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A genetic algorithm for determining nonadditive set functions in information fusion. (English) Zbl 0935.28014
Summary: As a class aggregation tool, the weighted average method is widely used in information fusion. It is the Lebesgue integral with respect to the weights, essentially. Due to some inherent interaction among diverse information sources, the weighted average method does not work well in many real problems. To describe the interaction, an intuitive and effective way is to replace the additive weights with a nonadditive set function defined on the power set of the set of all information sources. Instead of the weighted average method, we use the Choquet integral or some other nonlinear integrals, especially, the new nonlinear integral introduced by the authors recently. The crux of making such an improvement is how to determine the nonadditive set function from given input-output data when the nonlinear integral is viewed as a multi-input single-output system. In this paper, we employ a specially designed genetic algorithm to realize the optimization in determining the nonadditive set function.

MSC:
28E10 Fuzzy measure theory
68U35 Computing methodologies for information systems (hypertext navigation, interfaces, decision support, etc.)
68T05 Learning and adaptive systems in artificial intelligence
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[1] Denneberg, D., Non-additive measure and integral, (1994), Kluwer Boston · Zbl 0826.28002
[2] Grabisch, M., A new algorithm for identifying fuzzy measures and its application to pattern recognition, (), 145-150
[3] Harmanec, D.; Klir, G.J.; Wang, Z., Modal logic interpretation of Dempster-Shafer theory: an infinite case, Internat. J. approx. reason., 14, 2/3, 81-93, (1996) · Zbl 0935.03035
[4] Keller, J.M.; Osborn, J., Traininf the fuzzy integral, Internat. J. approx. reason., 15, 1-24, (1996)
[5] Klir, G.J.; Wang, Z.; Wang, W., Constructing fuzzy measures by transformations, Internat. J. fuzzy math., 4, 1, 207-215, (1996) · Zbl 0867.28015
[6] Murofushi, T.; Sugeno, M., An interpretation of fuzzy measure and the Choquet integral as an integral with respect to a fuzzy measure, Fuzzy sets and systems, 29, 201-227, (1989) · Zbl 0662.28015
[7] Murofushi, T.; Sugeno, M.; Machida, M., Non-monotonic fuzzy measures and the Choquet integral, Fuzzy sets and systems, 64, 73-86, (1994) · Zbl 0844.28015
[8] Pap, E., Null-additive set functions, (1995), Kluwer Boston · Zbl 0856.28001
[9] Wang, J., Determining fuzzy measures by using statistics and neural networks, (), 519-521
[10] Wang, Z.; Klir, G.J., Fuzzy measure theory, (1992), Plenum New York · Zbl 0812.28010
[11] Wang, Z.; Klir, G.J.; Harmanec, D., The preservation of structural characteristics of monotone set functions defined by fuzzy integral, Internat. J. fuzzy math., 3, 1, 229-240, (1995) · Zbl 0867.28016
[12] Wang, Z.; Klir, G.J.; Resconi, G., Expressing fuzzy measures by a model of modal logic: a discrete case, (), 3-13 · Zbl 0871.03019
[13] Wang, W.; Klir, G.J.; Wang, Z., Constructing fuzzy measures by rational transformations, Internat. J. fuzzy math., 4, 3, 665-675, (1996) · Zbl 0870.28012
[14] Wang, Z.; Klir, G.J.; Wang, W., Monotone set functions defined by Choquet integral, Fuzzy sets and systems, 81, 241-250, (1996) · Zbl 0878.28011
[15] Wang, Z.; Klir, G.J.; Wang, W., Fuzzy measures defined by fuzzy integral and their absolute continuity, J. math. anal. appl., 203, 150-165, (1996) · Zbl 0859.28015
[16] Wang, Z.; Klir, G.J., PFB-integrals and PFA-integrals with respect to monotone set functions, Internat. J. uncertainty fuzziness knowledge-based systems, 5, 2, 163-175, (1997) · Zbl 1232.28024
[17] Z. Wang, G.J. Klir, J. Wang, Neural networks used for determining belief measures and plausibility measures, Intell. Automat. Soft Comput., to appear.
[18] Wang, Z.; Leung, K.S.; Xu, K., A new nonlinear regression model used for multisource-multisensor data fusion: an application of nonlinear integrals and genetic algorithms, (), 299-306
[19] Z. Wang, K.S. Leung, J. Fang, A new type of nonlinear integrals and the algorithm for calculating, Fuzzy Sets and Systems, to appear.
[20] Wang, Z.; Wang, J., Using genetic algorithm for extension and Fitting of belief measures and plausibility measures, (), 348-350
[21] Wang, J.; Wang, Z., Detecting constructions of nonlinear integral systems from input-output data: an application of neural networks, (), 559-563
[22] Wang, Z.; Wang, J., Using genetic algorithms for γ-fuzzy measure Fitting and extension, (), 1871-1874 · Zbl 1225.68175
[23] Wang, J.; Wang, Z., Using neural networks to determine sugeno measures by statistics, Neural networks, 10, 1, 183-195, (1997)
[24] Wang, W.; Wang, Z.; Klir, G.J., Genetic algorithms for determining fuzzy measures from data, J. intell. fuzzy systems, 6, 2, 171-183, (1998)
[25] Xu, K.; Wang, Z.; Leung, K.S., Using a new type of nonlinear integral for multi-regression: an application of evolutionary algorithms in data mining, Ieee smc’98, (1998), submitted
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