Fuzzy Sets And Their Extensions: Representation, Aggregation And Models

Fuzzy Sets and Their Extensions: Representation, Aggregation and Models Intelligent Systems from Decision Making to Data Mining, Web Intelligence and Computer Vision Fuzzy sets are now more than 40 years old, and have come of age. However, the development of fuzzy set theory at the theoretical level, and its successful appli- tions to science and technology have often run in isolation. Only a little part of the theoretical apparatus was effectively used in past applications. The most prominent ones, namely fuzzy rule-based modeling and control engineering, were directly - spired from a seminal paper by Lot? Zadeh in 1973, suggesting how to use expert knowledge for synthetizing control laws, and from the ?rst experiments published by Abe Mamdani. Later in the eighties, when spectacular applications were bl- soming in Japan, fuzzy rule-based systems were systematized and simpli?ed by Michio Sugeno and colleagues, and became a basic approach to non-linear system modeling and control, soon hybridized with neural networks in the nineties. Thus fuzzy systems signi?cantly contributed to the raise of computational intelligence, and a lot of learning techniques for the construction of (supposedly interpretable) fuzzy models from data were developed under the ?ag of soft computing. Even if this area was quite successful, it is patent that the role, in the success of fuzzy logic, of new fuzzy set-related concepts developed quite at the same time in themathematicalnicheofthefuzzyset communitywaslimited.

This carefully edited book presents an up-to-date state of current research in the use of fuzzy sets and their extensions, paying attention to foundation issues and to their application to four important areas where fuzzy sets are seen to be an important tool for modelling and solving problems.

The book contains 34 chapters divided into two parts. The first part is divided into two sections. Section 1 contains four review papers introducing some non standard representations that extend fuzzy sets (type-2 fuzzy sets, Atanassov’s IFS, fuzzy rough sets and computing with words under the fuzzy sets perspective). Section 2 reviews different aggregation issues from a theoretical and practical point of view; this second part is divided into four sections. Section 3 is devoted to decision making, with seven papers that show how fuzzy sets and their extensions are an important tool for modelling choice problems. Section 4 includes eight papers that cover different aspects on the use of fuzzy sets and their extensions in data mining, giving an illustrative review of the state of the art on the topic. Section 5 is devoted to the emergent topic of web intelligence and contains four papers that show the use of fuzzy sets theory in some problems that can be tackled in this topic. Section 6 is devoted to the use of fuzzy sets and their extensions in the field of computer vision, suggesting how these can be an useful tool in this area.

This volume will be extremely useful to any non-expert reader who is keen to get a good overview on the latest developments in this research field. It will also support those specialists who wish to discover the latest results and trends in the abovementioned areas.