Proposed in 1965 by Lotfi Zadeh, the term “fuzzy logic” has emerged from a humble theory of fuzzy sets into an ever-expanding set of practical applications, ranging from approximate reasoning and image processing to decision support and control and expert systems. Interestingly, similar operations are used in fuzzy systems, whether for constructing a model or for simply trying to describe control behavior in a system.
One such operation is called the implication function. A fuzzy implication function is considered by most to be a primary operation in fuzzy logic. The inference processes in many fuzzy rule-based systems rely on these fuzzy operators to address uncertainty and approximate reasoning. For example, an expert might want to describe the behavior of a control in a particular system, and might attempt to express a set of rules that can be used to describe the behavior of this particular system. In classical logic, an expert can express such a rule as “If X, then Y”; this expression can also take the form of an implication: X implies Y. The same holds true with a rule in fuzzy logic, where the fuzzy implication can be expressed by starting with the rule “If X then Y,” and denoting it as an implication that X implies Y. In fuzzy logic, there are different classes of implication functions, depending on the application.
The editors of this book have assembled a collection of eight papers from a select group of researchers. The papers were selected because they provide relevant and useful information on the latest advances in the research area of fuzzy implication functions. The collection describes interesting and insightful aspects of fuzzy implication functions, including construction methods, new classes, common properties, dependencies, interval-valued fuzzy set theories, the distributivity equation, the binary operation *, an induced sup-* composition, and remaining open problems pertaining to either completely solved or partially resolved fuzzy implication functions.
Even though the contributions of these eight papers are impressive, I do not recommend this book for the practitioner who is casually investigating fuzzy logic. The information in the papers requires experience with fuzzy logic, targeted at either the serious researcher or the expert practitioner well versed in fuzzy logic. For those readers, I highly recommend this book to augment their current study of fuzziness and soft computing. The insights and perspectives will indeed prove valuable and well worth the time spent to understand the application of the new techniques and approaches to fuzzy implication.
Readers should consider leveraging a fuzzy logic toolbox such as the one found in the MATLAB software from MathWorks. The MATLAB fuzzy logic toolbox enables users to model complex system behaviors using simple logic rules, and then implement these rules in the MATLAB fuzzy inference system. This would help the reader validate and verify the advances in fuzzy implications function suggested by the authors.
For readers casually investigating fuzzy logic (possibly for the first time), I also recommend MATLAB or a similar software application package that facilitates the design and simulation of fuzzy logic systems. The study of fuzziness and soft computing will continue to expand in terms of usefulness and application, but this depends on more practitioners making the effort to learn more about it.
