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Measures of Fuzziness under Different Uses of Fuzzy Sets

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Advances in Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 298))

Abstract

In this paper we discuss on the relationship between fuzziness and its measuring on the one side, and the possible uses of fuzzy sets on the other side. We conclude that the usual axioms and measures of fuzziness disregard the commensurability assumption and view the fuzzy set as a collection of fuzzy singletons. We propose new axioms and a relation “less fuzzy than” for a conjunctive view of fuzzy sets under the commensurability assumption. We show that a measure of fuzziness previously introduced by the authors comply with our proposal.

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References

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Author information

Authors and Affiliations

  1. Edificio Científico-Tecnológico, European Centre for Soft Computing, Mieres, Asturias, Spain, 33600

    Daniel Sánchez & Enric Trillas

Authors
  1. Daniel Sánchez
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  2. Enric Trillas
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Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. Université Pierre et Marie Curie - Paris6, CNRS UMR 7606, DAPA, LIP6 8, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute, IONA College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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© 2012 Springer-Verlag Berlin Heidelberg

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Sánchez, D., Trillas, E. (2012). Measures of Fuzziness under Different Uses of Fuzzy Sets. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31715-6_4

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  • DOI: https://doi.org/10.1007/978-3-642-31715-6_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31714-9

  • Online ISBN: 978-3-642-31715-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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