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A Multi-Criteria Decision-Making Method Based on Heronian Mean Operators Under a Linguistic Hesitant Fuzzy Environment

Author

Listed:
  • Su-Min Yu

    (Business School, Central South University, Lushan South Road, Changsha 410083, P. R. China)

  • Huan Zhou

    (Business School, Central South University, Lushan South Road, Changsha 410083, P. R. China)

  • Xiao-Hong Chen

    (Business School, Central South University, Lushan South Road, Changsha, 410083, P. R. China)

  • Jian-Qiang Wang

    (Business School, Central South University, Lushan South Road, Changsha 410083, P. R. China)

Abstract

Linguistic hesitant fuzzy sets (LHFSs) are a very useful and appropriate means of expressing preferences of decision-makers; moreover their basic operations and comparison methods have been defined and applied to the solving of MCDM problems. However, there are a number of limitations in the related studies. In this paper, using information from existing studies, several new operations and a new order relationship are defined; moreover four linguistic hesitant fuzzy Heronian mean operators are proposed: the linguistic hesitant fuzzy arithmetic Heronian mean (LHFAHM) operator; the linguistic hesitant fuzzy weighted arithmetic Heronian mean (LHFWAHM) operator; the linguistic hesitant fuzzy geometric Heronian mean (LHFGHM) operator; and the linguistic hesitant fuzzy weighted geometric Heronian mean (LHFWGHM) operator. Furthermore, some useful and desirable properties of these operators are analyzed in some special cases, with respect to the different parameter values in these operators, are discussed. Additionally, an approach based on the LHFWAHM and LHFWGHM operators for solving MCDM problems is proposed. Finally, an illustrative example is provided to verify the validity and feasibility of the proposed approaches, and a comparison analysis is also presented to demonstrate the influences of different parameters on the results of decision-making.

Suggested Citation

  • Su-Min Yu & Huan Zhou & Xiao-Hong Chen & Jian-Qiang Wang, 2015. "A Multi-Criteria Decision-Making Method Based on Heronian Mean Operators Under a Linguistic Hesitant Fuzzy Environment," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(05), pages 1-35.
    • Handle: RePEc:wsi:apjorx:v:32:y:2015:i:05:n:s0217595915500359
    DOI: 10.1142/S0217595915500359
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    Citations

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    Cited by:

    1. Qian-Yun Tan & Cui-Ping Wei & Qi Liu & Xiang-Qian Feng, 2016. "The Hesitant Fuzzy Linguistic TOPSIS Method Based on Novel Information Measures," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-22, October.
    2. R. Krishankumar & K. S. Ravichandran & J. Premaladha & Samarjit Kar & Edmundas Kazimieras Zavadskas & Jurgita Antucheviciene, 2018. "A Decision Framework under a Linguistic Hesitant Fuzzy Set for Solving Multi-Criteria Group Decision Making Problems," Sustainability, MDPI, vol. 10(8), pages 1-21, July.
    3. Wu-E Yang & Chao-Qun Ma & Zhi-Qiu Han, 2017. "Linguistic multi-criteria decision-making with representing semantics by programming," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(2), pages 225-235, January.
    4. Mei Tang & Jie Wang & Jianping Lu & Guiwu Wei & Cun Wei & Yu Wei, 2019. "Dual Hesitant Pythagorean Fuzzy Heronian Mean Operators in Multiple Attribute Decision Making," Mathematics, MDPI, vol. 7(4), pages 1-27, April.
    5. Minghua Shi & Yuewen Xiao & Qing Wan, 2019. "Extended Heronian Mean Based on Hesitant Fuzzy Linguistic Information for Multiple Attribute Group Decision-Making," Complexity, Hindawi, vol. 2019, pages 1-19, August.
    6. Zengxian Li & Guiwu Wei & Hui Gao, 2018. "Methods for Multiple Attribute Decision Making with Interval-Valued Pythagorean Fuzzy Information," Mathematics, MDPI, vol. 6(11), pages 1-27, October.

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