Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions

This is an absolutely brilliant work focusing on both fundamental aspects of Fuzzy logic systems. Firstly an intuitive and physical understanding essential for diverse applications of fuzzy sets is developed while at the same time mathematically sound treatment of fundamentals is carried out. There is no other book which integrates clarity and the underlying mathematics to such high level. The treatment of type-2 fuzzy sets is unrivalled by all standards. Mendel is perhaps first time ever in a published book, gives a truly geometric and easy to understand description of type-2 fuzzy sets, making lives of PhD students like myself easier. However, book can be read and used for applications by any one with undergraduate degree in science, engineering or even finance etc and requires moderate mathematical maturity. All relevant mathematical aspects of fuzzy logic systems are covered in detailed in the book itself. The book begins with a comprehensive and deep treatment of type-1 logic system or in other words, ordinary fuzzy set theory. Then type-2 fuzzy is introduced early on with extremely easy to understand format. While theory of ordinary fuzzy logic is developed to the full extend in part 1, part two of the book, focuses on parallel development of type-2 fuzzy sets. There are no other works, except perhaps Mendel's own published papers, which have such easy to understand and easy to internalized treatment of relatively new and difficult area of type-2 fuzzy logic system. Throughout the easy to understand examples with detail applications of type-2 fuzzy logic system to engineering ranging from digital communications to knowledge mining are given. While mathematical aspects are covered in detail and without sacrificing required rigor, overall style is quite informal and very easy to read. The book successfully advocates the use of type-2 fuzzy logic systems as a generalization of type-1 fuzzy logic system while demonstrating increased applicable power of type-2 fuzzy systems to tackle difficult engineering and scientific problems including but not limited to time varying, systems, systems involving non-stationary noise processes and nonlinear systems. Relevant examples of above areas are considered in detail along with reasons to use type-2 fuzzy systems as a solution mechanism. Examples of application areas covered include equalizations of nonlinear and time-varying digital communications channels, rule based classifications of video traffic, knowledge mining using IF-THEN questionnaires and so on. This aspect makes this book quite unique and allows easier transition from described theory to the required applications for the reader. In the final analysis, this is the perhaps the only book available, which while stressing mathematical details relating to type-1 and type-2 fuzzy logic systems, provides physical and intuitive understanding drawn from detailed discussions and heavily supplemented with figures and pictures with remarkable