Conditions for Choquet integral representation of the comonotonically additive and monotone functional |
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| Authors: | Yasuo Narukawa Toshiaki Murofushi |
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| Affiliation: | a Toho Gakuen, 3-1-10 Naka, Kunitachi, Tokyo 186-0004, Japan
b Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259 Nagatuta, Midori-ku, Yokohama 226-8502, Japan |
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| Abstract: | If the universal set X is not compact but locally compact, a comonotonically additive and monotone functional (for short c.m.) on the class of continuous functions with compact support is not represented by one Choquet integral, but represented by the difference of two Choquet integrals. The conditions for which a c.m. functional can be represented by one Choquet integral are discussed. |
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| Keywords: | Nonadditive measure Fuzzy measure Cooperative game Choquet integral Comonotonic additivity |
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