Fuzzy sets were first proposed by Lotfi Zadeh in his seminal paper [366] in 1965, and ever since have been a center of many discussions, fervently admired and condemned. Both proponents and opponents consider the argu ments pointless because none of them would step back from their territory. And stiH, discussions burst out from a single sparkle like a conference pa per or a message on some fuzzy-mail newsgroup. Here is an excerpt from an e-mail messagepostedin1993tofuzzy-mail@vexpert. dbai. twvien. ac. at. by somebody who signed "Dave". , . . . Why then the "logic" in "fuzzy logic"? I don't think anyone has successfully used fuzzy sets for logical inference, nor do I think anyone wiH. In my admittedly neophyte opinion, "fuzzy logic" is a misnomer, an oxymoron. (1 would be delighted to be proven wrong on that. ) . . . I carne to the fuzzy literature with an open mind (and open wal let), high hopes and keen interest. I am very much disiHusioned with "fuzzy" per se, but I did happen across some extremely interesting things along the way. " Dave, thanks for the nice quote! Enthusiastic on the surface, are not many of us suspicious deep down? In some books and journals the word fuzzy is religiously avoided: fuzzy set theory is viewed as a second-hand cheap trick whose aim is nothing else but to devalue good classical theories and open up the way to lazy ignorants and newcomers.

Inhalt

1. Introduction.- 1.1 What are fuzzy classifiers?.- 1.2 The data sets used in this book.- 1.3 Notations and acronyms.- 1.4 Organization of the book.- 1.5 Acknowledgements.- 2. Statistical pattern recognition.- 2.1 Class, feature, feature space.- 2.2 Classifier, discriminant functions, classification regions.- 2.3 Clustering.- 2.4 Prior probabilities, class-conditional probability density functions, posterior probabilities.- 2.5 Minimum error and minimum risk classification. Loss matrix.- 2.6 Performance estimation.- 2.7 Experimental comparison of classifiers.- 2.8 A taxonomy of classifier design methods.- 3. Statistical classifiers.- 3.1 Parametric classifiers.- 3.2 Nonparametric classifiers.- 3.3 Finding k-nn prototypes.- 3.4 Neural networks.- 4. Fuzzy sets.- 4.1 Fuzzy logic, an oxymoron?.- 4.2 Basic definitions.- 4.3 Operations on fuzzy sets.- 4.4 Determining membership functions.- 5. Fuzzy if-then classifiers.- 5.1 Fuzzy if-then systems.- 5.2 Function approximation with fuzzy if-then systems.- 5.3 Fuzzy if-then classifiers.- 5.4 Universal approximation and equivalences of fuzzy if-then classifiers.- 6. Training of fuzzy if-then classifiers.- 6.1 Expert opinion or data analysis?.- 6.2 Tuning the consequents.- 6.3 Toning the antecedents.- 6.4 Tuning antecedents and consequents using clustering.- 6.5 Genetic algorithms for tuning fuzzy if-then classifiers.- 6.6 Fuzzy classifiers and neural networks: hybridization or identity?.- 6.7 Forget interpretability and choose a model.- 7. Non if-then fuzzy models.- 7.1 Early ideas.- 7.2 Fuzzy k-nearest neighbors (k-nn) designs.- 7.3 Generalized nearest prototype classifier (GNPC).- 8. Combinations of multiple classifiers using fuzzy sets.- 8.1 Combining classifiers: the variety of paradigms.- 8.2 Classifier selection.- 8.3 Classifier fusion.- 8.4 Experimental results.- 9. Conclusions: What to choose?.- A. Appendix: Numerical results.- A.1 Cone-torus data.- A.2 Normal mixtures data..- A.3 Phoneme data.- A.4 Satimage data.- References.