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

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Towards Advanced Data Analysis by Combining Soft Computing and Statistics

Part of the book series: Studies in Fuzziness and Soft Computing ((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.

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Authors and Affiliations

  1. IRIT, CNRS and Université de Toulouse, Toulouse, France

    Didier Dubois

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  1. Didier Dubois
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Correspondence to Didier Dubois .

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Editors and Affiliations

  1. Intelligent Data Analysis & Graphical, Models Research Unit, European Centre for Soft Computing, C/ Gonzalo Gutierre, Mieres, 33600, Asturias, Spain

    Christian Borgelt

  2. , Departamento de Estadistica e I. O. y, Universidad de Oviedo, C/Calvo Sotelo, s/n, Oviedo, 33071, Spain

    María Ángeles Gil

  3. Instituto Superior Técnico, Department of Mechanical Engineering, Technical University Lisbon, Av. Rovisco Pais 1, Lisboa, 1049-001, Portugal

    João M.C. Sousa

  4. Labo. Microelectronique, Université Catholique de Louvain, place du Levant 3, Leuven, 1348, Belgium

    Michel Verleysen

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Dubois, D. (2013). Statistical Reasoning with Set-Valued Information: Ontic vs. Epistemic Views. In: Borgelt, C., Gil, M., Sousa, J., Verleysen, M. (eds) Towards Advanced Data Analysis by Combining Soft Computing and Statistics. Studies in Fuzziness and Soft Computing, vol 285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30278-7_11

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  • DOI: https://doi.org/10.1007/978-3-642-30278-7_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30277-0

  • Online ISBN: 978-3-642-30278-7

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