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Programming model-based method for ranking objects from group decision making with interval-valued hesitant fuzzy preference relations

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Abstract

Interval-valued hesitant fuzzy preference relations (IVHFPRs) are useful that allow decision makers to apply several intervals in [0, 1] to denote the uncertain hesitation preference. To derive the reasonable ranking order from group decision making with preference relations, two topics must be considered: consistency and consensus. This paper focuses on group decision making with IVHFPRs. First, a multiplicative consistency concept for IVHFPRs is defined. Then, programming models for judging the consistency of IVHFPRs are constructed. Meanwhile, an approach for deriving the interval fuzzy priority weight vector is introduced that adopts the consistency probability distribution as basis. Subsequently, this paper builds several multiplicative consistency-based programming models for estimating the missing values in incomplete IVHFPRs. A consensus index is introduced to measure the agreement degree between individual IVHFPRs, and a method for increasing the consensus level is presented. Finally, a multiplicative consistency-and-consensus-based group decision-making method with IVHFPRs is offered, and a practical decision-making problem is selected to show the application of the new method.

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References

  1. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  MATH  MathSciNet  Google Scholar 

  2. Atanassov KT, Gargov G (1989) Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31(3):343–349

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen N, Xu ZS, Xia MM (2013) Interval-valued hesitant preference relation relations and their applications to group decision making. Knowl-Based Syst 37:528–540

    Article  Google Scholar 

  4. Chen N, Xu ZS, Xia MM (2013) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Modell 37:2197–2211

    Article  MathSciNet  MATH  Google Scholar 

  5. Gitinavard H, Mousavi SM, Vahdani B (2016) A new multi-criteria weighting and ranking model for group decision-making analysis based on interval-valued hesitant fuzzy sets to selection problems. Neural Comput Appl 27 (6):1593–1605

    Article  Google Scholar 

  6. Gonçalves C D F, Dias JAM, Machado VAC (2015) Multi-criteria decision methodology for selecting maintenance key performance indicators. Int J Manag Sci Eng Manag 10(3):215–223

    Google Scholar 

  7. Hao ZN, Xu ZS, Zhao H, Fujita H (2017) A dynamic weight determination approach based on the intuitionistic fuzzy Bayesian network and its application to emergency decision making, IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2017.2755001

  8. Jin FF, Ni ZW, Chen HY, Li YP, Zhou LG (2016) Multiple attribute group decision making based on interval-valued hesitant fuzzy information measures. Comput Ind En 101:103–115

    Article  Google Scholar 

  9. Liao HC, Si GS, Xu ZS, Fujita H (2018) Hesitant fuzzy linguistic preference utility set and its application in selection of fire rescue plans. Int J Environ Res Public Health 15(4):1–18

    Article  Google Scholar 

  10. Meng FY, Tan CQ (2017) Distance measures for intuitionistic hesitant fuzzy linguistic sets. Econ Comput Econ Cyber Stud Res 51(4):207–224

    Google Scholar 

  11. Meng FY, Tang J, An QX, Chen XH (2017) Decision making with intuitionistic linguistic preference relations. Int Trans Oper Res. https://doi.org/10.1111/itor.12383

  12. Meng FY, Zhang Q, Chen XH (2017) Fuzzy multichoice games with fuzzy characteristic functions. Group Decis Negot 26(3):262–276

    Article  Google Scholar 

  13. Meng FY, Tan CQ, Chen XH (2017) Multiplicative consistency analysis for interval reciprocal preference relations: a comparative study. Omega 68:17–38

    Article  Google Scholar 

  14. Meng FY, Chen XH (2014) An approach to interval-valued hesitant fuzzy multi-attribute decision making with incomplete weight information based on hybrid Shapley operators. Informatica 25(4):617–642

    Article  MATH  Google Scholar 

  15. Meng FY, Wang C, Chen XH, Zhang Q (2016) Correlation coefficients of interval-valued hesitant fuzzy sets and their application based on Shapley function. Int J Intell Syst 31(1):17–43

    Article  Google Scholar 

  16. Meng FY, Tang J, Fujita H (2019) Linguistic intuitionistic fuzzy preference relations and their application to multi-criteria decision making. Inform Fusion 46:77–90

    Article  Google Scholar 

  17. Ölçer I, Odabaşi A Y (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  MATH  Google Scholar 

  18. Pérez-Fernándeza R, Alonsob P, Bustincec H, Díazd I, Montesa S (2016) Applications of finite interval-valued hesitant fuzzy preference relations in group decision making. Inform Sci 326:89–101

    Article  MathSciNet  Google Scholar 

  19. Tanino T (1984) Fuzzy preference orderings in group decision making. Fuzzy Sets Syst 12(2):117–131

    Article  MathSciNet  MATH  Google Scholar 

  20. Tang J, An QX, Meng FY, Chen XH (2017) A natural method for ranking objects from hesitant fuzzy preference relations. Int J Inf Tech Decis Ma 16:1611–1646

    Article  Google Scholar 

  21. Tang J, Meng FY (2017) Decision making with multiplicative hesitant fuzzy linguistic preference relations. Neural Comput Appl. https://doi.org/10.1007/s00521-017-3227-x

  22. Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539

    MATH  Google Scholar 

  23. Wang YM, Chin KS (2008) A linear goal programming priority method for fuzzy analytic hierarchy process and its applications in new product screening. Int J Approx Reason 49(2):451–465

    Article  MATH  Google Scholar 

  24. Wang TC, Chen YH (2008) Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP. Inform Sci 178(19):3755–3765

    Article  MathSciNet  MATH  Google Scholar 

  25. Wang H, Xu Z (2015) Some consistency measures of extended hesitant fuzzy linguistic preference relations. Inform Sci 297:316–331

    Article  MathSciNet  MATH  Google Scholar 

  26. Wu ZB, Xu JP (2016) Possibility distribution based approach for MAGDM with hesitant fuzzy linguistic information. IEEE Trans Cy 46(3):694–705

    Article  Google Scholar 

  27. Wu J, Dai LF, Chiclana F, Fujita H, Herrera-Viedma E (2018) A minimum adjustment cost feedback mechanism based consensus model for group decision making under social network with distributed linguistic trust. Inform Fusion 41:232–242

    Article  Google Scholar 

  28. Xu ZS (2001) A practical method for priority of interval number complementary judgment matrix. Oper Res Manag Sci 10(1):16–19

    Google Scholar 

  29. Xu ZS, Xia MM (2011) Distance and similarity measures for hesitant fuzzy sets. Inform Sci 181:2128–2138

    Article  MathSciNet  MATH  Google Scholar 

  30. Xia MM, Xu ZS (2011) Methods for fuzzy complementary preference relations based on multiplicative consistency. Comput Ind En 61(4):930–935

    Article  Google Scholar 

  31. Xia MM, Xu ZS (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52(3):395–407

    Article  MathSciNet  MATH  Google Scholar 

  32. Xu YJ, Chen L, Rodríguez RM, Herrera F, Wang HM (2016) Deriving the priority weights from incomplete hesitant fuzzy preference relations in group decision making. Knowl-Based Syst 99:71–78

    Article  Google Scholar 

  33. Yuan JH, Li CB, Xu FQ, et al. (2016) A group decision making approach in interval-valued intuitionistic hesitant fuzzy environment with confidence levels. J Intell Fuzzy Syst 31(3):1909–1919

    Article  MATH  Google Scholar 

  34. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning–Part I. Inform Sci 8(3):199–249

    Article  MATH  Google Scholar 

  35. Zhang ZM, Wu C (2014) Deriving the priority weights from hesitant multiplicative preference relations in group decision making. Appl Soft Comput 25:107–117

    Article  Google Scholar 

  36. Zhang ZM, Wang C (2014) A decision support model for group decision making with hesitant multiplicative preference relations. Inform Sci 68:136–166

    Article  MathSciNet  MATH  Google Scholar 

  37. Zhang ZM, Wang C (2014) On the use of multiplicative consistency in hesitant fuzzy linguistic preference relations. Knowl-Based Syst 72:13–27

    Article  Google Scholar 

  38. 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 

  39. Zhang ZM, Wang C, Tian XD (2015) Multi–criteria group decision making with incomplete hesitant fuzzy preference relations. Appl Soft Comput 36:1–23

    Article  Google Scholar 

  40. Zhu B, Xu ZS (2014) Analytic hierarchy process-hesitant group decision making. Eur J Oper Res 239 (3):794–801

    Article  MathSciNet  MATH  Google Scholar 

  41. Zhu B, Xu ZS (2014) Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans Fuzzy Syst 22(1):35–45

    Article  MathSciNet  Google Scholar 

  42. Zhu B, Xu ZS, Xu JP (2014) Deriving a ranking from hesitant fuzzy preference relations under group decision making. IEEE Trans Cy 44(8):1328–1337

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 71571192, and 71671188), the Innovation-Driven Project of Central South University (No. 2018CX039), the Fundamental Research Funds for the Central Universities of Central South University (No. 2018zzts094), the State Key Program of National Natural Science of China (No. 71431006), and the Hunan Province Foundation for Distinguished Young Scholars of China (No. 2016JJ1024).

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Authors and Affiliations

  1. School of Management and Economics, Beijing Institute of Technology, Beijing, 100081, China

    Yuning Zhang

  2. School of Business, Central South University, Changsha, 410083, China

    Jie Tang & Fanyong Meng

  3. School of Management and Economics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Fanyong Meng

Authors
  1. Yuning Zhang
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  2. Jie Tang
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  3. Fanyong Meng
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Correspondence to Fanyong Meng.

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Zhang, Y., Tang, J. & Meng, F. Programming model-based method for ranking objects from group decision making with interval-valued hesitant fuzzy preference relations. Appl Intell 49, 837–857 (2019). https://doi.org/10.1007/s10489-018-1292-1

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