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On the Meaning of Fuzziness

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On Fuzziness

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 299))

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Abstract

Interpretation of the basic structures of fuzzy logic, notably that of possibility distribution, is an essential requirement to clarify their value as an important tool in automated reasoning. Despite its evident value, as shown by the multiplicity and importance of its applications, much of the discussion to this day about such notions as “possibility” or the “fuzzy paradigm” typically relies on illustrative examples while failing to provide clarifying insights into important conceptual matters. In this paper we review an interpretation of the basic notions of fuzzy logic in terms of metric and utilitarian notions such as similarity and utility that clarifies major semantic issues while establishing links to existing formal frameworks such as the notion of possible worlds and the theory of metric spaces. We remark that these ideas were present, albeit in an implicit fashion, in the pioneering applications of fuzzy logic to system control. We review also recent extensions of similarity-based interpretations to fuzzy evidence.

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Author information

Authors and Affiliations

  1. Unit: Collaborative Soft Intelligent Systems, European Centre for Soft Computing, Mieres, Spain

    Enrique H. Ruspini

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  1. Enrique H. Ruspini
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Editors and Affiliations

  1. , Edificio de Investigación, European Centre for Soft Computing, C Gonzalo Gutiérrez Quirós S/N, Mieres, 33600, Spain

    Rudolf Seising

  2. Edificio de Investigación, 3ª Planta., European Centre for Soft Computing, C Gonzalo Gutiérrez Quirós S/N, Mieres, 33600, Asturias, Spain

    Enric Trillas

  3. Edificio de Investigación, 3ª Planta., European Centre for Soft Computing, Asturias, Mieres, 33600, Spain

    Claudio Moraga

  4. , Department of Mathematic and Informatics, Università di Palermo, Via Archirafi 34, Palermo, 90123, Italy

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Ruspini, E.H. (2013). On the Meaning of Fuzziness. In: Seising, R., Trillas, E., Moraga, C., Termini, S. (eds) On Fuzziness. Studies in Fuzziness and Soft Computing, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35644-5_25

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  • DOI: https://doi.org/10.1007/978-3-642-35644-5_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35643-8

  • Online ISBN: 978-3-642-35644-5

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