Skip to main content

Advertisement

Springer Nature Link
Log in

Evaluating Green Supply Chain Management Practices Under Fuzzy Environment: A Novel Method Based on D Number Theory

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

The evaluation of green supply chain management (GSCM) practices is a typical multi-criteria decision making (MCDM) problem. Considering widely existed uncertainty, evaluating GSCM practices in a fuzzy environment becomes a fuzzy MCDM issue. Traditional fuzzy MCDM approaches solve the issue usually through fusing the fuzzy assessments on different criteria for each alternative. In the process, the fuzzy uncertainty of every assessment has been given much attention; however, the non-exclusiveness between fuzzy linguistic variables is often ignored especially when combining the fuzzy assessments. In this paper, the non-exclusiveness between fuzzy assessments represented by linguistic variables is fully taken into consideration. A theory called D number theory, as an extension of Dempster–Shafer theory, is used to deal with this non-exclusiveness. Based on D number theory, a novel method is proposed to evaluate GSCM practices in the fuzzy environment. The main contribution and advantage of the proposed method is being able to simultaneously cope with fuzziness, ambiguity, and non-exclusiveness involved in the process of evaluating GSCM practices. A numerical example and related analysis are provided to show the effectiveness of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Afzali, A., Rafsanjani, M.K., Saeid, A.B.: A fuzzy multi-objective linear programming model based on interval-valued intuitionistic fuzzy sets for supplier selection. Int. J. Fuzzy Syst. 18(5), 864–874 (2016)

    Article  MathSciNet  Google Scholar 

  2. Ahi, P., Searcy, C.: A comparative literature analysis of definitions for green and sustainable supply chain management. J. Clean. Prod. 52, 329–341 (2013)

    Article  Google Scholar 

  3. Bai, C., Sarkis, J.: Green supplier development: analytical evaluation using rough set theory. J. Clean. Prod. 18(12), 1200–1210 (2010)

    Article  Google Scholar 

  4. Chou, C.C.: The canonical representation of multiplication operation on triangular fuzzy numbers. Comput. Math. Appl. 45(10), 1601–1610 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cui, H., Liu, Q., Zhang, J., Kang, B.: An improved deng entropy and its application in pattern recognition. IEEE Access 7, 18284–18292 (2019)

    Article  Google Scholar 

  6. Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat. 38(2), 325–339 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  7. Deng, X.: Analyzing the monotonicity of belief interval based uncertainty measures in belief function theory. Int. J. Intell. Syst. 33(9), 1869–1879 (2018)

    Article  Google Scholar 

  8. Deng, X., Jiang, W.: Exploring the combination rules of D numbers from a perspective of conflict redistribution. In: Proceedings of the 20th International Conference on Information Fusion (FUSION), Xi’an, China, pp. 542–547, https://doi.org/10.23919/ICIF.2017.8009696 (2017)

  9. Deng, X., Jiang, W.: Dependence assessment in human reliability analysis using an evidential network approach extended by belief rules and uncertainty measures. Ann Nuclear Energy 117, 183–193 (2018a)

    Article  Google Scholar 

  10. Deng, X., Jiang, W.: An evidential axiomatic design approach for decision making using the evaluation of belief structure satisfaction to uncertain target values. Int. J. Intell. Syst. 33(1), 15–32 (2018b)

    Article  Google Scholar 

  11. Deng, X., Jiang, W.: D number theory based game-theoretic framework in adversarial decision making under a fuzzy environment. Int. J. Approx. Reason. 106, 194–213 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  12. Deng, X., Hu, Y., Deng, Y., Mahadevan, S.: Environmental impact assessment based on D numbers. Expert Syst. Appl. 41(2), 635–643 (2014a)

    Article  Google Scholar 

  13. Deng, X., Hu, Y., Deng, Y., Mahadevan, S.: Supplier selection using AHP methodology extended by D numbers. Expert Syst. Appl. 41(1), 156–167 (2014b)

    Article  Google Scholar 

  14. Deng, X., Han, D., Dezert, J., Deng, Y., Shyr, Y.: Evidence combination from an evolutionary game theory perspective. IEEE Trans. Cybern. 46(9), 2070–2082 (2016)

    Article  Google Scholar 

  15. Deng, X., Xiao, F., Deng, Y.: An improved distance-based total uncertainty measure in belief function theory. Appl. Intell. 46(4), 898–915 (2017)

    Article  Google Scholar 

  16. Deng, X., Jiang, W., Wang, Z.: Zero-sum polymatrix games with link uncertainty: a Dempster–Shafer theory solution. Appl. Math. Comput. 340, 101–112 (2019)

    Article  MathSciNet  Google Scholar 

  17. Deng, Y.: D numbers: theory and applications. J. Inf. Comput. Sci. 9(9), 2421–2428 (2012)

    Google Scholar 

  18. Dezert, J., Smarandache, F.: An introduction to DSmT for information fusion. New Math. Nat. Comput. 8(3), 343–359 (2012)

    Article  MATH  Google Scholar 

  19. Elmore, P.A., Petry, F.E., Yager, R.R.: Geospatial modeling using Dempster–Shafer theory. IEEE Trans. Cybern. 47(6), 1551–1561 (2017)

    Article  Google Scholar 

  20. Erol, I., Sencer, S., Sari, R.: A new fuzzy multi-criteria framework for measuring sustainability performance of a supply chain. Ecol. Econ. 70(6), 1088–1100 (2011)

    Article  Google Scholar 

  21. Fahimnia, B., Sarkis, J., Davarzani, H.: Green supply chain management: a review and bibliometric analysis. Int. J. Prod. Econ 162, 101–114 (2015)

    Article  Google Scholar 

  22. Fan, G., Zhong, D., Yan, F., Yue, P.: A hybrid fuzzy evaluation method for curtain grouting efficiency assessment based on an AHP method extended by D numbers. Expert Syst. Appl. 44, 289–303 (2016)

    Article  Google Scholar 

  23. Fei, L., Deng, Y., Hu, Y.: DS-VIKOR: A new multi-criteria decision-making method for supplier selection. Int. J. Fuzzy Syst. https://doi.org/10.1007/s40815-018-0543-y (2018)

  24. Govindan, K., Khodaverdi, R., Vafadarnikjoo, A.: Intuitionistic fuzzy based DEMATEL method for developing green practices and performances in a green supply chain. Expert Syst. Appl. 42(20), 7207–7220 (2015a)

    Article  Google Scholar 

  25. Govindan, K., Rajendran, S., Sarkis, J., Murugesan, P.: Multi criteria decision making approaches for green supplier evaluation and selection: a literature review. J. Clean. Prod. 98, 66–83 (2015b)

    Article  Google Scholar 

  26. Green Jr., K.W., Zelbst, P.J., Meacham, J., Bhadauria, V.S.: Green supply chain management practices: impact on performance. Supply Chain Manag. Int. J. 17(3), 290–305 (2012)

    Article  Google Scholar 

  27. Han, D., Dezert, J., Duan, Z.: Evaluation of probability transformations of belief functions for decision making. IEEE Trans. Syst. Man Cybern. Syst. 46(1), 93–108 (2016)

    Article  Google Scholar 

  28. Han, Y., Deng, Y.: An enhanced fuzzy evidential DEMATEL method with its application to identify critical success factors. Soft Comput. 22(15), 5073–5090 (2018)

    Article  Google Scholar 

  29. He, Z., Jiang, W.: An evidential dynamical model to predict the interference effect of categorization on decision making. Knowl. Based Syst. 150, 139–149 (2018a)

    Article  Google Scholar 

  30. He, Z., Jiang, W.: An evidential markov decision making model. Inf. Sci. 467, 357–372 (2018b)

    Article  MathSciNet  Google Scholar 

  31. He, Z., Jiang, W., Chan, F.T.S.: Evidential supplier selection based on interval data fusion. Int. J. Fuzzy Syst. 20(4), 1159–1171 (2017)

    Article  MathSciNet  Google Scholar 

  32. Hervani, A.A., Helms, M.M., Sarkis, J.: Performance measurement for green supply chain management. Benchmark. Int. J. 12(4), 330–353 (2005)

    Article  Google Scholar 

  33. Hsu, C.W., Kuo, T.C., Chen, S.H., Hu, A.H.: Using DEMATEL to develop a carbon management model of supplier selection in green supply chain management. J. Clean. Prod. 56, 164–172 (2013)

    Article  Google Scholar 

  34. Huang, Z., Lin, Yang J.W.: Uncertainty measurement with belief entropy on the interference effect in the quantum-like Bayesian networks. Appl. Math. Comput. 347, 417–428 (2019)

    Article  MathSciNet  Google Scholar 

  35. Jiang, W.: A correlation coefficient for belief functions. Int. J. Approx. Reason. 103, 94–106 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  36. Jiang, W., Hu, W.: An improved soft likelihood function for Dempster–Shafer belief structures. Int. J. Intell. Syst. 33(6), 1264–1282 (2018)

    Article  Google Scholar 

  37. Jiang, W., Huang, C.: A multi-criteria decision-making model for evaluating suppliers in green SCM. Int. J. Comput. Commun. Control 13(3), 337–352 (2018)

    Article  Google Scholar 

  38. Jiroušek, R., Shenoy, P.P.: A new definition of entropy of belief functions in the Dempster–Shafer theory. Int. J. Approx. Reason. 92, 49–65 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  39. Jousselme, A.L., Liu, C., Grenier, D., Bossé, É.: Measuring ambiguity in the evidence theory. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 36(5), 890–903 (2006)

    Article  Google Scholar 

  40. Kahraman, C., Oztaysi, B., Onar, S.C.: A comprehensive literature review of 50 years of fuzzy set theory. Int. J. Comput. Intell. Syst. 9, 3–24 (2016)

    Article  Google Scholar 

  41. Khaleghi, Bahador, Khamis, Alaa, Karray, O.F., Razavi, N.S.: Multisensor data fusion: a review of the state-of-the-art. Inf. Fus. 14(1), 28–44 (2013)

    Article  Google Scholar 

  42. Laosirihongthong, T., Adebanjo, D., Choon Tan, K.: Green supply chain management practices and performance. Ind. Manag. Data Syst. 113(8), 1088–1109 (2013)

    Article  Google Scholar 

  43. Li, Y., Deng, Y.: Generalized ordered propositions fusion based on belief entropy. Int. J. Comput. Commun. Control 13(5), 792–807 (2018)

    Article  Google Scholar 

  44. Liang, Y., Liu, J., Qin, J., Tu, Y.: An improved multi-granularity interval 2-tuple TODIM approach and its application to green supplier selection. Int. J. Fuzzy Syst. https://doi.org/10.1007/s40815-018-0546-8 (2018)

  45. Lin, R.J.: Using fuzzy DEMATEL to evaluate the green supply chain management practices. J. Clean. Prod. 40(2), 32–39 (2013)

    Article  Google Scholar 

  46. Lin, S., Li, C., Xu, F., Liu, D., Liu, J.: Risk identification and analysis for new energy power system in china based on D numbers and decision-making trial and evaluation laboratory (DEMATEL). J. Clean. Prod. 180, 81–96 (2018)

    Article  Google Scholar 

  47. Liu, H.C., You, J.X., Fan, X.J., Lin, Q.L.: Failure mode and effects analysis using D numbers and grey relational projection method. Expert Syst. Appl. 41(10), 4670–4679 (2014)

    Article  Google Scholar 

  48. Liu, T., Deng, Y., Chan, F.: Evidential supplier selection based on DEMATEL and game theory. Int. J. Fuzzy Syst. 20(4), 1321–1333 (2018)

    Article  Google Scholar 

  49. Luthra, S., Garg, D., Haleem, A.: The impacts of critical success factors for implementing green supply chain management towards sustainability: an empirical investigation of Indian automobile industry. J. Clean. Prod. 121, 142–158 (2016)

    Article  Google Scholar 

  50. Mirhedayatian, S.M., Azadi, M., Saen, R.F.: A novel network data envelopment analysis model for evaluating green supply chain management. Int. J. Prod. Econ. 147, 544–554 (2014)

    Article  Google Scholar 

  51. Musharraf, M., Hassan, J., Khan, F., Veitch, B., MacKinnon, S., Imtiaz, S.: Human reliability assessment during offshore emergency conditions. Saf. Sci. 59, 19–27 (2013)

    Article  Google Scholar 

  52. Oliveira, U.R.D., Espindola, L.S., Silva, I.R.D., Silva, I.N.D., Rocha, H.M.: A systematic literature review on green supply chain management: research implications and future perspectives. J. Clean. Prod. 187, 537–561 (2018)

    Article  Google Scholar 

  53. Pourjavad, E., Shahin, A.: The application of mamdani fuzzy inference system in evaluating green supply chain management performance. Int. J. Fuzzy Syst. 20(3), 901–912 (2018)

    Article  Google Scholar 

  54. Rostamzadeh, R., Govindan, K., Esmaeili, A., Sabaghi, M.: Application of fuzzy VIKOR for evaluation of green supply chain management practices. Ecol. Ind. 49, 188–203 (2015)

    Article  Google Scholar 

  55. Sari, K.: A novel multi-criteria decision framework for evaluating green supply chain management practices. Comput. Ind. Eng. 105, 338–347 (2017)

    Article  Google Scholar 

  56. Sarkis, J.: Green Supply Chain Management. Momentum Press, New York (2013)

    Google Scholar 

  57. Sarkis, J., Zhu, Q., Lai, Kh: An organizational theoretic review of green supply chain management literature. Int. J. Prod. Econ. 130(1), 1–15 (2011)

    Article  Google Scholar 

  58. Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  59. Shen, L., Olfat, L., Govindan, K., Khodaverdi, R., Diabat, A.: A fuzzy multi criteria approach for evaluating green supplier’s performance in green supply chain with linguistic preferences. Resour. Conserv. Recycl. 74, 170–179 (2013)

    Article  Google Scholar 

  60. Smets, P., Kennes, R.: The transferable belief model. Artif. Intell. 66(2), 191–234 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  61. Song, Y., Wang, X., Wu, W., Quan, W., Huang, W.: Evidence combination based on credibility and non-specificity. Pattern Anal. Appl. 21(1), 167–180 (2018)

    Article  MathSciNet  Google Scholar 

  62. Tseng, M.L., Lin, Y.H., Tan, K., Chen, R.H., Chen, Y.H.: Using TODIM to evaluate green supply chain practices under uncertainty. Appl. Math. Model. 38(11–12), 2983–2995 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  63. Tseng, M.L., Tan, K., Chiu, A.S.: Identifying the competitive determinants of firms’ green supply chain capabilities under uncertainty. Clean Technol. Environ. Policy 18(5), 1247–1262 (2016)

    Article  Google Scholar 

  64. Uygun, Ö., Dede, A.: Performance evaluation of green supply chain management using integrated fuzzy multi-criteria decision making techniques. Comput. Ind. Eng. 102, 502–511 (2016)

    Article  Google Scholar 

  65. Wu, K.J., Liao, C.J., Tseng, M.L., Chiu, A.S.: Exploring decisive factors in green supply chain practices under uncertainty. Int. J. Prod. Econ. 159, 147–157 (2015)

    Article  Google Scholar 

  66. Xiao, F.: A novel multi-criteria decision making method for assessing health-care waste treatment technologies based on D numbers. Eng. Appl. Artif. Intell. 71, 216–225 (2018)

    Article  Google Scholar 

  67. Xiao, F.: Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy. Inf. Fus. 46, 23–32 (2019)

    Article  Google Scholar 

  68. Xu, H., Deng, Y.: Dependent evidence combination based on shearman coefficient and pearson coefficient. IEEE Access 6(1), 11634–11640 (2018)

    Article  Google Scholar 

  69. Xu, X., Zheng, J., Yang, J.B., Xu, D.L., Chen, Y.W.: Data classification using evidence reasoning rule. Knowl. Based Syst. 116, 144–151 (2017)

    Article  Google Scholar 

  70. Yager, R.R.: A procedure for ordering fuzzy subsets of the unit interval. Inf. Sci. 24(2), 143–161 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  71. Yager, R.R.: Generalized orthopair fuzzy sets. IEEE Trans. Fuzzy Syst. 25(5), 1222–1230 (2017)

    Article  Google Scholar 

  72. Yager, R.R., Alajlan, N.: Decision making with ordinal payoffs under Dempster–Shafer type uncertainty. Int. J. Intell. Syst. 28(11), 1039–1053 (2013)

    Article  Google Scholar 

  73. Yager, R.R., Alajlan, N.: Dempster–Shafer belief structures for decision making under uncertainty. Knowl. Based Syst. 80, 58–66 (2015)

    Article  Google Scholar 

  74. Yager, R.R., Zadeh, L.A.: An Introduction to Fuzzy Logic Applications in Intelligent Systems, vol. 165. Springer, Berlin (2012)

    MATH  Google Scholar 

  75. Yager, R.R., Elmore, P., Petry, F.: Soft likelihood functions in combining evidence. Inf. Fus. 36, 185–190 (2017)

    Article  Google Scholar 

  76. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  MATH  Google Scholar 

  77. Zhou, X., Deng, X., Deng, Y., Mahadevan, S.: Dependence assessment in human reliability analysis based on D numbers and AHP. Nucl. Eng. Des. 313, 243–252 (2017)

    Article  Google Scholar 

  78. Zhu, Q., Sarkis, J., Lai, Kh: Confirmation of a measurement model for green supply chain management practices implementation. Int. J. Prod. Econ. 111(2), 261–273 (2008)

    Article  Google Scholar 

  79. Zhu, Q., Sarkis, J., Lai, Kh: Examining the effects of green supply chain management practices and their mediations on performance improvements. Int. J. Prod. Res. 50(5), 1377–1394 (2012)

    Article  Google Scholar 

Download references

Acknowledgements

The work is partially supported by National Natural Science Foundation of China (Program Nos. 61703338, 61671384), Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2018JQ6085).

Author information

Authors and Affiliations

  1. School of Electronics and Information, Northwestern Polytechnical University, Xi’an, 710072, China

    Xinyang Deng & Wen Jiang

Authors
  1. Xinyang Deng
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Wen Jiang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding authors

Correspondence to Xinyang Deng or Wen Jiang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deng, X., Jiang, W. Evaluating Green Supply Chain Management Practices Under Fuzzy Environment: A Novel Method Based on D Number Theory. Int. J. Fuzzy Syst. 21, 1389–1402 (2019). https://doi.org/10.1007/s40815-019-00639-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-019-00639-5

Keywords