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Hierarchical Punishment-Driven Consensus Model for Probabilistic Linguistic Large-Group Decision Making with Application to Global Supplier Selection

Abstract

Large-group decision making (LGDM) has attracted extensive attention and has been used to model complex decision problems. It is necessary to implement a consensus reaching process (CRP) due to the need to obtain a decision that is acceptable to the majority. The theory of probabilistic linguistic term sets (PLTSs) is very useful in addressing uncertain information in the decision-making process. In this paper, we develop a hierarchical punishment-driven consensus model for LGDM problems in the context of probabilistic linguistic information. The model has three stages. In the first stage, we define probabilistic linguistic large-group decision making. To improve the performance of PLTSs in the CRP, we redefine the rules governing their normalization and operations. In the second stage, the original large group is divided into several small subgroups by hierarchical clustering. In the third stage, we propose three levels of consensus measures and two adjustment strategies to refine the scope of measure and adjustment to the matrix element level. Then, a hierarchical punishment-driven consensus model is established that can provide guidance for adjustment and soften the human supervision of the CRP. Finally, a case study on global supplier selection illustrates the utility and applicability of the model, and a comparison with other linguistic models reveals its advantages.

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References

  1. Awasthi A, Govindan K, Gold S (2018) Multi-tier sustainable global supplier selection using a fuzzy AHP-VIKOR based approach. Int J Prod Econ 195:106–117

    Google Scholar 

  2. Bai CZ, Zhang R, Shen S, Huang CF, Fan X (2018) Interval-valued probabilistic linguistic term sets in multi-criteria group decision making. Int J Intell Syst 33(6):1301–1321

    Google Scholar 

  3. Bezdek JC, Ehrlich R, Full W (1984) FCM: the fuzzy c-means clustering algorithm. Comput Geosci 10(2–3):191–203

    Google Scholar 

  4. Cabrerizo FJ, Morente-Molinera JA, Pedrycz W, Taghavi A, Herrera-Viedma E (2018) Granulating linguistic information in decision making under consensus and consistency. Expert Syst Appl 99:83–92

    Google Scholar 

  5. Ding RX, Wang XQ, Shang K, Herrera F (2019) Social network analysis-based conflict relationship investigation and conflict degree-based consensus reaching process for large scale decision making using sparse representation. Inf Fusion 50:251–272

    Google Scholar 

  6. Dong Y, Zhuang Y, Chen K, Tai X (2006) A hierarchical clustering algorithm based on fuzzy graph connectedness. Fuzzy Sets Syst 157(13):1760–1774

    Google Scholar 

  7. Du ZJ, Yu SM, Xu XH (2020) Managing noncooperative behaviors in large-scale group decision-making: integration of independent and supervised consensus-reaching models. Inf Sci. https://doi.org/10.1016/j.ins.2020.03.100

    Article  Google Scholar 

  8. Gou X, Xu Z, Herrera F (2018) Consensus reaching process for large-scale group decision making with double hierarchy hesitant fuzzy linguistic preference relations. Knowl Based Syst 157:20–33

    Google Scholar 

  9. Herrera F, Herrera-Viedma E, Verdegay JL (1996) A linguistic decision process in group decision making. Group Decis Negot 5(2):165–176

    Google Scholar 

  10. Herrera F, Alonso S, Chiclana F, Herrera-Viedma E (2009) Computing with words in decision making: foundations, trends and prospects. Fuzzy Optim Decis Mak 8(4):337–364

    Google Scholar 

  11. Johnson S (1967) Hierarchical clustering schemes. Psychometrika 32(3):241–254

    Google Scholar 

  12. Kacprzyk J, Fedrizzi M (1988) A ‘soft’measure of consensus in the setting of partial (fuzzy) preferences. Eur J Oper Res 34(3):316–325

    Google Scholar 

  13. Kim B, Park KS, Jung SY, Park SH (2018) Offshoring and outsourcing in a global supply chain: impact of the arm’s length regulation on transfer pricing. Eur J Oper Res 266(1):88–98

    Google Scholar 

  14. Labella Á, Liu Y, Rodríguez RM, Martínez L (2018) Analyzing the performance of classical consensus models in large scale group decision making: a comparative study. Appl Soft Comput 67:677–690

    Google Scholar 

  15. Liu P, He L, Yu X (2016) Generalized hybrid aggregation operators based on the 2-dimension uncertain linguistic information for multiple attribute group decision making. Group Decis Negot 25(1):103–126

    Google Scholar 

  16. Massanet S, Riera JV, Torrens J, Herrera-Viedma E (2014) A new linguistic computational model based on discrete fuzzy numbers for computing with words. Inf Sci 258:277–290

    Google Scholar 

  17. Merigó JM, Gil-Lafuente AM (2013) Induced 2-tuple linguistic generalized aggregation operators and their application in decision-making. Inf Sci 236:1–16

    Google Scholar 

  18. Morente-Molinera JA, Kou G, Pang C, Cabrerizo FJ, Herrera-Viedma E (2019) An automatic procedure to create fuzzy ontologies from users’ opinions using sentiment analysis procedures and multi-granular fuzzy linguistic modelling methods. Inf Sci 476:222–238

    Google Scholar 

  19. Palomares I, Martínez L, Herrera F (2014) A consensus model to detect and manage noncooperative behaviors in large-scale group decision making. IEEE Trans Fuzzy Syst 22(3):516–530

    Google Scholar 

  20. Pang Q, Wang H, Xu Z (2016) Probabilistic linguistic term sets in multi–attribute group decision making. Inf Sci 369:128–143

    Google Scholar 

  21. Park JH, Gwak MG, Kwun YC (2011) Uncertain linguistic harmonic mean operators and their applications to multiple attribute group decision making. Computing 93(1):47–64

    Google Scholar 

  22. Quesada FJ, Palomares I, Martínez L (2015) Managing experts behavior in large-scale consensus reaching processes with uninorm aggregation operators. Appl Soft Comput 35:873–887

    Google Scholar 

  23. Reefke H, Sundaram D (2018) Sustainable supply chain management: decision models for transformation and maturity. Decis Support Syst 113:56–72

    Google Scholar 

  24. Rodríguez RM, Martínez L, Herrera F (2012) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20(1):109–119

    Google Scholar 

  25. Rodríguez RM, Labella Á, De Tré G, Martínez L (2018) A large scale consensus reaching process managing group hesitation. Knowl Based Syst 159:86–97

    Google Scholar 

  26. Saint S, Lawson JR (1994) Rules for reaching consensus: a modern approach to decision making. Jossey-Bass, San Francisco

    Google Scholar 

  27. Song Y, Li G (2019) A large-scale group decision-making with incomplete multi-granular probabilistic linguistic term sets and its application in sustainable supplier selection. J Oper Res Soc 70(5):827–841

    Google Scholar 

  28. Viswanadham N, Samvedi A (2013) Supplier selection based on supply chain ecosystem, performance and risk criteria. Int J Prod Res 51(21):6484–6498

    Google Scholar 

  29. Wu X, Liao H (2019) A consensus-based probabilistic linguistic gained and lost dominance score method. Eur J Oper Res 272(3):1017–1027

    Google Scholar 

  30. Wu Z, Xu J (2015) Possibility distribution-based approach for MAGDM with hesitant fuzzy linguistic information. IEEE Trans Cybern 46(3):694–705

    Google Scholar 

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

    Google Scholar 

  32. Wu Z, Xu J (2018) A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters. Inf Fusion 41:217–231

    Google Scholar 

  33. Wu T, Liu X, Liu F (2018) An interval type-2 fuzzy TOPSIS model for large scale group decision making problems with social network information. Inf Sci 432:392–410

    Google Scholar 

  34. Xu ZS (2005) Deviation measures of linguistic preference relations in group decision making. Omega 33:249–254

    Google Scholar 

  35. Xu ZS (2009) An interactive approach to multiple attribute group decision making with multigranular uncertain linguistic information. Group Decis Negot 18(2):119–145

    Google Scholar 

  36. Xu XH, Du ZJ, Chen XH (2015) Consensus model for multi-criteria large-group emergency decision making considering non-cooperative behaviors and minority opinions. Decis Support Syst 79:150–160

    Google Scholar 

  37. Xu XH, Du ZJ, Chen XH, Cai CG (2019) Confidence consensus-based model for large-scale group decision making: a novel approach to managing non-cooperative behaviors. Inf Sci 477:410–427

    Google Scholar 

  38. Yu SM, Wang J, Wang JQ, Li L (2018) A multi-criteria decision-making model for hotel selection with linguistic distribution assessments. Appl Soft Comput 67:741–755

    Google Scholar 

  39. Yücenur GN, Vayvay Özalp, Demire NÇ (2011) Supplier selection problem in global supply chains by AHP and ANP approaches under fuzzy environment. Int J Adv Manuf Technol 56(5–8):823–833

    Google Scholar 

  40. Zhang Y, Xu Z, Wang H, Liao H (2016) Consistency-based risk assessment with probabilistic linguistic preference relation. Appl Soft Comput 49:817–833

    Google Scholar 

  41. Zhang Y, Xu Z, Liao H (2017) A consensus process for group decision making with probabilistic linguistic preference relations. Inf Sci 414:260–275

    Google Scholar 

  42. Zuheros C, Li CC, Cabrerizo FJ, Dong YC, Herrera-Viedma E, Herrera F (2018) Computing with words: revisiting the qualitative scale. Int J Uncertain Fuzz Knowl Based Syst 26(Suppl. 2):127–143

    Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Number 71901151); the Major Project for National Natural Science Foundation of China (Grant Numbers 71991461, 91846301); the Natural Science Foundation of SZU (Grant Number 2019025); and the Special Fund Project of Scientific and Technological Innovation Cultivation for Guangdong University Students in 2019 (Grant Number pdjh2019b0025).

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Correspondence to Zhijiao Du.

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Yu, S., Du, Z. & Xu, X. Hierarchical Punishment-Driven Consensus Model for Probabilistic Linguistic Large-Group Decision Making with Application to Global Supplier Selection. Group Decis Negot (2020). https://doi.org/10.1007/s10726-020-09681-3

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Keywords

  • Probabilistic linguistic large-group decision making (PL-LGDM)
  • Hierarchical punishment-driven consensus model (HPDCM)
  • Global supplier selection
  • Hierarchical clustering
  • Hard adjustment
  • Soft adjustment