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Hesitant fuzzy programming technique for multidimensional analysis of hesitant fuzzy preferences

Author

Listed:
  • Xiaolu Zhang

    (Jiangxi University of Finance and Economics)

  • Zeshui Xu

    (Sichuan University)

  • Xiaoming Xing

    (Jiangxi University of Finance and Economics)

Abstract

The linear programming technique for multidimensional analysis of preferences (LINMAP) is the most representative method for handling the multiple criteria decision making (MCDM) problems with respect to the preference information over alternatives. This paper utilizes the main structure of LINMAP to develop a novel hesitant fuzzy mathematical programming technique to handle MCDM problems within the decision environment of hesitant fuzzy elements (HFEs). Considering the hesitancy of the decision maker, both the pair-wise comparison preference information over alternatives and the evaluation information of alternatives with criteria are represented by the HFEs. Based on the incomplete pair-wise preference judgments over alternatives, we propose the concepts of the hesitant fuzzy consistency and inconsistency indices. Furthermore, we construct a hesitant fuzzy mathematical programming model to derive the weights of criteria and the positive-ideal solution. In this hesitant fuzzy programming model both the objective function and partial constraints’ coefficients take the form of HFEs, and an effective approach based on the ranking method of HFEs is further developed to solve the new derived model. To address the incomplete and inconsistent preference structures of criteria weights, we introduce several deviation variables and establish the bi-objective nonlinear programming model. At length, we employ a green supplier selection problem to illustrate the feasibility and applicability of the proposed technique and conduct a comparison analysis to validate its effectiveness.

Suggested Citation

  • Xiaolu Zhang & Zeshui Xu & Xiaoming Xing, 2016. "Hesitant fuzzy programming technique for multidimensional analysis of hesitant fuzzy preferences," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(3), pages 789-817, July.
    • Handle: RePEc:spr:orspec:v:38:y:2016:i:3:d:10.1007_s00291-015-0420-0
    DOI: 10.1007/s00291-015-0420-0
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    References listed on IDEAS

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    1. Wan, Shu-Ping & Li, Deng-Feng, 2013. "Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees," Omega, Elsevier, vol. 41(6), pages 925-940.
    2. V. Srinivasan & Allan Shocker, 1973. "Linear programming techniques for multidimensional analysis of preferences," Psychometrika, Springer;The Psychometric Society, vol. 38(3), pages 337-369, September.
    3. Park, Kyung Sam & Kim, Soung Hie, 1997. "Tools for interactive multiattribute decisionmaking with incompletely identified information," European Journal of Operational Research, Elsevier, vol. 98(1), pages 111-123, April.
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    Cited by:

    1. Xiaoyue Liu & Dawei Ju, 2021. "Hesitant Fuzzy 2-Dimension Linguistic Programming Technique for Multidimensional Analysis of Preference for Multicriteria Group Decision Making," Mathematics, MDPI, vol. 9(24), pages 1-23, December.
    2. Galo, Nadya Regina & Calache, Lucas Daniel Del Rosso & Carpinetti, Luiz Cesar Ribeiro, 2018. "A group decision approach for supplier categorization based on hesitant fuzzy and ELECTRE TRI," International Journal of Production Economics, Elsevier, vol. 202(C), pages 182-196.
    3. Xiaolu Zhang, 2016. "New Interval-Valued Intuitionistic Fuzzy Behavioral MADM Method and Its Application in the Selection of Photovoltaic Cells," Energies, MDPI, vol. 9(10), pages 1-20, October.

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