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A novel distance-based multiple attribute decision-making with hesitant fuzzy sets

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Abstract

Up to now, various types of distance measures have been developed and investigated in-depth for hesitant fuzzy sets (HFSs). The analytical study of the existing distance measures for HFSs shows that they have still some limitations. In an attempt to overcome the limitations, this study develops a class of Hausdorff-based distances to measure the distance among HFSs which are not restricted to the same length of their hesitant fuzzy elements (HFEs) and of course the arranging order of values in the HFEs. Furthermore, these HFS distance measures do satisfy all well-known and essential axioms, specially, the triangle inequality property. Eventually, we present some examples to illustrate the efficiency of the new developed HFS distance measures together with a comparative analysis with other existing ones.

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References

  • Cabrerizo FJ, Al-Hmouz R, Morfeq A, Balamash AS, Martinez MA, Herrera-Viedma E (2017) Soft consensus measures in group decision making using unbalanced fuzzy linguistic information. Soft Comput 21:3037–3050

    Article  Google Scholar 

  • Dong Y, Chen X, Herrera F (2015) Minimizing adjusted simple terms in the consensus reaching process with hesitant linguistic assessments in group decision making. Inf Sci 297:95–117

    Article  MathSciNet  Google Scholar 

  • Dubuisson MP, Jain AK (1994) A modified Hausdorff distance for object matching. In: Proceedings of the 12th IAPR international conference on pattern recognition vol 1, pp 566–568

  • Farhadinia B (2013a) Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf Sci 240:129–144

    Article  MathSciNet  Google Scholar 

  • Farhadinia B (2013b) A novel method of ranking hesitant fuzzy values for multiple attribute decision-making problems. Int J Intell Syst 28:752–767

    Article  Google Scholar 

  • Farhadinia B (2014a) Distance and similarity measures for higher order hesitant fuzzy sets. Knowl Based Syst 55:43–48

    Article  Google Scholar 

  • Farhadinia B (2014b) A series of score functions for hesitant fuzzy sets. Inf Sci 277:102–110

    Article  MathSciNet  Google Scholar 

  • Farhadinia B (2016) Hesitant fuzzy set lexicographical ordering and its application to multi-attribute decision making. Inf Sci 327:233–245

    Article  MathSciNet  Google Scholar 

  • Farhadinia B, Herrera-Viedma E (2018) Sorting of decision-making methods based on their outcomes using dominance-vector hesitant fuzzy-based distance. Soft Comput. https://doi.org/10.1007/s00500-018-3143-8

    Article  MATH  Google Scholar 

  • Farhadinia B, Xu ZS (2017) Distance and aggregation-based methodologies for hesitant fuzzy decision making. Cognit Comput 9:81–94

    Article  Google Scholar 

  • Farhadinia B, Xu ZS (2019) Information measures for hesitant fuzzy sets and their extensions. Springer, Berlin

    Book  Google Scholar 

  • Hua T (2017) Model for evaluating the classification modes of the China’s college entrance examination with hesitant fuzzy information. Int J Knowl Based Intell Eng Syst 21:265–272

    Article  Google Scholar 

  • Hu J, Zhang X, Chen X, Liu Y (2016) Hesitant fuzzy information measures and their applications in multi-criteria decision making. Int J Syst Sci 47:62–76

    Article  MathSciNet  Google Scholar 

  • Hu J, Yang Y, Zhang X, Chen X (2018) Similarity and entropy measures for hesitant fuzzy sets. Int Trans Oper Res 25:857–886

    Article  MathSciNet  Google Scholar 

  • Li DQ, Zeng WY, Zhao YB (2015a) Note on distance measure of hesitant fuzzy sets. Inf Sci 321:103–115

    Article  MathSciNet  Google Scholar 

  • Li DQ, Zeng WY, Li JH (2015b) New distance and similarity measures on hesitant fuzzy sets and their applications in multiple criteria decision making. Eng Appl Artif Intell 40:11–16

    Article  Google Scholar 

  • Li CC, Rodriguez RM, Martinez L, Dong Y, Herrera F (2018) Consistency of hesitant fuzzy linguistic preference relations: an interval consistency index. Inf Sci 432:347–361

    Article  MathSciNet  Google Scholar 

  • Liu PD, Tang GL (2016) Multi-criteria group decision-making based on interval neutrosophic uncertain linguistic variables and Choquet integral. Cognit Comput 8:1036–56

    Article  Google Scholar 

  • Meng FY, Wang C, Chen XH (2016) Linguistic interval hesitant fuzzy sets and their application in decision making. Cognit Comput 8:52–68

    Article  Google Scholar 

  • Moral MJD, Chiclana F, Tapia JM, Herrera-Viedma E (2018) A comparative study on consensus measures in group decision making. Int J Intell Syst 33:1624–1638

    Article  Google Scholar 

  • Peng DH, Gao CY, Gao ZF (2013) Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision making. Appl Math Model 37:5837–5850

    Article  MathSciNet  Google Scholar 

  • Rodriguez RM, Bedregal B, Bustince H, Dong YC, Farhadinia B, Kahraman C, Martinez L, Torra V, Xu YJ, Xu ZS, Herrera F (2016) A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress. Inf Fus 29:89–97

    Article  Google Scholar 

  • Tang X, Peng Z, Ding H, Cheng M, Yang S (2018) Novel distance and similarity measures for hesitant fuzzy sets and their applications to multiple attribute decision making. J Intell Fuzzy Syst 34:3903–3916

    Article  Google Scholar 

  • Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539

    MATH  Google Scholar 

  • Wu Y, Li CC, Chen X, Dong Y (2018) Group decision making based on linguistic distributions and hesitant assessments: maximizing the support degree with an accuracy constraint. Inf Fusion 41:151–160

    Article  Google Scholar 

  • Xia MM, Xu ZS (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52:395–407

    Article  MathSciNet  Google Scholar 

  • Xu ZS (2012) Linguistic decision making: theory and methods. Science Press, Beijing

    Book  Google Scholar 

  • Xu ZS, Xia MM (2011) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181:2128–2138

    Article  MathSciNet  Google Scholar 

  • Zeng WY, Li DQ, Yin Q (2016) Distance and similarity measures between hesitant fuzzy sets and their application in pattern recognition. Pattern Recognit Lett 84:267–271

    Article  Google Scholar 

  • Zhang XL, Xu ZS (2015) Novel distance and similarity measures on hesitant fuzzy sets with applications to clustering analysis. J Intell Fuzzy Syst 28:2279–2296

    MathSciNet  Google Scholar 

  • Zhao N, Xu ZS, Liu FJ (2016) Group decision making with dual hesitant fuzzy preference relations. Cognit Comput 8:1119–43

    Article  Google Scholar 

  • Zhou XQ, Li QG (2012) Some new similarity measures for hesitant fuzzy sets and their applications in multiple attribute decision making. Comput Res Repos. arXiv:1211.4125

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Authors and Affiliations

  1. Department of Mathematics, Quchan University of Technology, Quchan, Iran

    Bahram Farhadinia

  2. Business School, Sichuan University, Chengdu, 610064, People’s Republic of China

    Zeshui Xu

Authors
  1. Bahram Farhadinia
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  2. Zeshui Xu
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Correspondence to Bahram Farhadinia.

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Communicated by V. Loia.

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Farhadinia, B., Xu, Z. A novel distance-based multiple attribute decision-making with hesitant fuzzy sets. Soft Comput 24, 5005–5017 (2020). https://doi.org/10.1007/s00500-019-04250-6

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