Marek and I have become intrigued by the problem of fitting the Sugeno integral, which has been relatively understudied. Some of the preliminary results were presented by Marek at EUSFLAT this year. (available online)
Title: Fitting Symmetric Fuzzy Measures for Discrete Sugeno Integration
Authors: M. Gagolewski and S. James
The Sugeno integral has numerous successful applications, including but not limited to the areas of decision making, preference modeling, and bibliometrics. Despite this, the current state of the de- velopment of usable algorithms for numerically fitting the underlying discrete fuzzy measure based on a sample of prototypical values – even in the simplest possible case, i.e., assuming the symmetry of the capac- ity – is yet to reach a satisfactory level. Thus, the aim of this paper is to present some results and observations concerning this class of data approximation problems.