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Separable Qualitative Capacities

Dubois, Didier and Faux, Francis and Prade, Henri and Rico, Agnès Separable Qualitative Capacities. (2018) In: International Conference on Scalable Uncertainty Management (SUM 2018), 3 October 2018 - 5 October 2018 (Milan, Italy).

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Official URL: https://doi.org/10.1007/978-3-030-00461-3_9

Abstract

The aim of this paper is to define the counterpart of separable belief functions for capacities valued on a finite totally ordered set. Evidence theory deals with the issue of merging unreliable elementary testimonies. Separable belief functions are the results of this merging process. However not all belief functions are separable. Here, we start with a possibility distribution on the power set of a frame of discernment that plays the role of a basic probability assignment. It turns out that any capacity can be induced by the qualitative counterpart of the definition of a belief function (replacing sum by max). Then, we consider a qualitative counterpart of Dempster rule of combination applied to qualitative capacities, via their qualitative Möbius transforms. We study the class of capacities, called separable capacities, that can be generated by applying this combination rule to simple support capacities, each focusing on a subset of the frame of discernment. We compare this decomposition with the one of general capacities as a maximum over a finite set of necessity measures. The relevance of this framework to the problem of information fusion from unreliable sources is explained.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to Springer editor. This papers appears in Volume 11142 of Lecture Notes in Computer Science ISSN : 0302-9743 ISBN: 978-3-030-00460-6 The original PDF is available at: https://link.springer.com/chapter/10.1007/978-3-030-00461-3_9
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Université Claude Bernard-Lyon I - UCBL (FRANCE)
Other partners > Université Lumière-Lyon 2 (FRANCE)
Laboratory name:
Funders:
Ministère de l'Enseignement Supérieur et de la recherche (FRANCE) - CIMI : Centre International de Mathématiques et d'Informatique (FRANCE) - ANR-11-LABX-0040-CIMI
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Deposited By: IRIT IRIT
Deposited On:23 May 2019 09:11

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