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Extensions of Linguistic Pythagorean Fuzzy Sets and Their Applications in Multi-attribute Group Decision-Making

In: Pythagorean Fuzzy Sets

Author

Listed:
  • Jun Wang

    (Beijing University of Chemical Technology, School of Economics and Management)

  • Xiaopu Shang

    (Beijing Jiaotong University, School of Economics and Management)

  • Wuhuan Xu

    (Beijing Jiaotong University, School of Economics and Management)

  • Chunliang Ji

    (Beijing Jiaotong University, School of Economics and Management)

  • Xue Feng

    (Beijing Jiaotong University, School of Economics and Management)

Abstract

Linguistic Pythagorean fuzzy sets (LPFSs), which use linguistic terms to represent membership degree and non-membership degree, have been proved to be effective to deal with uncertainties and vagueness in information and data. However, LPFSs still have drawbacks in depicting fuzzy decision-making information, i.e., they fail to handle multi-attribute group decision-making (MAGDM) situations wherein decision experts are hesitant among some series of linguistic terms when determining the linguistic membership and non-membership degrees. To efficiently and accurately express fuzzy attribute values provided by decision experts, this paper extends LPFSs to dual hesitant linguistic Pythagorean fuzzy sets (DHLPFSs), which allow the possible membership and non-membership degrees to be denoted by a collection of linguistic terms. We further study operational rules, ranking method, and aggregation operators of DHLPFSs, and based on these achievements, we introduce a new MAGDM method. To more comprehensively capture group’s evaluation information, we then generalize DHLPFSs to probabilistic DHLPFSs (PDHLPFSs), by taking probabilistic information of each linguistic term into count. For the sake of usage of PDHLPFSs in MAGDM problems, we continue to investigate their operations, comparison method, and aggregation operators and introduce a novel decision-making method. Finally, illustrative examples are provided to show the effectiveness of the new MAGDM methods.

Suggested Citation

  • Jun Wang & Xiaopu Shang & Wuhuan Xu & Chunliang Ji & Xue Feng, 2021. "Extensions of Linguistic Pythagorean Fuzzy Sets and Their Applications in Multi-attribute Group Decision-Making," Springer Books, in: Harish Garg (ed.), Pythagorean Fuzzy Sets, pages 367-405, Springer.
    • Handle: RePEc:spr:sprchp:978-981-16-1989-2_15
    DOI: 10.1007/978-981-16-1989-2_15
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