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Fuzzy Arithmetics for Fuzzy n-Poles: When Is Interactivity Irrelevant?

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Advances in Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 299))

Abstract

We consider binary operations on fuzzy quantities whose interaction is specified by means of a joint possibility distribution. When and to what extent is this interaction relevant? We discuss the problem and tackle it in the case of fuzzy quantities with a finite support, called below fuzzy n-poles. We give a criterion for total irrelevance, once the two fuzzy operands are specified. We argue that fuzzy arithmetics should take inspiration from the arithmetics of random variables rather than crisp arithmetics, so as to get rid of notational inconsistencies.

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References

  1. Fullér, R., Majlender, P.: On interactive fuzzy numbers. Fuzzy Sets and Systems 143(3), 355–369 (2004)

    Article  MathSciNet  Google Scholar 

  2. Fullér, R., Majlender, P.: On additions of interactive fuzzy numbers. Acta Polytechnica Hungarica (2), 59–73 (2005)

    Google Scholar 

  3. Klir, G.J., Folger, T.A.: Fuzzy sets, uncertainty and information. Prentice Hall (1988)

    Google Scholar 

  4. Dubois, D., Prade, H.: Fundamentals of fuzzy sets. Handbooks of fuzzy sets series. Kluwer Academic (2000)

    Google Scholar 

  5. Zimmermann, H.J.: Fuzzy set theory–and its applications. Springer (2001)

    Google Scholar 

  6. Nelsen, R.B.: An introduction to copulas. Springer (2006)

    Google Scholar 

  7. Voxman, W.: Canonical representations of discrete fuzzy numbers. Fuzzy Sets and Systems 118(3), 457–466 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Geosciences, University of Trieste, Italy

    Andrea Sgarro & Laura Franzoi

Authors
  1. Andrea Sgarro
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  2. Laura Franzoi
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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. CNRS UMR 7606, DAPA, LIP6 8, Université Pierre et Marie Curie - Paris6, 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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Sgarro, A., Franzoi, L. (2012). Fuzzy Arithmetics for Fuzzy n-Poles: When Is Interactivity Irrelevant?. 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 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31718-7_1

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  • DOI: https://doi.org/10.1007/978-3-642-31718-7_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31717-0

  • Online ISBN: 978-3-642-31718-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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