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Multiplicative consistency analysis for interval fuzzy preference relations: A comparative study

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  • Meng, Fanyong
  • Tan, Chunqiao
  • Chen, Xiaohong

Abstract

To examine the multiplicative consistency of interval fuzzy preference relations (IFPRs), this paper first analyzes the limitations associated with the previous consistency concepts. Accordingly, a new consistency concept is defined that is an extension of the crisp case and overcomes limitations in the previous concepts. Next, a linear programming model to judge the consistency of IFPRs is constructed, and an approach to derive multiplicative consistent IFPRs is introduced. Furthermore, goal-programming models to determine missing values in an incomplete IFPR are constructed that have the highest consistent level with respect to known values. Moreover, a multiplicative consistency and consensus based method for group decision making with IFPRs is developed that can address incomplete and inconsistent cases. Finally, two practical decision-making problems are offered to demonstrate the feasibility and efficiency of the new method, and an analysis of a numerical and theoretical comparison with several related methods is performed.

Suggested Citation

  • Meng, Fanyong & Tan, Chunqiao & Chen, Xiaohong, 2017. "Multiplicative consistency analysis for interval fuzzy preference relations: A comparative study," Omega, Elsevier, vol. 68(C), pages 17-38.
    • Handle: RePEc:eee:jomega:v:68:y:2017:i:c:p:17-38
    DOI: 10.1016/j.omega.2016.05.006
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    3. Jie Tang & Fanyong Meng & Francisco Javier Cabrerizo & Enrique Herrera-Viedma, 2020. "Group Decision Making with Interval-Valued Intuitionistic Multiplicative Linguistic Preference Relations," Group Decision and Negotiation, Springer, vol. 29(1), pages 169-206, February.
    4. Jie Tang & Qingxian An & Fanyong Meng & Xiaohong Chen, 2017. "A Natural Method for Ranking Objects from Hesitant Fuzzy Preference Relations," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(06), pages 1611-1646, November.
    5. Lihong Wang & Zaiwu Gong, 2017. "Priority of a Hesitant Fuzzy Linguistic Preference Relation with a Normal Distribution in Meteorological Disaster Risk Assessment," IJERPH, MDPI, vol. 14(10), pages 1-16, October.
    6. Mingwei Lin & Jiuhan Wei & Zeshui Xu & Riqing Chen, 2018. "Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators," Complexity, Hindawi, vol. 2018, pages 1-24, November.
    7. Fang Liu & Jia-Wei Zhang & Qin Yu & Ya-Nan Peng & Witold Pedrycz, 2020. "On weak consistency of interval additive reciprocal matrices," Fuzzy Optimization and Decision Making, Springer, vol. 19(2), pages 153-175, June.

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