Real-valued Choquet integrals with fuzzy-valued integrand

The Choquet integral of a real-valued function defined on a set of attributes with respect to a signed fuzzy measure is generalized for allowing a fuzzy-valued function to be its integrand while keeping its value to be a crisp real number. Thus, the Choquet integral can be used as a defuzzifying aggregation tool to deal with data set involving categorical attributes, linguistic variables, and/or fuzzy numbers. A numerical method with the relevant algorithm is developed to estimate the value of the Choquet integral for any given fuzzy-valued function.

[1]  E. Pap.  Null-Additive Set Functions , 1995 .

[2]  Esfandiar Eslami,et al.  Advances in soft computing: an introduction to fuzzy logic and fuzzy sets , 2002 .

[3]  Kwong-Sak Leung,et al.  Classification by nonlinear integral projections , 2003, IEEE Trans. Fuzzy Syst..

[4]  D. Denneberg.  Non-additive measure and integral , 1994 .

[5]  G. Choquet.  Theory of capacities , 1954 .

[6]  L. Zadeh.  Probability measures of Fuzzy events , 1968 .

[7]  L. Ludeman,et al.  Discrimination of cardiac arrhythmias using a fuzzy rule-based method , 1994, Computers in Cardiology 1994.

[8]  Kwong-Sak Leung,et al.  Learning nonlinear multiregression networks based on evolutionary computation , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[9]  Michel Grabisch,et al.  A new algorithm for identifying fuzzy measures and its application to pattern recognition , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[10]  Kwong-Sak Leung,et al.  Nonlinear nonnegative multiregressions based on Choquet integrals , 2000, Int. J. Approx. Reason..

[11]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[12]  Zhenyuan Wang,et al.  A new genetic algorithm for nonlinear multiregressions based on generalized Choquet integrals , 2003, The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03..

[13]  Kwong-Sak Leung,et al.  Fuzzy numbers and fuzzification of the Choquet integral , 2005, Fuzzy Sets Syst..

[14]  Lotfi A. Zadeh,et al.  Soft computing and fuzzy logic , 1994, IEEE Software.

[15]  Michel Grabisch,et al.  Fuzzy integral for classification and feature extraction , 2000 .

[16]  G. Klir,et al.  Fuzzy Measure Theory , 1993 .

[17]  Kwong-Sak Leung,et al.  A new type of nonlinear integrals and the computational algorithm , 2000, Fuzzy Sets Syst..

[18]  M. Sugeno,et al.  Non-monotonic fuzzy measures and the Choquet integral , 1994 .

[19]  Kwong-Sak Leung,et al.  Discover dependency pattern among attributes by using a new type of nonlinear multiregression , 2001, Int. J. Intell. Syst..

[20]  M. Sugeno,et al.  Some quantities represented by the Choquet integral , 1993 .

[21]  D. Dubois,et al.  FUZZY NUMBERS: AN OVERVIEW , 1993 .

[22]  Michel Grabisch,et al.  Application of the Choquet integral in multicriteria decision making , 2000 .

[23]  J. Buckley,et al.  An Introduction to Fuzzy Logic and Fuzzy Sets , 2002 .