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Multi-criteria sorting decision making based on dominance and opposition relations with probabilistic linguistic information

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  • Hong-gang Peng

    (Central South University)

  • Jian-qiang Wang

    (Central South University)

Abstract

The probabilistic linguistic term set (PLTS) is a powerful tool for describing linguistic evaluations derived from expert teams and has adequate capability to identify preferences among different evaluations. Due to the practicability of PLTSs, probabilistic linguistic decision making problems have been widely investigated in recent years. However, no study on probabilistic linguistic outranking relations has been conducted. This study aims to explore effective processing for the complex two-dimension structure of PLTSs and formulate probabilistic linguistic dominance and opposition relations for multi-criteria sorting decision making. Linguistic scale functions, which can generate different semantics for linguistic variables under different decision making environments, are introduced to deal with the linguistic terms in PLTSs. In this way, the probabilistic linguistic dominance degree, concordance and discordance indices are defined by systematically comparing the probabilities of PLTSs. Then, two kinds of outranking relations with dominance and opposition for PLTSs are formulated based on the defined outranking indices. Subsequently, an innovative sorting decision making framework is constructed by exploring the outranking relations between alternatives and characteristic actions under multiple criteria and implementing the outranking aggregation and exploitation. Finally, this framework is demonstrated using an illustrative example with result analyses and comparison discussions.

Suggested Citation

  • Hong-gang Peng & Jian-qiang Wang, 2020. "Multi-criteria sorting decision making based on dominance and opposition relations with probabilistic linguistic information," Fuzzy Optimization and Decision Making, Springer, vol. 19(4), pages 435-470, December.
    • Handle: RePEc:spr:fuzodm:v:19:y:2020:i:4:d:10.1007_s10700-020-09330-z
    DOI: 10.1007/s10700-020-09330-z
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    References listed on IDEAS

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    1. 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.
    2. Sui-zhi Luo & Hong-yu Zhang & Jian-qiang Wang & Lin Li, 2019. "Group decision-making approach for evaluating the sustainability of constructed wetlands with probabilistic linguistic preference relations," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(12), pages 2039-2055, December.
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    2. Chao Tian & Juan Juan Peng & Zhi Qiang Zhang & Mark Goh & Jian Qiang Wang, 2020. "A Multi-Criteria Decision-Making Method Based on Single-Valued Neutrosophic Partitioned Heronian Mean Operator," Mathematics, MDPI, vol. 8(7), pages 1-25, July.
    3. Xiao-Kang Wang & Yi-Ting Wang & Jian-Qiang Wang & Peng-Fei Cheng & Lin Li, 2020. "A TODIM-PROMETHEE Ⅱ Based Multi-Criteria Group Decision Making Method for Risk Evaluation of Water Resource Carrying Capacity under Probabilistic Linguistic Z-Number Circumstances," Mathematics, MDPI, vol. 8(7), pages 1-27, July.
    4. Min Xue & Chao Fu & Shanlin Yang, 2022. "A comparative analysis of probabilistic linguistic preference relations and distributed preference relations for decision making," Fuzzy Optimization and Decision Making, Springer, vol. 21(1), pages 71-97, March.
    5. Dan-Ping Li & Li Xie & Peng-Fei Cheng & Xiang-Hong Zhou & Cheng-Xun Fu, 2021. "Green Supplier Selection Under Cloud Manufacturing Environment: A Hybrid MCDM Model," SAGE Open, , vol. 11(4), pages 21582440211, November.
    6. Xiao-kang Wang & Sheng-hui Wang & Hong-yu Zhang & Jian-qiang Wang & Lin Li, 2021. "The Recommendation Method for Hotel Selection Under Traveller Preference Characteristics: A Cloud-Based Multi-Criteria Group Decision Support Model," Group Decision and Negotiation, Springer, vol. 30(6), pages 1433-1469, December.

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