On distorted probabilities and m-separable fuzzy measures

Authors:
Yasuo Narukawa;Vicenç Torra
Affiliations:
Toho Gakuen, 3-1-10 Naka, Kunitachi, Tokyo 186-0004, Japan and Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259 Nagatuta, Midori-ku, Yokohama 226-8 ...;IIIA-CSIC, Institut d'Investigació en Intel·ligència Artificial, Campus de Bellaterra, 08193 Bellaterra, Catalonia, Spain
Venue:
International Journal of Approximate Reasoning
Year:
2011

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Abstract

Fuzzy measures are used in conjunction with fuzzy integrals for aggregation. Their role in the aggregation is to permit the user to express the importance of the information sources (either criteria or experts). Due to the fact that fuzzy measures are set functions, the definition of such measures requires the definition of 2^n parameters, where n is the number of information sources. To make the definition easier, several families of fuzzy measures have been defined in the literature. In this paper m-separable fuzzy measures are introduced. We present some results on this type of measures and we relate them to some of the previous existing ones. We study generating functions for m-separable fuzzy measures and some properties related to these generating functions.