title: |
Fuzzy Measures on Finite Scales as Families of Possibility Measures |
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publication: |
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part of series: |
Advances in Intelligent Systems Research | |
| pages: | 822 - 829 | |
DOI: |
To be assigned soon (how to use a DOI) | |
author(s): |
Didier Dubois |
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publication date: |
July 2011 |
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keywords: |
Fuzzy measures, possibility theory, qualitative Moebius transform. |
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abstract: |
We show that any capacity or fuzzy measure ranging
on a qualitative scale can be viewed both as
the lower bound of a set of possibility measures,
and the upper bound of a set of necessity measures.
An algorithm is provided to compute the minimal
set of possibility measures dominating a given capacity.
This algorithm relies on the representation
of the capacity by means of its qualitative Moebius
transform, and the use of selection functions
of the corresponding focal sets. We also introduce
the counterpart of a contour function, that turns
out to be the union of all most specific possibility
distributions dominating the capacity. Finally we
show the connection between Sugeno integrals and
lower possibility measures. |
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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |