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Qualitative Capacities as Imprecise Possibilities

Dubois, Didier and Prade, Henri and Rico, Agnès Qualitative Capacities as Imprecise Possibilities. (2013) In: 12 th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2013), 8 July 2013 - 10 July 2013 (Utrecht, Netherlands).

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Official URL: http://dx.doi.org/10.1007/978-3-642-39091-3_15

Abstract

This paper studies the structure of qualitative capacities, that is, monotonic set-functions, when they range on a finite totally ordered scale equipped with an order-reversing map. These set-functions correspond to general representations of uncertainty, as well as importance levels of groups of criteria in multicriteria decision-making. More specifically, we investigate the question whether these qualitative set-functions can be viewed as classes of simpler set-functions, typically possibility measures, paralleling the situation of quantitative capacities with respect to imprecise probability theory. We show that any capacity is characterized by a non-empty class of possibility measures having the structure of an upper semi-lattice. The lower bounds of this class are enough to reconstruct the capacity, and their number is characteristic of its complexity. We introduce a sequence of axioms generalizing the maxitivity property of possibility measures, and related to the number of possibility measures needed for this reconstruction. In the Boolean case, capacities are closely related to non-regular multi-source modal logics and their neighborhood semantics can be described in terms of qualitative Moebius transforms.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to Springer editor. This papers appears in Volume 7958 Lecture Notes in Computer Science ISSN : 0302-9743. ISBN: 978-3-642-39090-6. The original PDF is available at : http://link.springer.com/chapter/10.1007%2F978-3-642-39091-3_15
HAL Id:hal-01212934
Audience (conference):National 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)
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Deposited By: IRIT IRIT
Deposited On:16 Sep 2015 08:43

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