Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A q-rung orthopair fuzzy multi-criteria group decision making method for supplier selection based on a novel distance measure


Supplier selection and evaluation is a crucial decision-making issue to establish an effective supply chain. Higher-order fuzzy decision-making methods have become powerful tools to support decision-makers in solving their problems effectively by reflecting uncertainty in calculations better than crisp sets in the last 3 decades. The q-rung orthopair fuzzy (q-ROF) sets which are the general form of both intuitionistic and Pythagorean fuzzy sets, have been recently introduced to provide decision-makers more freedom of expression than other fuzzy sets. In this paper, we introduce q-ROF TOPSIS and q-ROF ELECTRE as two separate methods and new approaches for group decision making to select the best supplier. As the existing distance measures in q-rung orthopair fuzzy environment have some drawbacks and generate counter-intuitive results, we propose a new distance measure along with its proofs to use in both q-ROF TOPSIS and q-ROF ELECTRE methods. Moreover, a comparison study is conducted to illustrate the superiority of the proposed distance measure. Subsequently, a comprehensive case study is performed with q-ROF TOPSIS and q-ROF ELECTRE methods separately to choose the best supplier for a construction company by rating the importance of criteria and alternatives under q-ROF environment. Finally, a comparison and parameter analysis are performed among the proposed q-ROF TOPSIS and q-ROF ELECTRE methods and existing q-ROF decision-making methods to demonstrate the effectiveness of our proposed methods.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8


  1. 1.

    Atanassov KT (1996) An equality between intuitionistic fuzzy sets. Fuzzy Sets Syst 79:257–258.

  2. 2.

    Beikkhakhian Y, Javanmardi M, Karbasian M, Khayambashi B (2015) The application of ISM model in evaluating agile suppliers selection criteria and ranking suppliers using fuzzy TOPSIS-AHP methods. Expert Syst Appl.

  3. 3.

    Boran FE, Akay D (2014) A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition. Inf Sci 255:45–57.

  4. 4.

    Boran FE, Genc S, Kurt M, Akay D (2009) A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst Appl 36:11363–11368.

  5. 5.

    Chen CT, Lin CT, Huang SF (2006) A fuzzy approach for supplier evaluation and selection in supply chain management. Int J Prod Econ 102:289–301.

  6. 6.

    Chen S-M (1995) Measures of similarity between vague sets. Fuzzy Sets Syst 74:217–223

  7. 7.

    Chen T-Y (2007) A note on distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets Syst 158:2523–2525.

  8. 8.

    Chou S-Y, Chang Y-H (2008) A decision support system for supplier selection based on a strategy-aligned fuzzy SMART approach. Expert Syst Appl 34:2241–2253.

  9. 9.

    Dengfeng L, Chuntian C (2002) New similarity measures of intuitionistic fuzzy sets and application to pattern recognitions. Pattern Recogn Lett 23:221–225

  10. 10.

    Dickson GW (1966) An analysis of vendor selection systems and decisions. J Purch 2:5–17.

  11. 11.

    Du WS (2018) Minkowski-type distance measures for generalized orthopair fuzzy sets. Int J Intell Syst 33:802–817

  12. 12.

    Fan L, Zhangyan X (2001) Similarity measures between vague sets. J Softw 12:922–927

  13. 13.

    Feng F, Fujita H, Ali MI, Yager RR, Liu X (2018) Another view on generalized intuitionistic fuzzy soft sets and related multiattribute decision making methods. IEEE Trans Fuzzy Syst 27:474–488

  14. 14.

    Feng F, Liang M, Fujita H, Yager RR, Liu X (2019) Lexicographic orders of intuitionistic fuzzy values and their relationships. Mathematics 7:166

  15. 15.

    Ghoushchi SJ, Milan MD, Rezaee MJ (2018) Evaluation and selection of sustainable suppliers in supply chain using new GP-DEA model with imprecise data. J Ind Eng Int 14:613–625.

  16. 16.

    Grzegorzewski P (2004) Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets Syst 148:319–328.

  17. 17.

    Gupta P, Lin C-T, Mehlawat MK, Grover N, Man Systems C (2015) A new method for intuitionistic fuzzy multiattribute decision making. IEEE Trans Syst Man Cybern Syst 46:1167–1179

  18. 18.

    Haq AN, Kannan G (2006) Fuzzy analytical hierarchy process for evaluating and selecting a vendor in a supply chain model. Int J Adv Manuf Technol 29:826–835.

  19. 19.

    Hong DH, Kim C (1999) A note on similarity measures between vague sets and between elements. Inf Sci 115:83–96

  20. 20.

    Hung W-L, Yang M-S (2004) Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recogn Lett 25:1603–1611.

  21. 21.

    Li D, Zeng W (2018) Distance measure of Pythagorean fuzzy sets. Int J Intell Syst 33:348–361.

  22. 22.

    Li Y, Zhongxian C, Degin Y (2002) Similarity measures between vague sets and vague entropy. J Comput Sci 29:129–132

  23. 23.

    Liang Z, Shi P (2003) Similarity measures on intuitionistic fuzzy sets. Pattern Recogn Lett 24:2687–2693.

  24. 24.

    Liu PD, Wang P (2018) Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making. Int J Intell Syst 33:259–280.

  25. 25.

    Mardani A, Nilashi M, Zavadskas EK, Awang SR, Zare H, Jamal NM (2018) Decision making methods based on fuzzy aggregation operators: 3 decades review from 1986 to 2017. Int J Inf Technol Decis Mak 17:391–466.

  26. 26.

    Memari A, Dargi A, Jokar MRA, Ahmad R, Rahim ARA (2019) Sustainable supplier selection: a multi-criteria intuitionistic fuzzy TOPSIS method. J Manuf Syst 50:9–24.

  27. 27.

    Mitchell HB (2003) On the Dengfeng–Chuntian similarity measure and its application to pattern recognition. Pattern Recogn Lett 24:3101–3104

  28. 28.

    Peng X, Liu L (2019) Information measures for q-rung orthopair fuzzy sets. Int J Intell Syst 34:1795–1834

  29. 29.

    Rashidi K, Cullinane K (2019) A comparison of fuzzy DEA and fuzzy TOPSIS in sustainable supplier selection: implications for sourcing strategy. Expert Syst Appl 121:266–281.

  30. 30.

    Rezaei J, Fahim PB, Tavasszy L (2014) Supplier selection in the airline retail industry using a funnel methodology: conjunctive screening method and fuzzy AHP. Expert Syst Appl 41:8165–8179.

  31. 31.

    Sanayei A, Mousavi SF, Yazdankhah A (2010) Group decision making process for supplier selection with VIKOR under fuzzy environment. Expert Syst Appl 37:24–30.

  32. 32.

    Shen C-Y, Yu K-T (2013) Strategic vender selection criteria. Procedia Comput Sci 17:350–356.

  33. 33.

    Simic D, Kovacevic I, Svircevic V, Simic S (2017) 50 years of fuzzy set theory and models for supplier assessment and selection: a literature review. J Appl Log 24:85–96.

  34. 34.

    Szmidt E, Kacprzyk J (2000) Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst 114:505–518.

  35. 35.

    Verma R, Merigó JM (2019) On generalized similarity measures for Pythagorean fuzzy sets and their applications to multiple attribute decision-making. Int J Intell Syst 34:2556–2583

  36. 36.

    Verma R, Sharma BD (2012) On generalized intuitionistic fuzzy divergence (relative information) and their properties. J Uncertain Syst 6:308–320

  37. 37.

    Verma R, Sharma BD (2014) A new measure of inaccuracy with its application to multi-criteria decision making under intuitionistic fuzzy environment. J Intell Fuzzy Syst 27:1811–1824

  38. 38.

    Vonderembse MA, Tracey M (1999) The impact of supplier selection criteria and supplier involvement on manufacturing performance. J Supply Chain Manag 35:33–39.

  39. 39.

    Wang H, Ju Y, Liu P (2019) Multi-attribute group decision-making methods based on q-rung orthopair fuzzy linguistic sets. Int J Intell Syst.

  40. 40.

    Wang P, Wang J, Wei G, Wei C (2019) Similarity measures of q-rung orthopair fuzzy sets based on cosine function and their applications. Mathematics 7:340

  41. 41.

    Wang R, Li Y (2018) A novel approach for green supplier selection under a q-rung orthopair fuzzy environment. Symmetry 10:687.

  42. 42.

    Wang WQ, Xin XL (2005) Distance measure between intuitionistic fuzzy sets. Pattern Recogn Lett 26:2063–2069.

  43. 43.

    Weber CA, Current JR, Benton WC (1991) Vendor selection criteria and methods. Eur J Oper Res 50:2–18.

  44. 44.

    Wei G, Gao H, Wei Y (2018) Some q-rung orthopair fuzzy Heronian mean operators in multiple attribute decision making. Int J Intell Syst 33:1426–1458.

  45. 45.

    Wilson EJ (1994) The relative importance of supplier selection criteria: a review and update. Int J Purch Mater Manag 30:34–41.

  46. 46.

    Wu MC, Chen TY (2011) The ELECTRE multicriteria analysis approach based on Atanassov’s intuitionistic fuzzy sets. Expert Syst Appl 38:12318–12327.

  47. 47.

    Xia MM, Xu ZS (2010) Some new similarity measures for intuitionistic fuzzy values and their application in group decision making. J Syst Sci Syst Eng 19:430–452.

  48. 48.

    Xu Z, Chen J (2008) An overview of distance and similarity measures of intuitionistic fuzzy sets. Int J Uncertain Fuzziness Knowl Based Syst 16:529–555.

  49. 49.

    Xu Z, Zhao N (2016) Information fusion for intuitionistic fuzzy decision making: an overview. Inf Fusion 28:10–23

  50. 50.

    Xu ZS, Yager RR (2009) Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim Decis Mak 8:123–139.

  51. 51.

    Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22:958–965.

  52. 52.

    Yager RR (2017) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25:1222–1230.

  53. 53.

    Yager RR, Alajlan N (2017) Approximate reasoning with generalized orthopair fuzzy sets. Inf Fusion 38:65–73.

  54. 54.

    Ye J (2011) Cosine similarity measures for intuitionistic fuzzy sets and their applications. Math Comput Model 53:91–97

  55. 55.

    Yu C, Shao Y, Wang K, Zhang L (2019) A group decision making sustainable supplier selection approach using extended TOPSIS under interval-valued Pythagorean fuzzy environment. Expert Syst Appl 121:1–17.

  56. 56.

    Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353.

  57. 57.

    Zhang X, Xu Z (2014) Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29:1061–1078.

Download references

Author information

Correspondence to Fatih Emre Boran.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Pinar, A., Boran, F.E. A q-rung orthopair fuzzy multi-criteria group decision making method for supplier selection based on a novel distance measure. Int. J. Mach. Learn. & Cyber. (2020).

Download citation


  • q-Rung orthopair fuzzy set
  • Distance measure
  • Supplier selection