Some Characterizations of k-Monotonicity Through the Bipolar Möbius Transform in Bi-Capacities
2005 ◽
Vol 9
(5)
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pp. 484-495
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Keyword(s):
This paper first proposes the bipolar Möbius transform as an extension of dividends of cooperative games to that of bi-cooperative games (bi-capacities) defined on 3N, which is different from the Möbius transform defined by Grabisch and Labreuche. The k-monotonicity of bi-capacities is characterized through each of the following notions: the bipolar and ordinary Möbius transforms, discrete derivatives, and partial derivatives of the piecewise multilinear extension of the ternary pseudo-Boolean function corresponding to the bi-capacities.
2005 ◽
Vol 49
(3)
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pp. 305-321
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Keyword(s):
2007 ◽
Vol 221
(12)
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pp. 1701-1715
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2007 ◽
Vol 359
(6)
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pp. 2675-2686
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1988 ◽
Vol 31
(2)
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pp. 159-167
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Keyword(s):