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Group prioritisation with unknown expert weights in incomplete linguistic context

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  • Dong Cheng
  • Faxin Cheng
  • Zhili Zhou
  • Juan Wang

Abstract

In this paper, we study a group prioritisation problem in situations when the expert weights are completely unknown and their judgement preferences are linguistic and incomplete. Starting from the theory of relative entropy (RE) and multiplicative consistency, an optimisation model is provided for deriving an individual priority vector without estimating the missing value(s) of an incomplete linguistic preference relation. In order to address the unknown expert weights in the group aggregating process, we define two new kinds of expert weight indicators based on RE: proximity entropy weight and similarity entropy weight. Furthermore, a dynamic-adjusting algorithm (DAA) is proposed to obtain an objective expert weight vector and capture the dynamic properties involved in it. Unlike the extant literature of group prioritisation, the proposed RE approach does not require pre-allocation of expert weights and can solve incomplete preference relations. An interesting finding is that once all the experts express their preference relations, the final expert weight vector derived from the DAA is fixed irrespective of the initial settings of expert weights. Finally, an application example is conducted to validate the effectiveness and robustness of the RE approach.

Suggested Citation

  • Dong Cheng & Faxin Cheng & Zhili Zhou & Juan Wang, 2017. "Group prioritisation with unknown expert weights in incomplete linguistic context," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(12), pages 2633-2643, September.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:12:p:2633-2643
    DOI: 10.1080/00207721.2017.1337947
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    References listed on IDEAS

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    1. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi, 2008. "On consistency measures of linguistic preference relations," European Journal of Operational Research, Elsevier, vol. 189(2), pages 430-444, September.
    2. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi & Dai, Min, 2008. "A comparative study of the numerical scales and the prioritization methods in AHP," European Journal of Operational Research, Elsevier, vol. 186(1), pages 229-242, April.
    3. Kou, Gang & Lin, Changsheng, 2014. "A cosine maximization method for the priority vector derivation in AHP," European Journal of Operational Research, Elsevier, vol. 235(1), pages 225-232.
    4. Alfredo Altuzarra & José María Moreno-Jiménez & Manuel Salvador, 2010. "Consensus Building in AHP-Group Decision Making: A Bayesian Approach," Operations Research, INFORMS, vol. 58(6), pages 1755-1773, December.
    5. Akyildiz, Burcu & Kadaifci, Cigdem & Topcu, Ilker, 2015. "A decision framework proposal for customer order prioritization: A case study for a structural steel company," International Journal of Production Economics, Elsevier, vol. 169(C), pages 21-30.
    6. Lipovetsky, Stan & Michael Conklin, W., 2002. "Robust estimation of priorities in the AHP," European Journal of Operational Research, Elsevier, vol. 137(1), pages 110-122, February.
    7. Forman, Ernest & Peniwati, Kirti, 1998. "Aggregating individual judgments and priorities with the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 108(1), pages 165-169, July.
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