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A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making

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  • Liu, Fang
  • Zhang, Wei-Guo
  • Wang, Zhong-Xing

Abstract

In decision making problems, there may be the cases where the decision makers express their judgements by using preference relations with incomplete information. Then one of the key issues is how to estimate the missing preference values. In this paper, we introduce an incomplete interval multiplicative preference relation and give the definitions of consistent and acceptable incomplete ones, respectively. Based on the consistency property of interval multiplicative preference relations, a goal programming model is proposed to complement the acceptable incomplete one. A new algorithm of obtaining the priority vector from incomplete interval multiplicative preference relations is given. The goal programming model is further applied to group decision-making (GDM) where the experts evaluate their preferences as acceptable incomplete interval multiplicative preference relations. An interval weighted geometric averaging (IWGA) operator is proposed to aggregate individual preference relations into a social one. Furthermore, the social interval multiplicative preference relation owns acceptable consistency when every individual one is acceptably consistent. Two numerical examples are carried out to show the efficiency of the proposed goal programming model and the algorithms.

Suggested Citation

  • Liu, Fang & Zhang, Wei-Guo & Wang, Zhong-Xing, 2012. "A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making," European Journal of Operational Research, Elsevier, vol. 218(3), pages 747-754.
    • Handle: RePEc:eee:ejores:v:218:y:2012:i:3:p:747-754
    DOI: 10.1016/j.ejor.2011.11.042
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    Cited by:

    1. Virgilio López-Morales, 2018. "A Reliable Method for Consistency Improving of Interval Multiplicative Preference Relations Expressed under Uncertainty," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(05), pages 1561-1585, September.
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    3. Bustince, H. & Jurio, A. & Pradera, A. & Mesiar, R. & Beliakov, G., 2013. "Generalization of the weighted voting method using penalty functions constructed via faithful restricted dissimilarity functions," European Journal of Operational Research, Elsevier, vol. 225(3), pages 472-478.
    4. 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.
    5. Cabrerizo, Francisco Javier & Herrera-Viedma, Enrique & Pedrycz, Witold, 2013. "A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts," European Journal of Operational Research, Elsevier, vol. 230(3), pages 624-633.
    6. Przybyła-Kasperek, Małgorzata & Wakulicz-Deja, Alicja, 2016. "The strength of coalition in a dispersed decision support system with negotiations," European Journal of Operational Research, Elsevier, vol. 252(3), pages 947-968.
    7. Wang, Zhou-Jing, 2015. "A note on “A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making”," European Journal of Operational Research, Elsevier, vol. 247(3), pages 867-871.
    8. Liu Fang & Peng Yanan & Zhang Weiguo & Pedrycz Witold, 2017. "On Consistency in AHP and Fuzzy AHP," Journal of Systems Science and Information, De Gruyter, vol. 5(2), pages 128-147, April.
    9. Gong, Zaiwu & Guo, Weiwei & Herrera-Viedma, Enrique & Gong, Zejun & Wei, Guo, 2020. "Consistency and consensus modeling of linear uncertain preference relations," European Journal of Operational Research, Elsevier, vol. 283(1), pages 290-307.
    10. 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.
    11. Wang, Zhou-Jing & Li, Kevin W., 2015. "A multi-step goal programming approach for group decision making with incomplete interval additive reciprocal comparison matrices," European Journal of Operational Research, Elsevier, vol. 242(3), pages 890-900.
    12. Xia, Meimei & Chen, Jian, 2015. "Multi-criteria group decision making based on bilateral agreements," European Journal of Operational Research, Elsevier, vol. 240(3), pages 756-764.
    13. Brunelli, Matteo & Fedrizzi, Michele, 2015. "Boundary properties of the inconsistency of pairwise comparisons in group decisions," European Journal of Operational Research, Elsevier, vol. 240(3), pages 765-773.
    14. Kedong Yin & Benshuo Yang & Xuemei Li, 2018. "Multiple Attribute Group Decision-Making Methods Based on Trapezoidal Fuzzy Two-Dimensional Linguistic Partitioned Bonferroni Mean Aggregation Operators," IJERPH, MDPI, vol. 15(2), pages 1-23, January.
    15. Zeshui Xu & Xiaoqiang Cai, 2014. "Deriving Weights from Interval Multiplicative Preference Relations in Group Decision Making," Group Decision and Negotiation, Springer, vol. 23(4), pages 695-713, July.

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