Statistical Reasoning with Set-Valued Information: Ontic vs. Epistemic Views

Didier Dubois (1, 2)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 QUB - Queen's University [Belfast]

Sets, hence fuzzy sets, may have a conjunctive or a disjunctive reading. In the conjunctive reading a (fuzzy) set represents an object of interest for which a (gradual rather than Boolean) composite description makes sense. In contrast disjunctive (fuzzy) sets refer to the use of sets as a representation of incomplete knowledge. They do not model objects or quantities, but partial information about an underlying object or a precise quantity. In this case the fuzzy set captures uncertainty, and its membership function is a possibility distribution.We call epistemic such fuzzy sets, since they represent states of incomplete knowledge. Distinguishing between ontic and epistemic fuzzy sets is important in information-processing tasks because there is a risk of misusing basic notions and tools, such as distance between fuzzy sets, variance of a fuzzy random variable, fuzzy regression, etc. We discuss several examples where the ontic and epistemic points of view yield different approaches to these concepts.

Domaines: Intelligence artificielle [cs.AI]

Didier Dubois. Statistical Reasoning with Set-Valued Information: Ontic vs. Epistemic Views. Borgelt, Christian and Gil, Maria Angeles and Sousa, Joao M.C. and Verleysen, Michel. Towards Advanced Data Analysis by Combining Soft Computing and Statistics, 285, Springer, pp.119-136, 2013, Studies in Fuzziness and Soft Computing book series (STUDFUZZ), 978-3-642-30277-0. ⟨10.1007/978-3-642-30278-7_11⟩. ⟨hal-03413936⟩