Finding the set of k-additive dominating measures viewed as a flow problem



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Miranda Menéndez, Pedro and Grabisch, Michel (2016) Finding the set of k-additive dominating measures viewed as a flow problem. In Information Processing and Management of Uncertainty in Knowledge-Based Systems. Communications in Computer and Information Science, 1 (610). Springer Verlag, pp. 11-22. ISBN 978-331940595-7

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n this paper we deal with the problem of obtaining the set of k-additive measures dominating a fuzzy measure. This problem extends the problem of deriving the set of probabilities dominating a fuzzy measure, an important problem appearing in Decision Making and Game Theory. The solution proposed in the paper follows the line developed by Chateauneuf and Jaffray for dominating probabilities and continued by Miranda et al. for dominating k-additive belief functions. Here, we address the general case transforming the problem into a similar one such that the involved set functions have non-negative Möbius transform; this simplifies the problem and allows a result similar to the one developed for belief functions. Although the set obtained is very large, we show that the conditions cannot be sharpened. On the other hand, we also show that it is possible to define a more restrictive subset, providing a more natural extension of the result for probabilities, such that it is possible to derive any k-additive dominating measure from it.

Item Type:Book Section
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16th International Conference, IPMU 2016 Eindhoven, The Netherlands, June 20–24, 2016 Proceedings, Part I

Uncontrolled Keywords:Dominance; Fuzzy measures; K-additivity
Subjects:Sciences > Mathematics > Logic, Symbolic and mathematical
ID Code:39276
Deposited On:07 Oct 2016 12:08
Last Modified:25 Nov 2016 08:44

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