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A New Definition of Evaluation/Defuzzification of an Interval Type-2 Fuzzy Set

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Strengthening Links Between Data Analysis and Soft Computing

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 315))

Abstract

In this paper we propose a new evaluation/defuzzification formula for an Interval Type-2 Fuzzy Quantity (IT2 FQ), that is an Interval Type-2 Fuzzy Set (IT2 FS) defined by two Type-1 Fuzzy Quantities (T1 FQs) having membership functions that may be neither convex nor normal. We start from a parametric formula to evaluate them and we propose to call the IT2 FQ value their average. To compare the results we obtain changing the parameters, we use the final output of an example of Interval Type-2 Fuzzy Logic System (IT2 FLS).

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Author information

Authors and Affiliations

  1. Department of Management, Economics, Mathematics and Statistics, University of Salento, Lecce, Italy

    Luca Anzilli & Gisella Facchinetti

  2. Department of Economics “Marco Biagi”, University of Modena and Reggio Emilia, Modena, Italy

    Tommaso Pirotti

Authors
  1. Luca Anzilli
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  2. Gisella Facchinetti
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  3. Tommaso Pirotti
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Corresponding author

Correspondence to Luca Anzilli .

Editor information

Editors and Affiliations

  1. Polish Academy of Sciences, Faculty of Mathematics and Information Sciences, Systems Research Institute and Warsaw University of Technology, Warsaw, Poland

    Przemyslaw Grzegorzewski

  2. Polish Academy of Sciences, Faculty of Mathematics and Information Sciences, Systems Research Institute and Warsaw University of Technology, Warsaw, Poland

    Marek Gagolewski

  3. Polish Academy of Sciences Systems Research Institute, Warsaw, Poland

    Olgierd Hryniewicz

  4. Departamento de Estadistica e I.O. y D.M., University of Oviedo, Oviedo, Spain

    María Ángeles Gil

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Anzilli, L., Facchinetti, G., Pirotti, T. (2015). A New Definition of Evaluation/Defuzzification of an Interval Type-2 Fuzzy Set. In: Grzegorzewski, P., Gagolewski, M., Hryniewicz, O., Gil, M. (eds) Strengthening Links Between Data Analysis and Soft Computing. Advances in Intelligent Systems and Computing, vol 315. Springer, Cham. https://doi.org/10.1007/978-3-319-10765-3_5

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  • DOI: https://doi.org/10.1007/978-3-319-10765-3_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10764-6

  • Online ISBN: 978-3-319-10765-3

  • eBook Packages: EngineeringEngineering (R0)

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