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JACIII Vol.9 No.5 pp. 484-495
doi: 10.20965/jaciii.2005.p0484
(2005)

Paper:

Some Characterizations of k-Monotonicity Through the Bipolar Möbius Transform in Bi-Capacities

Katsushige Fujimoto*, and Toshiaki Murofushi**

*College of Symbiotic Systems Science, Fukushima University, 1 Kanayagawa, Fukushima 960-1296, Japan

**Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47 Nagatsuta, Midori-ku, Yokohama 226-8502, Japan

Received:
November 5, 2004
Accepted:
February 16, 2005
Published:
September 20, 2005
Keywords:
bi-capacity, the bipolar Möbius transform, k-monotonicity, the Choquet integral
Abstract

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.

Cite this article as:
Katsushige Fujimoto and Toshiaki Murofushi, “Some Characterizations of k-Monotonicity Through the Bipolar Möbius Transform in Bi-Capacities,” J. Adv. Comput. Intell. Intell. Inform., Vol.9, No.5, pp. 484-495, 2005.
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Last updated on Aug. 03, 2021