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

Chapter
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 285)

## Abstract

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.

## Keywords

Interval Data Statistical Reasoning Belief Function Possibility Distribution Fuzzy Random Variable
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2013

## Authors and Affiliations

1. 1.IRIT, CNRS and Université de ToulouseToulouseFrance