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Optimization-driven group decision making with XOR comparison matrices

Author

Listed:
  • Chen, Ya-Ru
  • Liu, Fang
  • Bustince, Humberto
  • Huang, Hao
  • Zhong, Xian-Ci

Abstract

The “exclusive-or”(XOR) logic describes a situation where only one of multiple options can be chosen, which is used to give the XOR number for quantifying some uncertainty in pairwise comparisons. It is interesting to develop group decision making (GDM) model with XOR comparison matrices by investigating consistency of judgements and consensus of experts. First, the consistency/acceptable consistency of XOR comparison matrices is defined by considering the basic principle of XOR logic. A mathematical programming model is constructed to check the consistency/acceptable consistency of XOR comparison matrices. Second, for improving consistency of XOR comparison matrices, an optimization model is built to obtain a multiplicative preference relation with acceptable consistency from XOR comparison matrices. The model is further developed according to the idea of minimizing the number of adjusted variables. Third, a consensus index is established for reaching consensus in GDM, which is utilized to propose an iterative algorithm for improving the consensus level. An algorithm for GDM with XOR comparison matrices is developed, which yields an optimal solution under acceptable consistency and acceptable consensus. Finally, a case study with discussion comparison is reported to illustrate the applicability of the proposed model. The results help to construct an optimization-driven mechanism of reaching consensus in GDM under XOR environments.

Suggested Citation

  • Chen, Ya-Ru & Liu, Fang & Bustince, Humberto & Huang, Hao & Zhong, Xian-Ci, 2026. "Optimization-driven group decision making with XOR comparison matrices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PA), pages 763-786.
    • Handle: RePEc:eee:matcom:v:241:y:2026:i:pa:p:763-786
    DOI: 10.1016/j.matcom.2025.09.027
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    References listed on IDEAS

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    1. Mohapatra, Dhabaleswar & Chakraverty, S., 2025. "Type-2 fuzzy initial value problems under granular differentiability," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 435-447.
    2. Liu, Fang & Chen, Ya-Ru & Zhou, Da-Hai, 2023. "A two-dimensional approach to flexibility degree of XOR numbers with application to group decision making," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 267-287.
    3. Gupta, Soniya & Joshi, Dheeraj Kumar & Awasthi, Natasha & Pant, Manish & Joshi, Bhagawati prasad & Chaube, Shshank, 2024. "Distance and similarity measures of Hesitant bi-fuzzy set and its applications in renewable energy systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 321-336.
    4. S., Kavitha & N., Kendra & J., Satheeshkumar & T., Amudha & Manavalan, Balachandran, 2025. "Decision making based ensemble feature selection approach through a new score function in q-rung orthopair hesitant fuzzy environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 232(C), pages 362-381.
    5. Liu, Fang & Zou, Shu-Cai & Li, Qing, 2020. "Deriving priorities from pairwise comparison matrices with a novel consistency index," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    6. Hocine, Amine & Kouaissah, Noureddine, 2020. "XOR analytic hierarchy process and its application in the renewable energy sector," Omega, Elsevier, vol. 97(C).
    7. Meimei Xia & Jian Chen, 2015. "Studies on Interval Multiplicative Preference Relations and Their Application to Group Decision Making," Group Decision and Negotiation, Springer, vol. 24(1), pages 115-144, January.
    8. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    9. Rezaei, Jafar, 2015. "Best-worst multi-criteria decision-making method," Omega, Elsevier, vol. 53(C), pages 49-57.
    10. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    11. Thomas L. Saaty, 2013. "The Modern Science of Multicriteria Decision Making and Its Practical Applications: The AHP/ANP Approach," Operations Research, INFORMS, vol. 61(5), pages 1101-1118, October.
    12. Liu, Fang & Zhang, Wei-Guo & Zhang, Li-Hua, 2014. "Consistency analysis of triangular fuzzy reciprocal preference relations," European Journal of Operational Research, Elsevier, vol. 235(3), pages 718-726.
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