Caracterizing k-Additive Fuzzy Measures
Recently, Grabisch has proposed the concept of k-additive measures to cope with the complexity problem involved by the use of fuzzy measures . The concept has proven to be useful in multicriteria decision making, since it brings a model which is both flexible and simple to use.
KeywordsBinary Relation Aggregation Operator Fuzzy Measure Weak Order Ordered Weighted Average
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- A. Chateauneuf and J. Y. Jaffray. Characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion. Mathematical Social Sciences, 1989.Google Scholar
- T. Gajdos. Measuring inequalities without linearity in envy: Choquet integral for symmetric capacities. (Working paper).Google Scholar
- M. Grabisch. Pattern classification and feature extraction by fuzzy integral. In 3d European Congr. on Intelligent Techniques and Soft Computing (EUFIT), pages 1465–1469, Aachen (Germany), August 1995.Google Scholar
- M. Grabisch. k-additive measures: Recent issues and challenges. In 5th Int. Conf. on Soft Computing and Information/Intelligent Systems, pages 394–397, Izuka (Japan), October 1998.Google Scholar
- M. Grabisch. On lower and upper approximation of fuzzy measures by k-order additive measures. In 7th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU’98), pages 1577–1584, Paris (France), July 1998.Google Scholar
- K. Kao-Van and B. De Baets. A decomposition of k-additive Choquet and k-maxitive Sugeno integrals. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems,to appear.Google Scholar
- M. Sugeno. Theory of fuzzy integrals and its applications. PhD thesis, Tokyo Institute of Technology, 1974.Google Scholar