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A Group Consensus Model for Multiple Attributes Group Decision Making with Interval Belief Distribution and Interval Distributed Preference Relation

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Abstract

In multiple attributes group decision making (MAGDM), how to generate a consensus-based solution that is satisfactory to most of decision makers, is always a critical research issue. This paper proposes a group consensus model for MAGDM based on interval belief distribution (IBD) and interval distributed preference relation (IDPR). The transformation function from IBD to IDPR is first designed to unify IBD and IDPR. Two principles are presented to guarantee the satisfaction of internal consistency before and after the transformation. Based on the unification of IBD and IDPR, a consensus reaching process is developed. In the process, the group consensus at the attribute, alternative and global levels based on IDPRs is first measured, and a feedback mechanism consisting of identification rules and suggestion rules is then designed to help accelerate the convergence of group consensus. With the developed group consensus model, a consensus-based solution to the MAGDM problems with IBDs and IDPRs is generated. Finally, the proposed model is applied to a sustainable supplier selection problem of automobile enterprise in Wuhu, Anhui Province, China to demonstrate its correctness and effectiveness.

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References

  • Altuzarra A, Moreno Jiménez JM, Salvador M (2010) Consensus building in AHP-group decision making: a Bayesian approach. Oper Res 58(6):1755–1773

    Article  Google Scholar 

  • Blagojevic B, Srdjevic B, Srdjevic Z, Zoranovic T (2016) Heuristic aggregation of individual judgments in AHP group decision making using simulated annealing algorithm. Inf Sci 330:260–273

    Article  Google Scholar 

  • Bottero M, Ferretti V, Figueira JR, Greco S, Roy B (2018) On the Choquet multiple criteria preference aggregation model: theoretical and practical insights from a real-world application. Eur J Oper Res 271(1):120–140

    Article  Google Scholar 

  • Chen SM, Cheng SH, Tsai WH (2016) Multiple attribute group decision making based on interval-valued intuitionistic fuzzy aggregation operators and transformation techniques of interval-valued intuitionistic fuzzy values. Inf Sci 367–368:418–442

    Article  Google Scholar 

  • Dong YC, Zhang HJ (2014) Multiperson decision making with different preference representation structures: a direct consensus framework and its properties. Knowl-Based Syst 58:45–57

    Article  Google Scholar 

  • Dong YC, Zhang GQ, Hong WC, Xu YF (2010) Consensus models for AHP group decision making under row geometric mean prioritization method. Decis Support Syst 49(3):281–289

    Article  Google Scholar 

  • Dong YC, 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  Google Scholar 

  • Fan ZP, Xiao SH, Hu GF (2004) An optimization method for integrating two kinds of preference information in group decision-making. Comput Ind Eng 46(2):329–335

    Article  Google Scholar 

  • Fu C, Yang SL (2010) The group consensus based evidential reasoning approach for multiple attributive group decision analysis. Eur J Oper Res 206(3):601–608

    Article  Google Scholar 

  • Fu C, Yang SL (2012) An evidential reasoning based consensus model for multiple attribute group decision analysis problems with interval-valued group consensus requirements. Eur J Oper Res 223(1):167–176

    Article  Google Scholar 

  • Fu C, Yang SL (2012) The combination of dependence-based interval-valued evidential reasoning approach with balanced scorecard for performance assessment. Expert Syst Appl 39(3):3717–3730

    Article  Google Scholar 

  • Fu C, Xu DL, Yang SL (2016) Distributed preference relations for multiple attribute decision analysis. J Oper Res Soc 67(3):457–473

    Article  Google Scholar 

  • Fu C, Chang WJ, Liu WY, Yang SL (2019) Data-driven group decision making for diagnosis of thyroid nodule. Sci China Inf Sci 62(11):212–205

    Article  Google Scholar 

  • Fu C, Chang WJ, Xue M, Yang SL (2019) Multiple criteria group decision making with belief distributions and distributed preference relations. Eur J Oper Res 273(2):623–633

    Article  Google Scholar 

  • Gong ZW, Zhang HH, Forrest J, Li LS, Xu XX (2015) Two consensus models based on the minimum cost and maximum return regarding either all individuals or one individual. Eur J Oper Res 240(1):183–192

    Article  Google Scholar 

  • Gong ZW, Guo WW, Słowiński R (2021) Transaction and interaction behavior-based consensus model and its application to optimal carbon emission reduction. Omega 104:102491

    Article  Google Scholar 

  • Guo WW, Gong ZW, Xu XX, Krejcar O, Herrera-Viedma E (2021) Linear uncertain extensions of the minimum cost consensus model based on uncertain distance and consensus utility. Inf Fusion 70:12–26

    Article  Google Scholar 

  • Guo WW, Gong ZW, Zhang WG, Xu YX (2022) Minimum cost consensus modeling under dynamic feedback regulation mechanism considering consensus principle and tolerance level. Eur J Oper Res. https://doi.org/10.1016/j.ejor.2022.08.033

    Article  Google Scholar 

  • Herrera F, Herrera-Viedma E, Verdegay JL (1996) Direct approach processes in group decision making using linguistic OWA operators. Fuzzy Sets Syst 79(2):175–190

    Article  Google Scholar 

  • Jahanshahloo GR, Lotfi FH, Izadikhah M (2006) An algorithmic method to extend TOPSIS for decision-making problems with interval data. Appl Math Comput 175(2):1375–1384

    Article  Google Scholar 

  • Jiang YP, Fan ZP, Ma J (2008) A method for group decision making with multi-granularity linguistic assessment information. Inf Sci 178(4):1098–1109

    Article  Google Scholar 

  • Liu PD (2017) Multiple attribute group decision making method based on interval-valued intuitionistic fuzzy power Heronian aggregation operators. Comput Ind Eng 108:199–212

    Article  Google Scholar 

  • Liu BS, Shen YH, Chen XH, Sun H, Chen YA (2014) complex multi-attribute large-group PLS decision-making method in the interval-valued intuitionistic fuzzy environment. Appl Math Modell 38(17):4512–4527

    Article  Google Scholar 

  • Liu Y, Fan ZP, Zhang X (2016) A method for large group decision-making based on evaluation information provided by participators from multiple groups. Inf Fusion 29:132–141

    Article  Google Scholar 

  • Liu WQ, Dong YC, Chiclana F, Cabrerizo FJ, Herrera Viedma E (2017) Group decision-making based on heterogeneous preference relations with self-confidence. Fuzzy Optim Decis Mak 16(4):429–447

    Article  Google Scholar 

  • Liu Y, Fu C, Xue M, Chang WJ, Yang SL (2018) Interval-valued distributed preference relation and its application to group decision making. PLoS ONE 13(6):e0198393

    Article  Google Scholar 

  • Li GX, Kou G, Peng Y (2018) A group decision making model for integrating heterogeneous information. IEEE Trans Syst Man Cybern Syst 48(6):982–992

    Article  Google Scholar 

  • Meng FY, Chen SM, Yuan RP (2020) Group decision making with heterogeneous intuitionistic fuzzy preference relations. Inf Sci 523:197–219

    Article  Google Scholar 

  • Ölçer AI, Odabaşi AY (2005) A new fuzzy multiple attributive group decision making methodology and its application to propulsion/manoeuvring system selection problem. Eur J Oper Res 166(1):93–114

    Article  Google Scholar 

  • Wang YM, Yang JB, Xu DL, Chin KS (2006) The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees. Eur J Oper Res 175(1):35–66

    Article  Google Scholar 

  • Wan SP, Xu J, Dong JY (2016) Aggregating decision information into interval-valued intuitionistic fuzzy numbers for heterogeneous multi-attribute group decision making. Knowl-Based Syst 113:155–170

    Article  Google Scholar 

  • Wu T, Liu XW (2016) An interval type-2 fuzzy clustering solution for large-scale multiple-criteria group decision-making problems. Knowl-Based Syst 114:118–127

    Article  Google Scholar 

  • Wu ZB, Xu JP (2016) Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations. Omega 65:28–40

    Article  Google Scholar 

  • Xu J, Wan SP, Dong JY (2016) Aggregating decision information into Atanassov’s intuitionistic fuzzy numbers for heterogeneous multi-attribute group decision making. Appl Soft Comput 41:331–351

    Article  Google Scholar 

  • Zhang ZM, Wang C, Tian XD (2015) A decision support model for group decision making with hesitant fuzzy preference relations. Knowl-Based Syst 86:77–101

    Article  Google Scholar 

Download references

Acknowledgements

This research is supported by the National Natural Science Foundation of China (Grant Nos. 72101074), the Fundamental Research Funds for the Central Universities (Grant Nos. JZ2021HGTA0139 and JZ2021HGQA0203), and the NanJing Xiaozhuang University High Level Cultivation Project (Grant No. 2022NXY16).

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Authors and Affiliations

  1. School of Management, Hefei University of Technology, Box 270, Hefei, 230009, Anhui, People’s Republic of China

    Yin Liu, Wenjun Chang & Xuefei Jia

  2. Business School of Nanjing, Xiaozhuang University, Nanjing, 211171, Jiangsu, People’s Republic of China

    Yin Liu

  3. Key Laboratory of Process Optimization and Intelligent Decision-Making, Ministry of Education, Hefei, 230009, Anhui, People’s Republic of China

    Wenjun Chang & Xuefei Jia

  4. Ministry of Education Engineering Research Center for Intelligent Decision-Making and Information System Technologies, Hefei, 230009, Anhui, People’s Republic of China

    Wenjun Chang & Xuefei Jia

Authors
  1. Yin Liu
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  2. Wenjun Chang
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  3. Xuefei Jia
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Correspondence to Wenjun Chang.

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Liu, Y., Chang, W. & Jia, X. A Group Consensus Model for Multiple Attributes Group Decision Making with Interval Belief Distribution and Interval Distributed Preference Relation. Group Decis Negot 32, 701–727 (2023). https://doi.org/10.1007/s10726-023-09821-5

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