Classification by fuzzy integral: performance and tests

Abstract This paper presents an attempt to characterize the performance of methods of classification based on fuzzy integral. After an introductory explanation about the approach, a lower bound of the minimal number of training samples is found, and it is shown that a minimum squared error criterion leads to the best approximate for the optimal Bayes classifier. Some tests on simulated and real data are provided.

[1]  Michel Grabisch,et al.  Interactive determination of a utility function represented as a fuzzy integral , 1993, Inf. Sci..

[2]  Sholom M. Weiss,et al.  An Empirical Comparison of Pattern Recognition, Neural Nets, and Machine Learning Classification Methods , 1989, IJCAI.

[3]  James C. Bezdek,et al.  Fuzzy models—What are they, and why? [Editorial] , 1993, IEEE Transactions on Fuzzy Systems.

[4]  Hung T. Nguyen,et al.  Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference , 1994 .

[5]  James M. Keller,et al.  A fuzzy K-nearest neighbor algorithm , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  Michio Sugeno,et al.  Fuzzy t -conorm integral with respect to fuzzy measures: generalization of Sugeno integral and choquet integral , 1991 .

[7]  Bruce W. Suter,et al.  The multilayer perceptron as an approximation to a Bayes optimal discriminant function , 1990, IEEE Trans. Neural Networks.

[8]  James C. Bezdek,et al.  A Review of Probabilistic, Fuzzy, and Neural Models for Pattern Recognition , 1996, J. Intell. Fuzzy Syst..

[9]  M. Sugeno,et al.  An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy , 1989 .

[10]  菅野 道夫,et al.  Theory of fuzzy integrals and its applications , 1975 .

[11]  M. Sugeno,et al.  Multi-attribute classification using fuzzy integral , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.

[12]  M. Grabisch.  On the use of fuzzy integral as a fuzzy connective , 1993, [Proceedings 1993] Second IEEE International Conference on Fuzzy Systems.

[13]  D. Dubois,et al.  Weighted fuzzy pattern matching , 1988 .

[14]  D. Dubois,et al.  Unfair coins and necessity measures: Towards a possibilistic interpretation of histograms , 1983 .

[15]  M. Sugeno,et al.  Fuzzy measure of fuzzy events defined by fuzzy integrals , 1992 .

[16]  M. Sugeno,et al.  A theory of fuzzy measures: Representations, the Choquet integral, and null sets , 1991 .

[17]  James M. Keller,et al.  Possibility expectation and its decision making algorithm , 1992, [1992 Proceedings] IEEE International Conference on Fuzzy Systems.

[18]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[19]  James M. Keller,et al.  Information fusion in computer vision using the fuzzy integral , 1990, IEEE Trans. Syst. Man Cybern..