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Flexible Fuzzy Numbers for Likert Scale-Based Evaluations

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Soft Computing Applications (SOFA 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1221))

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Abstract

In this paper, a novel class of fuzzy numbers called the flexible fuzzy numbers is introduced and its application in Likert scale-based evaluations is presented. We point out that depending on its shape parameter, the membership function of a flexible fuzzy number can take various forms. Next, we show that if the shape parameter is fixed, then the set of flexible fuzzy numbers is closed under the multiplication by scalar, fuzzy addition and weighted average operations. Then, as a generalization of the flexible fuzzy numbers we introduce the extended flexible fuzzy numbers which can have different left hand side and right hand side shape parameters. Here, we introduce an important asymptotic property of the extended flexible fuzzy numbers that allows us to perform approximate fuzzy arithmetic operations over them. The pliancy of these fuzzy numbers make them well suited to multi-dimensional Likert scale-based fuzzy evaluations in many areas of management.

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Author information

Authors and Affiliations

  1. Department of Computer Algorithms and Artificial Intelligence, University of Szeged, Árpád tér 2, 6720, Szeged, Hungary

    József Dombi

  2. Institute of Business Economics, Eötvös Loránd University, Egyetem tér 1-3, 1053, Budapest, Hungary

    Tamás Jónás

  3. Research and Development Department, Flextronics International Ltd., Hangár u. 5-37, 1183, Budapest, Hungary

    Tamás Jónás

Authors
  1. József Dombi
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  2. Tamás Jónás
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Corresponding author

Correspondence to Tamás Jónás .

Editor information

Editors and Affiliations

  1. “Aurel Vlaicu” University of Arad, Faculty of Engineering, Arad, Romania

    Valentina Emilia Balas

  2. Faculty of Engineering and Information Technology, University of Technology Sydney, Centre for Artificial Intelligence, Sydney, Australia

    Lakhmi C. Jain

  3. Faculty of Engineering, “Aurel Vlaicu” University of Arad, Arad, Arad, Romania

    Marius Mircea Balas

  4. Department of Information Technology and Programming, Azerbaijan Technical University, Baku, Azerbaijan

    Shahnaz N. Shahbazova

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Dombi, J., Jónás, T. (2021). Flexible Fuzzy Numbers for Likert Scale-Based Evaluations. In: Balas, V., Jain, L., Balas, M., Shahbazova, S. (eds) Soft Computing Applications. SOFA 2018. Advances in Intelligent Systems and Computing, vol 1221. Springer, Cham. https://doi.org/10.1007/978-3-030-51992-6_8

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