%0 Conference Proceedings
%T Qualitative Capacities as Imprecise Possibilities.
%+ Institut de recherche en informatique de Toulouse (IRIT)
%+ Entrepôts, Représentation et Ingénierie des Connaissances (ERIC)
%A Dubois, Didier
%A Prade, Henri
%A Rico, Agnés
%< avec comité de lecture
%( Symbolic and Quantitative Approaches to Reasoning with Uncertainty
%B 12 th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2013)
%C Utrecht, Netherlands
%N 7958
%P pp. 169-180
%8 2013-07-08
%D 2013
%K Incertadriaqual
%Z Computer Science [cs]/Artificial Intelligence [cs.AI]
%Z Computer Science [cs]/Machine Learning [cs.LG]
%Z Computer Science [cs]/Logic in Computer Science [cs.LO]
%Z Computer Science [cs]/Computation and Language [cs.CL]Conference papers
%X 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.
%G English
%2 https://hal.archives-ouvertes.fr/hal-01212934/document
%2 https://hal.archives-ouvertes.fr/hal-01212934/file/dubois_12772.pdf
%L hal-01212934
%U https://hal.archives-ouvertes.fr/hal-01212934
%~ CNRS
%~ ERIC
%~ UNIV-TLSE2
%~ UNIV-LYON2
%~ SMS
%~ UNIV-LYON1
%~ UNIV-TLSE3