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An Alpha-Cut Evaluation of Interval-Valued Fuzzy Sets for Application in Decision Making

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Fuzzy Logic and Applications (WILF 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11291))

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Abstract

In this paper we deal with the problem of evaluating an interval-valued fuzzy set, that is a fuzzy quantity delimited by two (lower and upper) membership functions. The problem of associating this type of set with a real number has been dealt with in different ways. Karnik and Mendel proposed an algorithm for computing the mean of centroids of membership functions that lie within the area delimited by the lower and upper memberships. Nie and Tan choose a simpler way by calculating the centroid of the average of the lower and upper membership functions. In both cases, the value obtained is useful not only in ranking problems but also as a value of defuzzification if the set is the final output of a fuzzy inference system. Since in this last case the obtained set is usually not normal and not convex, the centroid seems to be the only useful defuzzifier. Our purpose is to show that other methods based on alpha-cuts, usually applied in convex type-1 case, can also provide useful answers.

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Authors and Affiliations

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

    Luca Anzilli & Gisella Facchinetti

Authors
  1. Luca Anzilli
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  2. Gisella Facchinetti
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Correspondence to Luca Anzilli .

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Editors and Affiliations

  1. Széchenyi István University, Győr, Hungary

    Robert Fullér

  2. Ca’ Foscari University of Venice, Venice, Italy

    Silvio Giove

  3. University of Genoa, Genoa, Italy

    Francesco Masulli

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Anzilli, L., Facchinetti, G. (2019). An Alpha-Cut Evaluation of Interval-Valued Fuzzy Sets for Application in Decision Making. In: Fullér, R., Giove, S., Masulli, F. (eds) Fuzzy Logic and Applications. WILF 2018. Lecture Notes in Computer Science(), vol 11291. Springer, Cham. https://doi.org/10.1007/978-3-030-12544-8_16

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  • DOI: https://doi.org/10.1007/978-3-030-12544-8_16

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  • Online ISBN: 978-3-030-12544-8

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