Soft Computing

, Volume 22, Issue 22, pp 7445–7461 | Cite as

A scientific decision-making framework for supplier outsourcing using hesitant fuzzy information

  • R. Krishankumar
  • K. S. RavichandranEmail author
  • K. K. Murthy
  • A. B. Saeid


Supply chain management (SCM) is an attractive area for research which has seen tremendous growth in the past decades. From the literature we observe that, supplier outsourcing (SO) is a highly explored research field in SCM which lacks significant scientific contribution. The major concern in SO is the decision makers’ (DMs) viewpoint which are often vague and imprecise. To better handle such imprecision, in this paper, we propose a new two-stage decision-making framework called TSDMF, which uses hesitant fuzzy information as input. In the first stage, the DMs’ preferences are aggregated using a newly proposed simple hesitant fuzzy-weighted geometry operator, which uses hesitant fuzzy weights for better understanding the importance of each DM. Following this, in the second stage, criteria weights are estimated using newly proposed hesitant fuzzy statistical variance method and finally, a new ranking method called three-way hesitant fuzzy VIKOR (TWHFV) is proposed by extending the VIKOR ranking method to hesitant fuzzy environment. This ranking method uses three categories viz., cost, benefit and neutral along with Euclid distance for its formulation. The practicality of the proposed TSDMF is verified by demonstrating a supplier outsourcing example in an automobile factory. The robustness of TWHFV is realized by using sensitivity analysis and other strengths of TSDMF are discussed by comparison with another framework.


Supplier outsourcing Hesitant fuzzy VIKOR Standard variance Aggregation Decision making 



We the authors thank the funding agency, University Grants Commission (UGC) for their financial support through Rajiv Gandhi National Fellowship (RGNF) scheme under the award number: F./2015-17/RGNF-2015-17-TAM-83. We also thank the Department of Science and Technology (DST), India for their financial aid in setting up a cloud environment under the FIST programme (Award Number: SR/FST/ETI-349/2013). We also express our heartfelt thanks to SASTRA University for offering us an excellent infrastructure to carry out our research work. Finally, we express our sincere thanks to the editor and to the anonymous reviewers for their constructive comments.

Compliance with ethical standards

Conflict of interest

All authors of this research paper declare that, there is no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Chai J, Ngai EWT (2015) Multi-perspective strategic supplier selection in uncertain environments. Int J Prod Econ 166:215–225. CrossRefGoogle Scholar
  2. Chai J, Liu JNK, Ngai EWT (2013) Application of decision-making techniques in supplier selection: a systematic review of literature. Expert Syst Appl 40(10):3872–3885. CrossRefGoogle Scholar
  3. Chang KH (2015) Enhanced assessment of a supplier selection problem by integration of soft sets and hesitant fuzzy linguistic term set. Proc Inst Mech Eng Part B J Eng Manuf 229(9):1635–1644. CrossRefGoogle Scholar
  4. Charulatha B, Rodrigues P, Chitralekha T (2013) A comparative study of different distance metrics that can be used in Fuzzy Clustering Algorithms. IJETTCS.
  5. Chen N, Xu Z (2015) Hesitant fuzzy ELECTRE II approach: a new way to handle multi-criteria decision making problems. Inf Sci 292:175–197. CrossRefGoogle Scholar
  6. Choi J, Bai SX, Geunes J, Edwin Romeijn H (2007) Manufacturing delivery performance for supply chain management. Math Comput Model 45(1–2):11–20. MathSciNetCrossRefzbMATHGoogle Scholar
  7. Chýna V, Kuncová M, Sekni J (2013) Estimation of weights in multi-criteria decision-making optimization models. In Proceedings of 30th international conference mathematical methods in economics, pp. 355–360Google Scholar
  8. Darabi S, Heydari J (2016) An interval- valued hesitant fuzzy ranking method based on group decision analysis for green supplier selection. IFAC-PapersOnLine 49(2):12–17. CrossRefGoogle Scholar
  9. Dong JY, Yuan FF, Wan SP (2017) Extended VIKOR method for multiple criteria decision-making with linguistic hesitant fuzzy information. Comput Ind Eng 112:305–319. CrossRefGoogle Scholar
  10. Fahmi A, Kahraman C, Bilen Ü (2016) ELECTRE I method using hesitant linguistic term sets: an application to supplier selection. Int J Comput Intell Syst 9(1):153–167. CrossRefGoogle Scholar
  11. Fülöp J (2001) Introduction to decision making methods. Oper ResGoogle Scholar
  12. Gitinavard H, Mousavi SM, Vahdani B (2015) A balancing and ranking method based on hesitant fuzzy sets for solving decision-making problems under uncertainty. Int J Eng 28(2):214–223Google Scholar
  13. 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. CrossRefGoogle Scholar
  14. Gitinavard H, Ghaderi H, Pishvaee MS (2017) Green supplier evaluation in manufacturing systems: a novel interval-valued hesitant fuzzy group outranking approach. Soft Comput. CrossRefGoogle Scholar
  15. Gul M, Celik E, Aydin N, Gumas A, Guneri A (2016) A state of the art literature review of VIKOR and its fuzzy extensions on applications. Appl Soft Comput 46:60–89. CrossRefGoogle Scholar
  16. Jin F, Pei L, Chen H, Zhou L (2014) Interval-valued intuitionistic fuzzy continuous weighted entropy and its application to multi-criteria fuzzy group decision making. Knowl-Based Syst 59:132–141. CrossRefGoogle Scholar
  17. Li J, Wang J (2017) An extended QUALIFLEX method under probability hesitant fuzzy environment for selecting green suppliers. Int J Fuzzy Syst 19:40815. MathSciNetCrossRefGoogle Scholar
  18. Liang D, Xu Z, Liu D (2017) Three-way decisions based on decision-theoretic rough sets with dual hesitant fuzzy information. Inf Sci 396:127–143. CrossRefGoogle Scholar
  19. Liao H, Xu Z (2013) A VIKOR-based method for hesitant fuzzy multi-criteria decision making. Fuzzy Optim Decis Mak 12(4):373–392. MathSciNetCrossRefGoogle Scholar
  20. Liao H, Xu Z (2014) Some new hybrid weighted aggregation operators under hesitant fuzzy multi-criteria decision making environment. J Intell Fuzzy Syst 26(4):1601–1617. MathSciNetCrossRefzbMATHGoogle Scholar
  21. Liao H, Xu Z (2015) Consistency of the fused intuitionistic fuzzy preference relation in group intuitionistic fuzzy analytic hierarchy process. Appl Soft Comput 35:812–826. CrossRefGoogle Scholar
  22. Liao H, Xu Z, Xia M (2014a) Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making. Int J Inf Technol Decis Mak 13(1):47–76. CrossRefGoogle Scholar
  23. Liao H, Xu Z, Zeng XJ (2014b) Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Inf Sci 271:125–142. MathSciNetCrossRefzbMATHGoogle Scholar
  24. Liao H, Xu Z, Zeng X-J (2014c) Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Trans Fuzzy Syst. CrossRefGoogle Scholar
  25. Liu W, Liao H (2017) A bibliometric analysis of fuzzy decision research during 1970–2015. Int J Fuzzy Syst. CrossRefGoogle Scholar
  26. Liu S, Chan FTS, Ran W (2016) Decision making for the selection of cloud vendor: an improved approach under group decision-making with integrated weights and objective/subjective attributes. Expert Syst Appl 55:37–47. CrossRefGoogle Scholar
  27. Mahmoudi A, Sadi-Nezhad S, Makui A, Vakili MR (2016) An extension on PROMETHEE based on the typical hesitant fuzzy sets to solve multi-attribute decision-making problem. Kybernetes 45(8):1213–1231. CrossRefGoogle Scholar
  28. Mardani A, Zavadskas EK, Govindan K, Senin AA, Jusoh A (2016) VIKOR technique: a systematic review of the state of the art literature on methodologies and applications. Sustainability 8(1):1–38. CrossRefGoogle Scholar
  29. O’Haire C, McPheeters M, Nakamoto E, LaBrant L, Most C, Lee K, Oregon Evidence-based Practice Center and the Vanderbilt Evidence-based Practice Center (2011) Engaging stakeholders to identify and prioritize future research needs. Methods future research needs report no. 4, (11-EHC044-EF).
  30. Opricovic S, Tzeng GH (2004) Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur J Oper Res 156(2):445–455. CrossRefzbMATHGoogle Scholar
  31. Öztayşi B, Sürer Ö (2014) Supply chain management under fuzziness. Supply Chain Manag Under Fuzziness 313:199–224. MathSciNetCrossRefGoogle Scholar
  32. Ren Z, Xu Z, Wang H (2017) Dual hesitant fuzzy VIKOR method for multi-criteria group decision making based on fuzzy measure and new comparison method. Inf Sci 388–389:1–16. CrossRefGoogle Scholar
  33. Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York, pp 579–606Google Scholar
  34. Saaty TL, Ozdemir MS (2003) Why the magic number seven plus or minus two. Math Comput Model 38(3):233–244. MathSciNetCrossRefzbMATHGoogle Scholar
  35. Simić D, Kovačević I, Svirčević V, Simić S (2017) 50 years of fuzzy set theory and models for supplier assessment and selection: a literature review. J Appl Log 24:85–96. MathSciNetCrossRefzbMATHGoogle Scholar
  36. Sinwar D, Kaushik R (2014) Study of Euclidean and Manhattan distance metrics using simple k-means clustering. Int J Res Appl Sci Eng Technol (IJRASET) 2(5):270–274Google Scholar
  37. Spearman C (1904) The proof and measurement of association between two things. Am J Psychol 15(1):72–101CrossRefGoogle Scholar
  38. Taciana C, Gussen G (2015) Hesitant fuzzy analytic hierarchy process. In: IEEE international conference on fuzzy system, pp 1–7Google Scholar
  39. Tang S-L (2017) Green supplier selection model with hesitant fuzzy information. J Intell Fuzzy Syst 32(1):189–195. CrossRefzbMATHGoogle Scholar
  40. Thakur GS, Thakur R, Singh R (2014) New hesitant fuzzy operators. Fuzzy Inf Eng 6(3):379–392MathSciNetCrossRefGoogle Scholar
  41. Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. IEEE International Conference on Fuzzy Systems. CrossRefzbMATHGoogle Scholar
  42. Tyagi SK (2016) Multiple attribute decision making using hesitant triangular fuzzy sets. In: International conference on electrical, electronics, and optimization techniques (ICEEOT), pp 1502–1510.
  43. Wang H, Xu Z (2016) Multi-groups decision making using intuitionistic-valued hesitant fuzzy information. Int J Comput Intell Syst 9(3):468–482. CrossRefGoogle Scholar
  44. Wood DA (2016) Supplier selection for development of petroleum industry facilities, applying multi-criteria decision making techniques including fuzzy and intuitionistic fuzzy TOPSIS with flexible entropy weighting. J Nat Gas Sci Eng 28(December):594–612. CrossRefGoogle Scholar
  45. Xia M, Xu Z (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52(3):395–407. MathSciNetCrossRefzbMATHGoogle Scholar
  46. Xia M, Xu Z (2012) Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment. Inf Fusion 13(1):31–47. CrossRefGoogle Scholar
  47. Xu, Z. (2014). Hesitant fuzzy sets theory. In: Studies in fuzziness and soft computing, vol 314. CrossRefGoogle Scholar
  48. Xu Z, Liao H (2015) Intuitionistic fuzzy analytic hierarchy process. IEEE Trans Fuzzy Syst. CrossRefGoogle Scholar
  49. Xu Z, Xia M (2011a) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181(11):2128–2138. MathSciNetCrossRefzbMATHGoogle Scholar
  50. Xu Z, Xia M (2011b) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181(11):2128–2138. MathSciNetCrossRefzbMATHGoogle Scholar
  51. Xu Z, Zhang X (2013) Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information. Knowl-Based Syst 52:53–64. CrossRefGoogle Scholar
  52. Xue M, Du Y (2017) A group decision-making model based on regression method with hesitant fuzzy preference relations. Math Problems Eng 2017:1–8MathSciNetCrossRefGoogle Scholar
  53. Yu D, Li D-F, Merigó JM (2016a) Dual hesitant fuzzy group decision making method and its application to supplier selection. Int J Mach Learn Cybern 7:819–831. CrossRefGoogle Scholar
  54. Yu D, Li D-F, Merigó JM (2016b) Dual hesitant fuzzy group decision making method and its application to supplier selection. Int J Mach Learn Cybernet 7:819–831. CrossRefGoogle Scholar
  55. Yücel A, Güneri AF (2011) A weighted additive fuzzy programming approach for multi-criteria supplier selection. Expert Syst Appl 38(5):6281–6286. CrossRefGoogle Scholar
  56. Yue Z (2011) A method for group decision-making based on determining weights of decision makers using TOPSIS. Appl Math Model 35(4):1926–1936. MathSciNetCrossRefzbMATHGoogle Scholar
  57. Zhang Z (2016) Multi-criteria decision-making using interval-valued hesitant fuzzy QUALIFLEX methods based on a likelihood-based comparison approach. Neural Comput Appl. CrossRefGoogle Scholar
  58. Zhang Z (2017) Multi-criteria decision-making using interval-valued hesitant fuzzy QUALIFLEX methods based on a likelihood-based comparison approach. Neural Comput Appl 28(7):1835–1854. CrossRefGoogle Scholar
  59. Zhang X, Xu Z (2015) Hesitant fuzzy QUALIFLEX approach with a signed distance-based comparison method for multiple criteria decision analysis. Expert Syst Appl 42(2):873–884. MathSciNetCrossRefGoogle Scholar
  60. Zhang Y, Wang Y, Wang J (2014) Objective attributes weights determining based on shannon information entropy in hesitant fuzzy multiple attribute decision making. Math Probl Eng. CrossRefGoogle Scholar
  61. Zhang X, Xu Z, Xing X (2016) Hesitant fuzzy programming technique for multidimensional analysis of hesitant fuzzy preferences. OR Spectr 38:789–817. MathSciNetCrossRefzbMATHGoogle Scholar
  62. Zhao X, Lin R, Wei G (2014) Hesitant triangular fuzzy information aggregation based on Einstein operations and their application to multiple attribute decision making. Expert Syst Appl 41(1):1086–1094. CrossRefGoogle Scholar
  63. Zhao H, You JX, Liu HC (2016) Failure mode and effect analysis using MULTIMOORA method with continuous weighted entropy under interval-valued intuitionistic fuzzy environment. Soft Comput. CrossRefGoogle Scholar
  64. Zhaoxia Z, De X, Jiang G (2013) A strategic decision framework for sustainability in supply chain. In: Proceedings of the 5th international conference on intelligent human-machine systems and cybernetics, IHMSC 2013. 1:7–10.
  65. Zhou X, Li Q (2014) Multiple attribute decision making based on hesitant fuzzy Einstein geometric aggregation operators. J Appl Math. CrossRefGoogle Scholar
  66. Zhu B, Xu Z, Zhang R, Hong M (2016) Hesitant analytic hierarchy process. Eur J Oper Res 250(2):602–614. MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ICT, School of ComputingSASTRA UniversityThanjavurIndia
  2. 2.Department of Pure Mathematics, Faculty of Mathematics and ComputerShahid Bahonar University of KermanKermanIran

Personalised recommendations