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AIMS Mathematics

2021, Volume 6, Issue 6: 6603-6629. doi: 10.3934/math.2021389
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Research article

A group decision making method considering both the consistency and consensus of intuitionistic multiplicative preference relations

  • 1.
    School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, China
  • 2.
    Business School, Shandong University of Technology, Zibo 255049, China
  • Received: 20 February 2021 Accepted: 12 April 2021 Published: 16 April 2021

  • MSC : 03E72, 90B50

  • This paper aims to develop a new group decision making (GDM) approach with intuitionistic multiplicative preference relations (IMPRs) by considering the consistency and consensus. Using the distance between a given IMPR and its corresponding underlying consistent IMPR, the concept of acceptably consistent IMPR is introduced, then an automatic algorithm is designed to repair the inconsistent IMPR to be of acceptable consistency. Meanwhile, each decision maker's consensus level is evaluated by the deviation between his/her individual IMPR and the group IMPR, and another algorithm for reaching acceptable level of consensus is provided. Moreover, the consensus improving process can guarantee that the modified IMPRs still be acceptably consistent, then the normalized intuitionistic multiplicative priority weight vector can be obtained from a mathematical programming model. A step-by-step algorithm based on the consistency and consensus of IMPRs is offered. Finally, two examples and the corresponding comparative analyses are presented to demonstrate the effectiveness of the proposed method.

    Citation: Tao Li, Liyuan Zhang. A group decision making method considering both the consistency and consensus of intuitionistic multiplicative preference relations[J]. AIMS Mathematics, 2021, 6(6): 6603-6629. doi: 10.3934/math.2021389

    Related Papers:

  • This paper aims to develop a new group decision making (GDM) approach with intuitionistic multiplicative preference relations (IMPRs) by considering the consistency and consensus. Using the distance between a given IMPR and its corresponding underlying consistent IMPR, the concept of acceptably consistent IMPR is introduced, then an automatic algorithm is designed to repair the inconsistent IMPR to be of acceptable consistency. Meanwhile, each decision maker's consensus level is evaluated by the deviation between his/her individual IMPR and the group IMPR, and another algorithm for reaching acceptable level of consensus is provided. Moreover, the consensus improving process can guarantee that the modified IMPRs still be acceptably consistent, then the normalized intuitionistic multiplicative priority weight vector can be obtained from a mathematical programming model. A step-by-step algorithm based on the consistency and consensus of IMPRs is offered. Finally, two examples and the corresponding comparative analyses are presented to demonstrate the effectiveness of the proposed method.


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    [1] R. Urena, F. Chiclana, J. A. Morente-Molinera, E. Herrera-Viedma, Managing incomplete preference relations in decision making: A review and future trends, Inform. Sciences, 302 (2015), 14–32. doi: 10.1016/j.ins.2014.12.061
    [2] S. A. Orlovsky, Decision-making with a fuzzy preference relation, Fuzzy Set. Syst., 1 (1978), 155–167. doi: 10.1016/0165-0114(78)90001-5
    [3] T. L. Saaty, The Analytic Hierarchy Process, McGraw-Hill, New York, 1980.
    [4] Z. S. Xu, Deviation measures of linguistic preference relations in group decision making, Omega, 33 (2005), 249–254. doi: 10.1016/j.omega.2004.04.008
    [5] J. Tang, F. Y. Meng, S. L. Zhang, Consistency comparison analysis of decision making with intuitionistic fuzzy preference relations, IEEE T. Eng. Manage., 2019, https://doi.org/10.1109/TEM.2019.2919559.
    [6] M. M. Xia, Z. S. Xu, H. C. Liao, Preference relations based on intuitionistic multiplicative information, IEEE T. Fuzzy Syst., 21 (2013), 113–133. doi: 10.1109/TFUZZ.2012.2202907
    [7] F. F. Jin, Z. W. Ni, L. D. Pei, H. Y. Chen, Y. P. Li, X. H. Zhu, et al. A decision support model for group decision making with intuitionistic fuzzy linguistic preference relations, Neural Comput. Appl., 31 (2019), 1103–1124.
    [8] F. Y. Meng, J. Tang, Y. L. Zhang, Programming model-based group decision making with multiplicative linguistic intuitionistic fuzzy preference relations, Comput. Ind. Eng., 136 (2019), 212–224. doi: 10.1016/j.cie.2019.07.019
    [9] Y. M. Song, G. X. Li, D. Ergu, N. Liu, An optimisation-based method to conduct consistency and consensus in group decision making under probabilistic uncertain linguistic preference relations, J. Oper. Res. Soc., 2021, https://doi.org/10.1080/01605682.2021.1873079.
    [10] H. C. Liao, Z. S. Xu, M. M. Xia, Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making, Int. J. Inf. Tech. Decis., 13 (2014), 47–76. doi: 10.1142/S0219622014500035
    [11] 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. doi: 10.1016/j.cie.2019.06.036
    [12] G. X. Li, G. Kou, Y. Peng, A group decision making model for integrating heterogeneous information, IEEE Trans. Syst. Man Cybern. syst., 48 (2016), 982–992.
    [13] F. Y. Meng, S. M. Chen, R. P. Yuan, Group decision making with heterogeneous intuitionistic fuzzy preference relations, Inform. Sciences, 523 (2020), 197–219. doi: 10.1016/j.ins.2020.03.010
    [14] G. X. Li, G. Kou, Y. H. Li, Y. Peng, A group decision making approach for supplier selection with multi-period fuzzy information and opinion interaction among decision makers, J. Oper. Res. Soc., 2021, https://doi.org/10.1080/01605682.2020.1869917.
    [15] F. Y. Meng, J. Tang, F. Hamido, Linguistic intuitionistic fuzzy preference relations and their application to multi-criteria decision making, Inform. Fusion, 46 (2019), 77–90. doi: 10.1016/j.inffus.2018.05.001
    [16] H. Y. Wu, P. J. Ren, Z. S. Xu, Addressing site selection for earthquake shelters with hesitant multiplicative linguistic preference relation, Inform. Sciences, 516 (2020), 370–387. doi: 10.1016/j.ins.2019.12.059
    [17] E. Szmidt, J. Kacprzyk, A consensus-reaching process under intuitionistic fuzzy preference relations, Int. J. Intell. Syst., 18 (2003), 837–852. doi: 10.1002/int.10119
    [18] B. Zhu, Z. S. Xu, J. P. Xu, Deriving a ranking from hesitant fuzzy preference relations under group decision making, IEEE T. Cybernetics, 44 (2014), 1328–1337. doi: 10.1109/TCYB.2013.2283021
    [19] M. M. Xia, Z. S. Xu, Group decision making based on intuitionistic multiplicative aggregation operators, Appl. Math. Model., 37 (2013), 5120–5133. doi: 10.1016/j.apm.2012.10.029
    [20] D. J. Yu, L. C. Fang, Intuitionistic multiplicative aggregation operators with their application in group decision making, J. Intell. Fuzzy Syst., 27 (2014), 131–142. doi: 10.3233/IFS-130984
    [21] Y. Jiang, Z. S. Xu, Aggregating information and ranking alternatives in decision making with intuitionistic multiplicative preference relations, Appl. Soft Comput., 22 (2014), 162–177. doi: 10.1016/j.asoc.2014.04.043
    [22] W. Y. Qian, L. L. Niu, Intuitionistic multiplicative preference relation and its application in group decision making, J. Intell. Fuzzy Syst., 30 (2016), 2859–2870. doi: 10.3233/IFS-151836
    [23] Z. M. Ma, Z. S. Xu, Hyperbolic scales involving appetites-based intuitionistic multiplicative preference relations for group decision making, Inform. Sciences, 451 (2018), 310–325.
    [24] H. Garg, Generalized interaction aggregation operators in intuitionistic fuzzy multiplicative preference environment and their application to multicriteria decision-making, Appl. Intell., 48 (2018), 2120–2136. doi: 10.1007/s10489-017-1066-1
    [25] M. M. Xia, Z. S. Xu, J. Chen, Algorithms for improving consistency or consensus of reciprocal [0, 1]-valued preference relations, Fuzzy Set. Syst., 216 (2013), 108–133. doi: 10.1016/j.fss.2012.09.016
    [26] Z. S. Xu, Priority weight intervals derived from intuitionistic multiplicative preference relations, IEEE T. Fuzzy Syst., 21 (2013), 642–654. doi: 10.1109/TFUZZ.2012.2226893
    [27] Y. Jiang, Z. S. Xu, X. H. Yu, Group decision making based on incomplete intuitionistic multiplicative preference relations, Inform. Sciences, 295 (2015), 33–52. doi: 10.1016/j.ins.2014.09.043
    [28] F. Y. Meng, J. Tang, Z. S. Xu, Deriving priority weights from intuitionistic fuzzy multiplicative preference relations, Int. J. Intell. Syst., 34 (2019), 2937–2969. doi: 10.1002/int.22179
    [29] F. F. Jin, Z. W. Ni, L. D. Pei, H. Y. Chen, Y. p. LI, Goal programming approach to derive intuitionistic multiplicative weights based on intuitionistic multiplicative preference relations, Int. J. Mach. Learn. Cyb., 9 (2018), 641–650. doi: 10.1007/s13042-016-0590-3
    [30] Z. Zhang, C. H. Guo, Deriving priority weights from intuitionistic multiplicative preference relations under group decision-making settings, J. Oper. Res. Soc. 68 (2017), 1582–1599.
    [31] Z. M. Zhang, W. Pedrycz, Models of mathematical programming for intuitionistic multiplicative preference relations, IEEE T. Fuzzy Syst., 25 (2017), 945–957. doi: 10.1109/TFUZZ.2016.2587326
    [32] Z. M. Zhang, W. Pedrycz, Intuitionistic multiplicative group analytic hierarchy process and its use in multicriteria group decision-making, IEEE T. Cybernetics, 48 (2018), 1950–1962. doi: 10.1109/TCYB.2017.2720167
    [33] Z. M. Zhang, S. M. Chen, C. Wang, Group decision making with incomplete intuitionistic multiplicative preference relations, Inform. Sciences, 516 (2020), 560–571. doi: 10.1016/j.ins.2019.12.042
    [34] T. Li, L. Y. Zhang, Z. Y. Yang, Two algorithms for group decision making based on the consistency of intuitionistic multiplicative preference relation, J. Intell. Fuzzy Syst., 38 (2020), 2197–2210. doi: 10.3233/JIFS-190996
    [35] P. J. Ren, Z. S. Xu, H. C. Liao, Intuitionistic multiplicative analytic hierarchy process in group decision making, Comput. Ind. Eng., 101 (2016), 513–524. doi: 10.1016/j.cie.2016.09.025
    [36] X. Yang, Z. J. Wang, A decision making model based on intuitionistic multiplicative preference relations with acceptable consistency, IEEE Access, 7 (2019), 109195–109207. doi: 10.1109/ACCESS.2019.2933457
    [37] W. Yang, S. T. Jhang, S. G. Shi, Z. M. Ma, A novel method to derive the intuitionistic multiplicative priority vector for the intuitionistic multiplicative preference relation, J. Intell. Fuzzy Syst., 39 (2020), 1371–1380. doi: 10.3233/JIFS-200128
    [38] Y. Jiang, Z. S. Xu, X. H. Yu, Compatibility measures and consensus models for group decision making with intuitionistic multiplicative preference relations, Appl. Soft Comput., 13 (2013), 2075–2086. doi: 10.1016/j.asoc.2012.11.007
    [39] C. Y. Xu, Z. M. Ma, Symmetric intuitionistic multiplicative aggregation operator for group decision making in intuitionistic multiplicative environments, J. Intell. Fuzzy Syst., 36 (2019), 5909–5918. doi: 10.3233/JIFS-181735
    [40] C. Zhang, H. C. Liao, L. Luo, Z. S. Xu, Distance-based consensus reaching process for group decision making with intuitionistic multiplicative preference relations, Appl. Soft Comput., 88 (2020), 1–17.
    [41] Z. M. Zhang, W. Pedrycz, Goal programming approaches to managing consistency and consensus for intuitionistic multiplicative preference relations in group decision making, IEEE T. Fuzzy Syst., 26 (2018), 3261–3275. doi: 10.1109/TFUZZ.2018.2818074
    [42] Z. B. Wu, J. P. Xu, A consistency and consensus based decision support model for group decision making with multiplicative preference relations, Decis. Support Syst., 52 (2012), 757–767. doi: 10.1016/j.dss.2011.11.022
    [43] Z. B. Wu, J. P. Xu, A concise consensus support model for group decision making with reciprocal preference relations based on deviation measures, Fuzzy Set. Syst., 206 (2012), 58–73. doi: 10.1016/j.fss.2012.03.016
    [44] H. C. Liao, Z. S. Xu, X. J. Zeng, J. M. Merigo, Framework of group decision making with intuitionistic fuzzy preference information, IEEE T. Fuzzy Syst., 23 (2015), 1211–1226. doi: 10.1109/TFUZZ.2014.2348013
    [45] J. F. Chu, X. W. Liu, Y. M. Wang, K. S. Chin, A group decision making model considering both the additive consistency and group consensus of intuitionistic fuzzy preference relations, Comput. Ind. Eng., 101 (2016), 227–242. doi: 10.1016/j.cie.2016.08.018
    [46] H. C. Liao, Z. S. Xu, Consistency of the fused intuitionistic fuzzy preference relation in group intuitionistic fuzzy analytic hierarchy process, Appl. Soft Comput., 35 (2015), 812–826. doi: 10.1016/j.asoc.2015.04.015
    [47] Y. Jiang, Z. S. Xu, M. Gao, Methods for ranking intuitionistic multiplicative numbers by distance measures in decision making, Comput. Ind. Eng., 88 (2015), 100–109. doi: 10.1016/j.cie.2015.06.015
    [48] Z. M. Zhang, W. Pedrycz, A consistency and consensus-based goal programming method for group decision-making with interval-valued intuitionistic multiplicative preference relations, IEEE T. Cybernetics, 49 (2019), 3640–3654. doi: 10.1109/TCYB.2018.2842073
    [49] Z. J. Wang, Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations, Appl. Math. Model., 37 (2013), 6377–6388. doi: 10.1016/j.apm.2013.01.021
    [50] E. H. Viedma, S. Alonso, F. Chiclana, F. Herrera, A consensus model for group decision making with incomplete fuzzy preference relations, IEEE T. Fuzzy Syst., 15 (2007), 863–877. doi: 10.1109/TFUZZ.2006.889952
    [51] H. C. Liao, Z. M. Li, X. J. Zeng, W. S. Liu, A comparison of distinct consensus measures for group decision making with intuitionistic fuzzy preference relations, Int. J. Comput. Int. Sys., 10 (2017), 456–469. doi: 10.2991/ijcis.2017.10.1.31
    [52] M. J. Moral, F. Chiclana, J. M. Tapia, E. H. Viedma, A comparative study on consensus measures in group decision making, Int. J. Intell. Syst., 33 (2018), 1–15. doi: 10.1002/int.21958
    [53] F. Y. Meng, J. Tang, F. J. Cabrerizo, E. H. Viedma, A rational and consensual method for group decision making with interval-valued intuitionistic multiplicative preference relations, Eng. Appl. Artif. Intel., 90 (2020), 1–17.
    [54] Z. M. Zhang, C. Wu, W. Pedrycz, A novel group decision-making method for interval-valued intuitionistic multiplicative preference relations, IEEE T. Fuzzy Syst., 28 (2020), 1799–1814. doi: 10.1109/TFUZZ.2019.2922917
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