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Extensions of Ordinary Fuzzy Sets: A Comparative Literature Review

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Intelligent and Fuzzy Techniques: Smart and Innovative Solutions (INFUS 2020)

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Abstract

Fuzzy sets extensions have been often used in the modeling of problems including vagueness and impreciseness in order to better define the membership functions together with the hesitancy of decision makers. More than 20 different extensions of ordinary fuzzy sets have appeared in the literature after the introductions of ordinary fuzzy sets by Zadeh (1965). These sets involve interval-type fuzzy sets, type-2 fuzzy sets, hesitant fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets, q-rung orthopair fuzzy sets, spherical fuzzy sets, picture fuzzy sets, fermatean fuzzy sets, etc. Mainly, these extensions can be divided into two classes: extensions with two independent membership parameters and extensions with three independent membership parameters. In this paper, we briefly classify these extensions and present some comparative graphical illustrations.

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Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Istanbul Technical University, Macka, Besiktas, 34367, Istanbul, Turkey

    Cengiz Kahraman, Basar Oztaysi & Sezi Cevik Onar

  2. Department of Industrial Engineering, Istanbul Bilgi University, Istanbul, Turkey

    Irem Otay

Authors
  1. Cengiz Kahraman
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  2. Basar Oztaysi
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  3. Irem Otay
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  4. Sezi Cevik Onar
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Corresponding author

Correspondence to Cengiz Kahraman .

Editor information

Editors and Affiliations

  1. Department of Industrial Engineering, Istanbul Technical University, Istanbul, Turkey

    Cengiz Kahraman

  2. Department of Industrial Engineering, Istanbul Technical University, Istanbul, Turkey

    Sezi Cevik Onar

  3. Department of Industrial Engineering, Istanbul Technical University, Ä°stanbul, Turkey

    Basar Oztaysi

  4. Department of Industrial Engineering, Istanbul Technical University, Istanbul, Turkey

    Irem Ucal Sari

  5. Industrial Engineering Department, Yildiz Technical University, Istanbul, Turkey

    Selcuk Cebi

  6. Industrial Engineering Department, Galatasaray University, Istanbul, Turkey

    A. Cagri Tolga

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Kahraman, C., Oztaysi, B., Otay, I., Onar, S.C. (2021). Extensions of Ordinary Fuzzy Sets: A Comparative Literature Review. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I., Cebi, S., Tolga, A. (eds) Intelligent and Fuzzy Techniques: Smart and Innovative Solutions. INFUS 2020. Advances in Intelligent Systems and Computing, vol 1197. Springer, Cham. https://doi.org/10.1007/978-3-030-51156-2_193

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