Identification of Fuzzy Measures with Distorted Probability Measures
Aoi Honda*,**, and Yoshiaki Okazaki*
*Department of Systems Innovation and Informatics, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka 820-8502, Japan
**Department of Computer science and Mathematics, University of Paris I, Panthéon-Sorbonne 72, rue Regnault, 75013 Paris, France
We consider the identification of fuzzy measures using a class of distorted probabilities – a scale transformation of probabilities. A fuzzy measure, which is a nonadditive set function with a high degree of freedom, enables us to express complicated interactions among evaluative items. Because of the high degree of freedom, however, it is difficult to identify all of the values μ(A) for every event A from known data μ(B), B ∈ A, where A is generally a small subclass of events. In this paper, we classify fuzzy measures by introducing “type,” and propose an identifying fuzzy measures using a classified class of distorted probabilities.