On the Informational Comparison of Qualitative Fuzzy Measures

Didier Dubois (1, 2) , Henri Prade (1, 2) , Agnès Rico (3)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 CNRS - Centre National de la Recherche Scientifique
3 ERIC - Equipe de Recherche en Ingénierie des Connaissances

Fuzzy measures or capacities are the most general representation of uncertainty functions. However, this general class has been little explored from the point of view of its information content, when degrees of uncertainty are not supposed to be numerical, and belong to a finite qualitative scale, except in the case of possibility or necessity measures. The thrust of the paper is to define an ordering relation on the set of qualitative capacities expressing the idea that one is more informative than another, in agreement with the possibilistic notion of relative specificity. To this aim, we show that the class of qualitative capacities can be partitioned into equivalence classes of functions containing the same amount of information. They only differ by the underlying epistemic attitude such as pessimism or optimism. A meaningful information ordering between capacities can be defined on the basis of the most pessimistic (resp. optimistic) representatives of their equivalence classes. It is shown that, while qualitative capacities bear strong similarities to belief functions, such an analogy can be misleading when it comes to information content.

Mots clés: Fuzzy measures; Possibility theory; Qualitative reasoning; Information content

Domaines: Intelligence artificielle [cs.AI]; Apprentissage [cs.LG]; Logique en informatique [cs.LO]; Informatique et langage [cs.CL]

Didier Dubois, Henri Prade, Agnès Rico. On the Informational Comparison of Qualitative Fuzzy Measures. 15th International Conference, Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU 2014), Jul 2014, Montpellier, France. pp.216-225, ⟨10.1007/978-3-319-08795-5_23⟩. ⟨hal-01147279⟩