Modelling data by the Choquet integral

Abstract

Abstract. The chapter makes a survey of works dealing with the Choquet integral as a general non linear regression model. It is shown that its use is however limited to commensurate variables, as it is the case for example for multicriteria evaluation and multiattribute classification. A large part is devoted to the various methods of identifying parameters of the model, essentially quadratic programming and genetic algorithms. A new approach based on genetic algorithms is also described. Lastly, related works on classification and subjective evaluation are mentionned.

Fuzzy Measures and Integrals in MCDA

“…Other learning methods have been tried, principally using genetic algorithms (see in particular Wang [74], Kwon and Sugeno [45], and Grabisch [23]). …”

“…In such cases, only meta-heuristic methods can be used, as genetic algorithms, simulated annealing, etc. There exist some works in this direction, although most of the time used for the Choquet integral, which is questionable [74,23].…”

“…Following the pionnering works of Sugeno [70], many researchers in the eighties in Japan have applied in practical problems the Sugeno integral, for example to opinion poll [62], and later the Choquet integral (see a summary of main works in [36]). More recent applications can be found in [35,23], see also [27,42].…”

Efficient Learning of Classifiers Based on the 2-Additive Choquet Integral

“…In machine learning, it is less common so far, although the interest in using the Choquet integral as a mathematical tool for tackling problems like classification, regression and ranking is increasing [4,5,6,7,8,9].…”

On the VC-Dimension of the Choquet Integral

“…Nevertheless, the interest in using the Choquet integral as a mathematical tool in machine learning is increasing, and several papers on its use for problems like classification and regression have been published recently [4][5][6][7][8].…”