Abstract
This paper mainly provides a group decision-making (GDM) method based on linguistic interval-valued intuitionistic fuzzy preference relations (LIVIFPRs), where consistency and consensus analysis is conducted. The multiplicative consistency of LIVIFPRs is first introduced, and a consistency-based model is built to ascertain the missing values of an incomplete LIVIFPR. Considering the smallest distance, an optimization model is established to repair the unacceptably multiplicatively consistent LIVIFPR to have acceptable consistency. Meanwhile, the linguistic interval-valued intuitionistic fuzzy priority weights of LIVIFPR are constructed via the optimal solutions of a programming model. Then, Algorithm I for decision-making with one incomplete LIVIFPR is presented. For the GDM problem, the weights of experts are determined before aggregating the individual LIVIFPRs. Moreover, when the consensus of an individual LIVIFPR is unacceptable, a mathematical model is utilized to reach the consensus requirement. Subsequently, Algorithm II for GDM with incomplete LIVIFPRs is proposed step-by-step. Finally, the new GDM method is used to evaluate four Chinese express companies, and the advantages of this approach are demonstrated by performing a comparison analysis.
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References
Liao HC, Xu ZS (2014) Priorities of intuitionistic fuzzy preference relation based on multiplicative consistency. IEEE T Fuzzy Syst 22(6):1669–1681
Yang W, Jhang ST, Shi SG, Xu ZS, Ma ZM (2020) A novel additive consistency for intuitionistic fuzzy preference relations in group decision making. Appl Intell 50:4342–4356
Yang W, Jhang ST, Fu ZW, Xu ZS, Ma ZM (2021) A novel method to derive the intuitionistic fuzzy priority vectors from intuitionistic fuzzy preference relations. Soft Comput 25:147–159
Oh H, Kim H, Kim H, Kim C (2022) A method for improving the multiplicative inconsistency based on indeterminacy of an intuitionistic fuzzy preference relation. Inform Sci 602:1–12
Xu ZS, Yager RR (2009) Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim Decis Making 8:123–139
Wan SP, Wang W, Dong JY (2018) A three-phase method for group decision making with interval-valued intuitionistic fuzzy preference relations. IEEE T Fuzzy Syst 26(2):998–1010
Tang J, Meng FY, Zhang YL (2018) Decision making with interval-valued intuitionistic fuzzy preference relations based on additive consistency analysis. Inform Sci 467:115–134
Wan SP, Xu GL, Dong JY (2020) An Atanassov intuitionistic fuzzy programming method for group decision making with interval-valued Atanassov intuitionistic fuzzy preference relations. Appl Soft Comput 95:106556
Zhang ZM, Chen SM (2021) Optimization-based group decision making using interval-valued intuitionistic fuzzy preference relations. Inform Sci 561:352–370
Wang W, Wan SP (2021) A comprehensive group decision-making method with interval-valued intuitionistic fuzzy preference relations. Soft Comput 25:343–362
Meng FY, Tang J, Wang P, Chen XH (2018) A programming-based algorithm for interval-valued intuitionistic fuzzy group decision making. Knowl-Based Syst 144:122–143
Wan SP, Wang W, Dong JY (2018) A group decision-making method considering both the group consensus and multiplicative consistency of interval-valued intuitionistic fuzzy preference relations. Inform Sci 466:109–128
Zhang SL, Tang J, Meng FY, Yuan RP (2021) A group decision making method with interval-valued intuitionistic fuzzy preference relations and its application in the selection of cloud computing vendors for SMEs. Informatica 32(1):163–193
Kim YG, Yang WC, Choe TR (2021) Some methods considering multiplicative consistency and consensus in group decision making with interval-valued intuitionistic fuzzy preference relations. Int J Uncertain Fuzz 29(3):353–383
Zhang ZM, Pedrycz W (2022) Analysis of acceptably multiplicative consistency and consensus for incomplete interval-valued intuitionistic fuzzy preference relations. IEEE T Fuzzy Syst 30(2):486–499
Li CC, Dong YC, Liang HM, Pedrycz W, Herrera F (2022) Data-driven method to learning personalized individual semantics to support linguistic multi-attribute decision making. Omega 111:102642
Zhang HM (2014) Linguistic intuitionistic fuzzy sets and application in MAGDM. J Appl Math 2014:432092
Pei LD, Jin FF, Ni ZW, Chen HY, Tao ZF (2017) An automatic iterative decision-making method for intuitionistic fuzzy linguistic preference relations. Int J Syst Sci 48(13):2779–2793
Meng FY, Tang J, Hamido F (2019) Linguistic intuitionistic fuzzy preference relations and their application to multi-criteria decision making. Inform Fusion 46:77–90
Zhang LY, Liang CL, Li T, Yang WT (2022) A two-stage EDM method based on KU-CBR with the incomplete linguistic intuitionistic fuzzy preference relations. Comput Ind Eng 172:108552
Jin FF, Ni ZW, Pei LD, Chen HY, Li YP, Zhu XH, Ni LP (2019) A decision support Model for group decision making with intuitionistic fuzzy linguistic preferences relations. Neural Comput Appl 31:1103–1124
Garg H, Kumar K (2019) Linguistic interval-valued Atanassov intuitionistic fuzzy sets and their applications to group decision-making problems. IEEE T Fuzzy Syst 27(12):2302–2311
Garg H, Kumar K (2019) An extended technique for order preference by similarity to ideal solution group decision-making method with linguistic interval-valued intuitionistic fuzzy information. J Multi-Criteria Dec 26:16–26
Liu PD, Qin XY (2019) A new decision-making method based on interval-valued linguistic intuitionistic fuzzy information. Cogn Comput 11:125–144
Qin YC, Qi QF, Shi PZ, Scott PJ, Jiang XQ (2020) Linguistic interval-valued intuitionistic fuzzy Archimedean prioritised aggregation operators for multi-criteria decision making. J Intell Fuzzy Syst 38(4):4643–4666
Garg H, Kumar K (2020) Group decision making approach based on possibility degree measure under linguistic interval-valued intuitionistic fuzzy set environment. J Ind Manag Optim 16(1):445–467
Qin YC, Cui XL, Huang MF, Zhong YR, Tang ZM, Shi PZ (2020) Linguistic interval-valued intuitionistic fuzzy Archimedean power Muirhead mean operators for multiattribute group decision-making. Complexity 2020:2373762
Xu L, Liu Y, Liu HB (2020) Linguistic interval-valued intuitionistic fuzzy copula Heronian mean operators for multiattribute group decision-making. J Math-UK 2020:6179468
Zhu WB, Shuai B, Zhang SH (2020) The linguistic interval-valued intuitionistic fuzzy aggregation operators based on extended Hamacher t-norm and s-norm and their application. Symmetry 12(4):668
Aliya F, Fazli A, Hussain SSB (2020) Geometric operators based on linguistic interval-valued intuitionistic neutrosophic fuzzy number and their application in decision making. Ann Opt The Prac 3(1):47–71
Xu L, Yi L, Liu HB (2021) Linguistic interval-valued intuitionistic fuzzy copula power aggregation operators for multiattribute group decision making. J Intell Fuzzy Syst 40(1):605–624
Tang J, Meng FY, Cabrerizo FJ, Herrera-Viedma E (2019) A procedure for group decision making with interval-valued intuitionistic linguistic fuzzy preference relations. Fuzzy Optim Decis Ma 18:493–527
Wan SP, Xu GL, Dong JY (2016) A novel method for group decision making with interval-valued Atanassov intuitionistic fuzzy preference relations. Inform Sci 372:53–71
Zhang ZM, Chen SM, Wang C (2020) Group decision making based on multiplicative consistency and consensus of fuzzy linguistic preference relations. Inform Sci 509:71–86
Yang ZY, Zhang LY, Li T (2021) Group decision making with incomplete interval-valued q-rung orthopair fuzzy preference relations. Int J Intell Syst 36:7274–7308
Zhang ZM, Pedrycz W (2019) A consistency and consensus-based goal programming method for group decision-making with interval-valued intuitionistic multiplicative preference relations. IEEE T Cybern 49(10):3640–3654
Xing YM, Wu J, Chiclana F, Yu GF, Cao MS, Herrera-Viedma E (2023) A bargaining game based feedback mechanism to support consensus in dynamic social network group decision making. Inform Fusion 93:363–382
Ji FX, Wu J, Chiclana F, Wang S, Fujita H, Herrera-Viedma E (2023) The overlapping community driven feedback mechanism to support consensus in social network group decision making. IEEE T Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2023.3241062
Li T, Zhang LY (2021) A group decision making method considering both the consistency and consensus of intuitionistic multiplicative preference relations. AIMS Math 6(6):6603–6629
Liu JP, Fang MD, Jin FF, Tao ZF, Chen HY, Du PC (2021) Pythagorean fuzzy linguistic decision support model based on consistency-adjustment strategy and consensus reaching process. Soft Comput 25:8205–8221
Meng FY, Tang J, Xu ZS (2019) Exploiting the priority weights from interval linguistic fuzzy preference relations. Soft Comput 23:583–597
Dogan O, Deveci M, Canıtez F, Kahraman C (2020) A corridor selection for locating autonomous vehicles using an interval-valued intuitionistic fuzzy AHP and TOPSIS method. Soft Comput 24:8937–8953
Verma R, Chandra S (2021) Interval-valued intuitionistic fuzzy-analytic hierarchy process for evaluating the impact of security attributes in fog based internet of things paradigm. Comput Commun 175:35–46
Alimohammadlou M, Khoshsepehr Z (2022) Investigating organizational sustainable development through an integrated method of interval-valued intuitionistic fuzzy AHP and WASPAS. Environ Dev Sustain 24:2193–2224
Garg H (2020) Linguistic interval-valued Pythagorean fuzzy sets and their application to multiple attribute group decision-making process. Cogn Comput 12:1313–1337
Verma R, Agarwal N (2022) Multiple attribute group decision-making based on generalized aggregation operators under linguistic interval-valued Pythagorean fuzzy environment. Granul Comput 7:591–632
Khan MSA, Khan AS, Khan IA, Mashwani WK, Hussain F (2021) Linguistic interval-valued q-rung orthopair fuzzy TOPSIS method for decision making problem with incomplete weight. J Intell Fuzzy Syst 40(3):4223–4235
Gurmani SH, Chen HY, Bai YH (2021) The operational properties of linguistic interval valued q-rung orthopair fuzzy information and its VIKOR model for multi-attribute group decision making. J Intell Fuzzy Syst 41(6):7063–7079
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This work is supported by the National Social Science Foundation of China (No.19CGL045).
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Tao Li: Methodology, Software, Writing-original draft. Liyuan Zhang: Conceptualization, Methodology, Writing-original draft. Zhenglong Zhang: Writing-reviewing and editing.
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Li, T., Zhang, L. & Zhang, Z. The consistency and consensus analysis for group decision-making with incomplete linguistic interval-valued intuitionistic fuzzy preference relations. Appl Intell 53, 23500–23521 (2023). https://doi.org/10.1007/s10489-023-04605-5
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DOI: https://doi.org/10.1007/s10489-023-04605-5