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Distance-based nonlinear programming models to identify and adjust inconsistencies for linguistic preference relations

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Abstract

This paper studies the ordinal and additive inconsistency problems of linguistic preference relations. First, the definition of ordinal consistency of a linguistic preference relation is proposed. Based on the definition of adjacency matrix of a linguistic preference relation, the necessary and sufficient conditions of a linguistic preference relation being ordinally consistent are given. Then, a distance-based nonlinear programming method is developed to identify and adjust the ordinal and additive inconsistencies for linguistic preference relations. The proposed methods can not only solve the ordinal inconsistency, additive inconsistency problems, respectively, but also solve the ordinal and additive inconsistency problems simultaneously. Finally, numerical examples and comparative analysis are provided to show the effectiveness and advantages of the proposed methods.

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Acknowledgements

This work was partly supported by the Key Project of National Natural Science Foundation of China (No.71433003), the National Natural Science Foundation of China (NSFC) (No.71471056), the Fundamental Research Funds for the Central Universities (No. 2015B23014), Excellent Innovative Talent Program of Hohai University, sponsored by Qing Lan Project of Jiangsu Province.

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Authors and Affiliations

  1. Business School, Hohai University, Nanjing, 211100, People’s Republic of China

    Yejun Xu

  2. College of Mathematical Sciences, Yangzhou University, Yangzhou, 225002, People’s Republic of China

    Cuiping Wei

  3. School of Business, Qingdao University, Qingdao, 266071, People’s Republic of China

    Hao Sun

Authors
  1. Yejun Xu
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  2. Cuiping Wei
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  3. Hao Sun
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Correspondence to Yejun Xu or Hao Sun.

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The authors declare that they have no conflict of interest.

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Communicated by V. Loia.

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Xu, Y., Wei, C. & Sun, H. Distance-based nonlinear programming models to identify and adjust inconsistencies for linguistic preference relations. Soft Comput 22, 4833–4849 (2018). https://doi.org/10.1007/s00500-017-2671-y

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