an engine; and two of the Sugeno type: the problem of controlling the balance of a bar and ball, and the problem of controlling control the balance of an inverted pendulum. When the interval type-2 fuzzy logic system is used to model the behavior of the systems, the results show better stabilization because the uncertainty analysis is better. As such, the authors conclude that the proposed method, based on fuzzy systems, fuzzy controllers and the harmony search optimization algorithm, improves the behavior of complex control plants.

The second edition of this textbook provides a fully updated approach to fuzzy sets and systems that can model uncertainty — i.e., “type-2” fuzzy sets and systems. The author demonstrates how to overcome the limitations of classical fuzzy sets and systems, enabling a wide range of applications from time-series forecasting to knowledge mining to control. In this new edition, a bottom-up approach is presented that begins by introducing classical (type-1) fuzzy sets and systems, and then explains how they can be modified to handle uncertainty. The author covers fuzzy rule-based systems – from type-1 to interval type-2 to general type-2 – in one volume. For hands-on experience, the book provides information on accessing MatLab and Java software to complement the content. The book features a full suite of classroom material.

This book explores recent perspectives on type-2 fuzzy sets. Written as a tribute to Professor Jerry Mendel for his pioneering works on type-2 fuzzy sets and systems, it covers a wide range of topics, including applications to the Go game, machine learning and pattern recognition, as well as type-2 fuzzy control and intelligent systems. The book is intended as a reference guide for the type-2 fuzzy logic community, yet it aims also at other communities dealing with similar methods and applications.

The two-volume set LNAI 9692 and LNAI 9693 constitutes the refereed proceedings of the 15th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2016, held in Zakopane, Poland in June 2016. The 134 revised full papers presented were carefully reviewed and selected from 343 submissions. The papers included in the first volume are organized in the following topical sections: neural networks and their applications; fuzzy systems and their applications; evolutionary algorithms and their applications; agent systems, robotics and control; and pattern classification. The second volume is divided in the following parts: bioinformatics, biometrics and medical applications; data mining; artificial intelligence in modeling and simulation; visual information coding meets machine learning; and various problems of artificial intelligence.