Search Advanced

AIMS Mathematics

2024, Volume 9, Issue 10: 28870-28894. doi: 10.3934/math.20241401
Previous Article Next Article
Research article

Managing incomplete general hesitant linguistic preference relations and their application

  • School of Computer and Software, Nanjing Vocational University of Industry Technology, Nanjing, 210023, China
  • Received: 26 August 2024 Revised: 19 September 2024 Accepted: 29 September 2024 Published: 14 October 2024

  • MSC : 03E72, 94D05

  • Hesitant linguistic preference relations (HLPRs) are useful tools for decision makers (DMs) to express their qualitative judgements. However, the traditional HLPRs have one prominent drawback, which is to sort the linguistic values in a hesitant linguistic set. This will distort the DMs' initial judgements. In the present paper, a revised definition of HLPR, called general HLPR (GHLPR), was proposed. A characterization was explored for LPRs. Then, the characterization was extended to GHLPRs. Based on the characterization, the estimation of unknown entries in incomplete GHLPRs were carried out by two algorithms. The group decision-making problems with incomplete GHLPRs were settled by another algorithm. Finally, a case study was illustrated, and comparisons showed that our methods were more reasonable than the existent methods.

    Citation: Lei Zhao. Managing incomplete general hesitant linguistic preference relations and their application[J]. AIMS Mathematics, 2024, 9(10): 28870-28894. doi: 10.3934/math.20241401

    Related Papers:

  • Hesitant linguistic preference relations (HLPRs) are useful tools for decision makers (DMs) to express their qualitative judgements. However, the traditional HLPRs have one prominent drawback, which is to sort the linguistic values in a hesitant linguistic set. This will distort the DMs' initial judgements. In the present paper, a revised definition of HLPR, called general HLPR (GHLPR), was proposed. A characterization was explored for LPRs. Then, the characterization was extended to GHLPRs. Based on the characterization, the estimation of unknown entries in incomplete GHLPRs were carried out by two algorithms. The group decision-making problems with incomplete GHLPRs were settled by another algorithm. Finally, a case study was illustrated, and comparisons showed that our methods were more reasonable than the existent methods.



    加载中


    [1] T. L. Saaty, The analytic hierarchy process, New York: McGraw-Hill, 1980. https://doi.org/10.21236/ADA214804
    [2] T. Tanino, Fuzzy preference orderings in group decision making, Fuzzy Set. Syst., 12 (1984), 117–131. https://doi.org/10.1016/0165-0114(84)90032-0 doi: 10.1016/0165-0114(84)90032-0
    [3] C. C. Li, Y. C. Dong, Y. J. Xu, F. Chiclana, E. Herrera-Viedma, F. Herrera, An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and fusion: Taxonomy and future directions, Inform. Fusion, 52 (2019), 143–156. https://doi.org/10.1016/j.inffus.2018.12.004 doi: 10.1016/j.inffus.2018.12.004
    [4] Y. J. Xu, Q. Q. Wang, F. Chiclana, E. Herrera-Viedma, A local adjustment method to improve multiplicative consistency of fuzzy reciprocal preference relations, IEEE Trans. Syst. Man Cy.-S., 53 (2023), 5702–5714. https://doi.org/10.1109/TSMC.2023.3275167 doi: 10.1109/TSMC.2023.3275167
    [5] M. Q. Li, Z. Y. Wang, Y. J. Xu, W. J. Dai, Two-stage group decision making methodology with hesitant fuzzy preference relations under social network: Multiplicative consistency determination and personalized feedback, Inform. Sciences, 681 (2024), 121155. https://doi.org/10.1016/j.ins.2024.121155 doi: 10.1016/j.ins.2024.121155
    [6] X. Liu, Y. Y. Zhang, Y. J. Xu, M. Q. Li, E. Herrera-Viedma, A consensus model for group decision-making with personalized individual self-confidence and trust semantics: A perspective on dynamic social network interactions, Inform. Sciences, 627 (2023), 147–168. https://doi.org/10.1016/j.ins.2023.01.087 doi: 10.1016/j.ins.2023.01.087
    [7] F. Herrera, A sequential selection process in group decision making with a linguistic assessment approach, Inform. Sciences, 85 (1995), 223–239. https://doi.org/10.1016/0020-0255(95)00025-K doi: 10.1016/0020-0255(95)00025-K
    [8] V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst., 25 (2010), 529–539. https://doi.org/10.1002/int.20418 doi: 10.1002/int.20418
    [9] M. W. Jang, J. H. Park, M. J. Son, Probabilistic picture hesitant fuzzy sets and their application to multi-criteria decision-making, AIMS Math., 8 (2023), 8522–8559. https://doi.org/10.3934/math.2023429 doi: 10.3934/math.2023429
    [10] A. Nazra, Jenison, Y. Asdi, Zulvera, Generalized hesitant intuitionistic fuzzy N-soft sets-first result, AIMS Math., 7 (2022), 12650–12670. https://doi.org/10.3934/math.2022700 doi: 10.3934/math.2022700
    [11] W. Y. Zeng, R. Ma, D. Q. Li, Q. Yin, Z. S. Xu, A. M. Khalil, Novel operations of weighted hesitant fuzzy sets and their group decision making application, AIMS Math., 7 (2022), 14117–14138. https://doi.org/10.3934/math.2022778 doi: 10.3934/math.2022778
    [12] A. Dey, T. Senapati, M. Pal, G. Y. Chen, A novel approach to hesitant multi-fuzzy soft set based decision-making, AIMS Math., 5 (2020), 1985–2008. https://doi.org/10.3934/math.2020132 doi: 10.3934/math.2020132
    [13] R. M. Rodríguez, L. Martı́nez, F. Herrera, Hesitant fuzzy linguistic term sets for decision making, IEEE T. Fuzzy Syst., 20 (2012), 109–119. https://doi.org/10.1109/TFUZZ.2011.2170076 doi: 10.1109/TFUZZ.2011.2170076
    [14] M. M. Xia, Z. S. Xu, Managing hesitant information in GDM problems under fuzzy and multiplicative preference relations, Int. J. Uncertain. Fuzz., 21 (2013), 865–897. https://doi.org/10.1142/S0218488513500402 doi: 10.1142/S0218488513500402
    [15] Y. J. Xu, W. J. Dai, J. Huang, M. Q. Li, E. Herrera-Viedma, Some models to manage additive consistency and derive priority weights from hesitant fuzzy preference relations, Inform. Sciences, 586 (2022), 450–467. https://doi.org/10.1016/j.ins.2021.12.002 doi: 10.1016/j.ins.2021.12.002
    [16] Y. J. Xu, M. Q. Li, F. Chiclana, E. Herrera-Viedma, Multiplicative consistency ascertaining, inconsistency repairing, and weights derivation of hesitant multiplicative preference relations, IEEE T. Syst. Man Cy-S., 52 (2022), 6806–6821. https://doi.org/10.1109/TSMC.2021.3099862 doi: 10.1109/TSMC.2021.3099862
    [17] B. Zhu, Z. S. Xu, Consistency measures for hesitant fuzzy linguistic preference relation, IEEE T. Fuzzy Syst., 22 (2014), 35–45. https://doi.org/10.1109/TFUZZ.2013.2245136 doi: 10.1109/TFUZZ.2013.2245136
    [18] Z. M. Zhang, C. Wu, On the use of multiplicative consistency in hesitant fuzzy linguistic preference relations, Knowl.-Based Syst., 72 (2014), 13–27. http://dx.doi.org/10.1016/j.knosys.2014.08.026 doi: 10.1016/j.knosys.2014.08.026
    [19] Z. B. Wu, J. P. Xu, Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations, Omega, 65 (2016), 28–40. http://dx.doi.org/10.1016/j.omega.2015.12.005 doi: 10.1016/j.omega.2015.12.005
    [20] X. Chen, L. J. Peng, Z. B. Wu, W. Pedrycz, Controlling the worst consistency index for hesitant fuzzy linguistic preference relations in consensus optimization models, Comput. Ind. Eng., 143 (2020), 106423. https://doi.org/10.1016/j.cie.2020.106423 doi: 10.1016/j.cie.2020.106423
    [21] C. L. Zheng, Y. Y. Zhou, L. G. Zhou, H. Y. Chen, Clustering and compatibility-based approach for large-scale group decision making with hesitant fuzzy linguistic preference relations: An application in e-waste recycling, Expert Syst. with Appl., 197 (2022), 116615. https://doi.org/10.1016/j.eswa.2022.116615 doi: 10.1016/j.eswa.2022.116615
    [22] P. Wu, L. G. Zhou, H. Y. Chen, Z. F. Tao, Additive consistency of hesitant fuzzy linguistic preference relation with a new expansion principle for hesitant fuzzy linguistic term sets, IEEE T. Fuzzy Syst., 27 (2019), 716–730. https://doi.org/10.1109/TFUZZ.2018.2868492 doi: 10.1109/TFUZZ.2018.2868492
    [23] Y. J. Xu, F. J. Cabrerizo, E. Herrera-Viedma, A consensus model for hesitant fuzzy preference relations and itsapplication in water allocation management, Appl. Soft Comput., 58 (2017), 265–284. https://doi.org/10.1016/j.asoc.2017.04.068 doi: 10.1016/j.asoc.2017.04.068
    [24] C. C. Li, R. M. Rodríguez, F. Herrera, L. Martínez, Y. C. Dong, Consistency of hesitant fuzzy linguistic preference relations: An interval consistency index, Inform. Sciences, 432 (2018), 347–361. https://doi.org/10.1016/j.ins.2017.12.018 doi: 10.1016/j.ins.2017.12.018
    [25] C. C. Li, R. M. Rodríguez, L. Martínez, Y. C. Dong, F. Herrera, Personalized individual semantics based on consistency in hesitant linguistic group decision making with comparative linguistic expressions, Knowl.-Based Syst., 145 (2018), 156–165. https://doi.org/10.1016/j.knosys.2018.01.011 doi: 10.1016/j.knosys.2018.01.011
    [26] Y. J. Xu, X. W. Wen, H. Sun, H. M. Wang, Consistency and consensus models with local adjustment strategy for hesitant fuzzy linguistic preference relations, Int. J. Fuzzy Syst., 20 (2018), 2216–2233. https://doi.org/10.1007/s40815-017-0438-3 doi: 10.1007/s40815-017-0438-3
    [27] H. B. Liu, L. Jiang, Optimizing consistency and consensus improvement process for hesitant fuzzy linguistic preference relations and the application in group decision making, Inform. Fusion, 56 (2020), 114–127. https://doi.org/10.1016/j.inffus.2019.10.002 doi: 10.1016/j.inffus.2019.10.002
    [28] M. Fedrizz, S. Giove, Incomplete pairwise comparison and consistency optimization, Eur. J. Oper. Res., 183 (2007), 303–313. https://doi.org/10.1016/j.ejor.2006.09.065 doi: 10.1016/j.ejor.2006.09.065
    [29] Z. S. Xu, Incomplete linguistic preference relations and their fusion, Inform. Fusion, 7 (2006), 331–337. https://doi.org/10.1016/j.inffus.2005.01.003 doi: 10.1016/j.inffus.2005.01.003
    [30] Y. J. Xu, C. Y. Li, X. W. Wen, Missing values estimation and consensus building for incomplete hesitant fuzzy preference relations with multiplicative consistency, Int. J. Comput. Int. Syst., 11 (2018), 101–119. https://doi.org/10.2991/ijcis.11.1.9 doi: 10.2991/ijcis.11.1.9
    [31] Y. L. Lu, Y. J. Xu, E. Herrera-Viedma, Consensus progress for large-scale group decision making in social networks with incomplete probabilistic hesitant fuzzy information, Appl. Soft Comput., 126 (2022), 109249. https://doi.org/10.1016/j.asoc.2022.109249 doi: 10.1016/j.asoc.2022.109249
    [32] Y. L. Lu, Y. J. Xu, J. Huang, J. Wei, Social network clustering and consensus-based distrust behaviors management for large-scale group decision-making with incomplete hesitant fuzzy preference relations, Appl. Soft Comput., 117 (2022), 108373. https://doi.org/10.1016/j.asoc.2021.108373 doi: 10.1016/j.asoc.2021.108373
    [33] J. Huang, Y. J. Xu, X. W. Wen, X. T. Zhu, E. Herrera-Viedma, Deriving priorities from the fuzzy best-worst method matrix and its applications: A perspective of incomplete reciprocal preference relation, Inform. Sciences, 634 (2023), 761–778. https://doi.org/10.1016/j.ins.2023.03.125 doi: 10.1016/j.ins.2023.03.125
    [34] P. Wu, H. Y. Li, J. M. Merigó, L. G. Zhou, Integer programming modeling on group decision making with incomplete hesitant fuzzy linguistic preference relations, IEEE Access, 7 (2019), 136867–136881. https://doi.org/10.1109/ACCESS.2019.2942412 doi: 10.1109/ACCESS.2019.2942412
    [35] H. B. Liu, Y. Ma, L. Jiang, Managing incomplete preferences and consistency improvement in hesitant fuzzy linguistic preference relations with applications in group decision making, Inform. Fusion, 51 (2019), 19–29. https://doi.org/10.1016/j.inffus.2018.10.011 doi: 10.1016/j.inffus.2018.10.011
    [36] Z. L. Li, Z. Zhang, W. Y. Yu, Consensus reaching with consistency control in group decision making with incomplete hesitant fuzzy linguistic preference relations, Comput. Ind. Eng., 170 (2022), 108311. https://doi.org/10.1016/j.cie.2022.108311 doi: 10.1016/j.cie.2022.108311
    [37] P. J. Ren, Z. N. Hao, X. X. Wang, X. J. Zeng, Z. S. Xu, Decision-making models based on incomplete hesitant fuzzy linguistic preference relation with application to site selection of hydropower stations, IEEE T. Eng. Manage., 69 (2022), 904–915. https://doi.org/10.1109/TEM.2019.2962180 doi: 10.1109/TEM.2019.2962180
    [38] Y. M. Song, G. X. Li, A mathematical programming approach to manage group decision making with incomplete hesitant fuzzy linguistic preference relations, Comput. Ind. Eng., 135 (2019), 467–475. https://doi.org/10.1016/j.cie.2019.06.036 doi: 10.1016/j.cie.2019.06.036
    [39] F. Herrera, E. Herrera-Viedma, J. L. Verdegay, Direct approach processes in group decision making using linguistic OWA operators, Fuzzy Set. Syst., 79 (1994), 175–190. https://doi.org/10.1016/0165-0114(95)00162-X doi: 10.1016/0165-0114(95)00162-X
    [40] Z. S. Xu, A method based on linguistic aggregation operators for group decision making with linguistic preference relations, Inform. Sciences, 166 (2004), 19–30. https://doi.org/10.1016/j.ins.2003.10.006 doi: 10.1016/j.ins.2003.10.006
    [41] Y. C. Dong, Xu, Y. F., H. Y. Li, On consistency measures of linguistic preference relations, Eur. J. Oper. Res., 189 (2008), 430–444. https://doi.org/10.1016/j.ejor.2007.06.013 doi: 10.1016/j.ejor.2007.06.013
    [42] H. Wang, Extended hesitant fuzzy linguistic term sets and their aggregation in group decision making, Int. J. Comput. Int. Syst., 8 (2015), 14–33. https://doi.org/10.1016/j.ejor.2007.06.013 doi: 10.1016/j.ejor.2007.06.013
    [43] H. C. Liao, Z. S. Xu, X.-J. Zeng, J. M. Merigó, Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets, Knowl.-Based Syst., 76 (2015), 127–138. http://dx.doi.org/10.1016/j.knosys.2014.12.009 doi: 10.1016/j.knosys.2014.12.009
    [44] E. Herrera-Viedma, F. Herrera, F. Chiclana, M. Luque, Some issues on consistency of fuzzy preference relations, Eur. J. Oper. Res., 154 (2004), 98–109. https://doi.org/10.1016/S0377-2217(02)00725-7 doi: 10.1016/S0377-2217(02)00725-7
    [45] Y. J. Xu, K. W. Li, H. M. Wang, Incomplete interval fuzzy preference relations and their applications, Comput. Ind. Eng., 67 (2014), 93–103. https://doi.org/10.1016/j.cie.2013.10.010 doi: 10.1016/j.cie.2013.10.010
    [46] M. Tang, H. C. Liao, Z. M. Li, Z. S. Xu, Nature disaster risk evaluation with a group decision making method based on incomplete hesitant fuzzy linguistic preference relations, Int. J. Env. Res. Pub. He, 15 (2018), 751. https://doi.org/10.3390/ijerph15040751 doi: 10.3390/ijerph15040751
    [47] Y. J. Xu, F. Ma, F. Tao, H. M. Wang, Some methods to deal with unacceptable incomplete 2-tuple fuzzy linguistic preference relations in group decision making, Knowl.-Based Syst., 56 (2014), 179–190. http://dx.doi.org/10.1016/j.knosys.2013.11.008 doi: 10.1016/j.knosys.2013.11.008
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(25) PDF downloads(1) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(2)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog