Fuzzy Measures on Finite Scales as Families of Possibility Measures

DOI

10.2991/eusflat.2011.148How to use a DOI?

Keywords

Fuzzy measures, possibility theory, qualitative Moebius transform.

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.

Copyright

© 2011, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Didier Dubois
PY  - 2011/08
DA  - 2011/08
TI  - Fuzzy Measures on Finite Scales as Families of Possibility Measures
BT  - Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)
PB  - Atlantis Press
SP  - 822
EP  - 829
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2011.148
DO  - 10.2991/eusflat.2011.148
ID  - Dubois2011/08
ER  -