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Score Function-Based Effective Ranking of Interval-Valued Fermatean Fuzzy Sets and Its Applications to Multi-criteria Decision Making Problem

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Real Life Applications of Multiple Criteria Decision Making Techniques in Fuzzy Domain

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 420))

Abstract

Fermatean fuzzy sets (FFSs), an orthopair fuzzy set proposed by Senapati and Yager (Journal of Ambient Intelligence and Humanized Computing 11:663–674, 2020, [24]), can handle the situation with ambiguous and incomplete information in a more effective manner than the Pythagorean fuzzy sets presented by Yager (Pythagorean fuzzy subsets, 2013 Joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), pp 57–61, 2013, [2]) and the intuitionistic fuzzy sets presented by Atanassov (Fuzzy Sets and Systems 20:87–96, 1986, [3]). Sergi et al. (Journal of Intelligent & Fuzzy Systems 42:365–376, 2022, [40]) initiated interval-valued Fermatean fuzzy sets (IVFFSs) and established IVFFS ordering, as well as some mathematical operations. In addition, Jeevraj (Expert Systems with Applications 185:1–20, 2021, [37]) introduced the concept of a score and accuracy function for IVFFSs. The main objective of this chapter is to suggest some score functions for acceptable ranking of IVFFSs, as well as the interval-valued Fermatean fuzzy TOPSIS method for solving multi-criteria decision making problems. Here, we have proposed six new variants of score functions for effective ranking of interval-valued Fermatean fuzzy sets. Depending on various types of score functions, we have used a TOPSIS-based multi-criteria decision making (MCDM) problem in which decision makers’ (DMs’) preference knowledge is summarized in the pattern of interval-valued Fermatean fuzzy sets. To illustrate the usefulness of the proposed method, a computational paradigm has been considered. Finally, concluding remarks and future scope of research have been mentioned.

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Author information

Authors and Affiliations

  1. Department of Computer and Information Science, Raiganj University, Raiganj, 733134, India

    Laxminarayan Sahoo

  2. Department of Mathematics, Narajole Raj College, Paschim Medinipur, West Bengal, 721211, India

    Akul Rana

  3. School of Mathematics and Statistics, Southwest University, Beibei, Chongqing, 400715, China

    Tapan Senapati

  4. Machine Intelligence Institute, Iona College, New Rochelle, NY, 10801, USA

    Ronald R. Yager

Authors
  1. Laxminarayan Sahoo
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  2. Akul Rana
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  3. Tapan Senapati
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  4. Ronald R. Yager
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Correspondence to Laxminarayan Sahoo .

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Editors and Affiliations

  1. Department of Computer and Information Science, Raiganj University, Raiganj, West Bengal, India

    Laxminarayan Sahoo

  2. School of Mathematics and Statistics, Southwest University, Chongqing, China

    Tapan Senapati

  3. Iona College, Machine Intelligence Institute, New Rochelle, NY, USA

    Ronald R. Yager

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Sahoo, L., Rana, A., Senapati, T., Yager, R.R. (2023). Score Function-Based Effective Ranking of Interval-Valued Fermatean Fuzzy Sets and Its Applications to Multi-criteria Decision Making Problem. In: Sahoo, L., Senapati, T., Yager, R.R. (eds) Real Life Applications of Multiple Criteria Decision Making Techniques in Fuzzy Domain. Studies in Fuzziness and Soft Computing, vol 420. Springer, Singapore. https://doi.org/10.1007/978-981-19-4929-6_20

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