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Z probabilistic linguistic term sets and its application in multi-attribute group decision making

Author

Listed:
  • Jiahui Chai

    (Chongqing University of Posts and Telecommunications)

  • Sidong Xian

    (Chongqing University of Posts and Telecommunications)

  • Sichong Lu

    (Chongqing University of Posts and Telecommunications)

Abstract

Probabilistic linguistic term set solves the problem of probabilistic distribution of linguistic terms. Due to the objective and subjective factors such as the decision makers’experience and preference, the credibility of the linguistic terms is different. However, current studies on PLTSs ignore this difference. In this paper, we first propose a novel concept called Z probabilistic linguistic term set (ZPLTS). As an extension of existing tools, it takes advantage of the fact that Z-number can represent both information and corresponding credibility. At the same time, we discuss the normalization, operational rules, ranking method and distance measure for ZPLTSs. Then, we propose a new weight calculation method, an aggregation-based method and an extended TOPSIS method, and apply them to multi-attribute group decision making in Z probabilistic linguistic environment. Finally, a numerical example and some comparisons with other methods illustrate the necessity and effectiveness of the proposed method.

Suggested Citation

  • Jiahui Chai & Sidong Xian & Sichong Lu, 2021. "Z probabilistic linguistic term sets and its application in multi-attribute group decision making," Fuzzy Optimization and Decision Making, Springer, vol. 20(4), pages 529-566, December.
    • Handle: RePEc:spr:fuzodm:v:20:y:2021:i:4:d:10.1007_s10700-021-09351-2
    DOI: 10.1007/s10700-021-09351-2
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    References listed on IDEAS

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    1. Xu, Zeshui, 2005. "Deviation measures of linguistic preference relations in group decision making," Omega, Elsevier, vol. 33(3), pages 249-254, June.
    2. Huchang Liao & Xiaomei Mi & Zeshui Xu, 2020. "A survey of decision-making methods with probabilistic linguistic information: bibliometrics, preliminaries, methodologies, applications and future directions," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 81-134, March.
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    Cited by:

    1. Ameeth Sooklall & Jean Vincent Fonou-Dombeu, 2022. "An Enhanced ELECTRE II Method for Multi-Attribute Ontology Ranking with Z-Numbers and Probabilistic Linguistic Term Set," Future Internet, MDPI, vol. 14(10), pages 1-36, September.
    2. Sidong Xian & Ke Qing & Ling Tang & Huilan Pan, 2023. "A Multi-criteria Group Decision Making Based on Possibility Degree Matrix and $$\mathbb {ZPDHL}$$ ZPDHL -VIKOR Method," Group Decision and Negotiation, Springer, vol. 32(3), pages 633-666, June.

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