A general framework for upper and lower possibilities and necessities
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Entropy of discrete fuzzy measures
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - special issue on measures and aggregation: formal aspects and applications to clustering and decision
Making Discrete Sugeno Integrals More Discriminant
International Journal of Approximate Reasoning
Capacity Refinements and Their Application to Qualitative Decision Evaluation
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
A Simple Modal Logic for Reasoning about Revealed Beliefs
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Paper: Evidence measures based on fuzzy information
Automatica (Journal of IFAC)
Inferential processes leading to possibility and necessity
Information Sciences: an International Journal
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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.