Annals of Operations Research

, Volume 272, Issue 1–2, pp 139–157 | Cite as

A novel supplier selection method that integrates the intuitionistic fuzzy weighted averaging method and a soft set with imprecise data

  • Kuei-Hu ChangEmail author
S.I.:Advances in Theoretical and Applied Combinatorial Optimization


Along with advances in technology and the advent of the information age, supply chain competition will become the core strategy of enterprises that are in pursuit of a competitive advantage. Supplier selection and evaluation are key issues in the success of a competitive enterprise. Supplier selection for an enterprise is a typical multicriteria decision-making problem that includes qualitative and quantitative criteria. However, some input information can be missing or nonexistent in selecting suppliers, rendering it more difficult to choose the best supplier. To this end, the traditional supplier selection approach does not consider the ordered weights of the values of attributes, causing biased conclusions. Moreover, there is a significant amount of fuzzy and intuitionistic fuzzy information in real-world situations, for which the traditional approach in choosing the best supplier becomes no longer applicable. To solve these issues, this study proposes a novel supplier selection method, integrating the intuitionistic fuzzy weighted averaging method and the soft set with imprecise data, in identifying the best supplier in a supply chain. To illustrate our proposed method, a numerical example of the supplier selection problem is adopted. This paper also compares the results of the fuzzy weighted averaging, intuitionistic fuzzy weighted averaging, and intuitionistic fuzzy dependent aggregation operator methods in dealing with missing or nonexistent data. Based on our results, the proposed method is reasonable, effective, and better reflects real-world situations with regard to supplier selection.


Supplier selection Intuitionistic fuzzy set Soft set Multi-criteria decision making Ordered weighted geometric averaging 



The authors would like to thank the Ministry of Science and Technology, Taiwan, for financially supporting this research under Contract Nos. MOST 105-2410-H-145-002 and MOST 106-2410-H-145-001.


  1. Aktas, H. (2015). Some algebraic applications of soft sets. Applied Soft Computing, 28, 327–331.CrossRefGoogle Scholar
  2. Ali, M. I., Feng, F., Liu, X. Y., Min, W. K., & Shabir, M. (2009). On some new operations in soft set theory. Computers & Mathematics with Applications, 57(9), 1547–1553.CrossRefGoogle Scholar
  3. Ali, M. I., & Shabir, M. (2014). Logic connectives for soft sets and fuzzy soft sets. IEEE Transactions on Fuzzy Systems, 22(6), 1431–1442.CrossRefGoogle Scholar
  4. Atanassov, K.T. (1983). Intuitionistic fuzzy sets. Central Tech Library, Bulgarian Academy Science, Sofia, Bulgaria. Report 1697/84.Google Scholar
  5. Chan, F. T. S., & Kumar, N. (2007). Global supplier development considering risk factors using fuzzy extended AHP-based approach. Omega, International Journal of Management Science, 35(4), 417–431.CrossRefGoogle Scholar
  6. Chang, K. H. (2009). Evaluate the orderings of risk for failure problems using a more general RPN methodology. Microelectronics Reliability, 49(12), 1586–1596.CrossRefGoogle Scholar
  7. Chang, K. H. (2014). A more general risk assessment methodology using soft sets based ranking technique. Soft Computing, 18(1), 169–183.CrossRefGoogle Scholar
  8. Chang, K. H. (2015). Enhanced assessment of a supplier selection problem by integration of soft sets and hesitant fuzzy linguistic term set. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 229(9), 1635–1644.CrossRefGoogle Scholar
  9. Chang, K. H. (2016). A novel reliability allocation approach using the OWA tree and soft set. Annals of Operations Research, 244(1), 3–22.CrossRefGoogle Scholar
  10. Chang, K. H., Chang, Y. C., Chain, K., & Chung, H. Y. (2016). Integrating soft set theory and fuzzy linguistic model to evaluate the performance of training simulation systems. PLos ONE, 11(9), e0162092.CrossRefGoogle Scholar
  11. Chang, K. H., & Cheng, C. H. (2010). A risk assessment methodology using intuitionistic fuzzy set in FMEA. International Journal of Systems Science, 41(12), 1457–1471.CrossRefGoogle Scholar
  12. Chang, K. H., & Wen, T. C. (2010). A novel efficient approach for DFMEA combining 2-tuple and the OWA operator. Expert Systems with Applications, 37(3), 2362–2370.CrossRefGoogle Scholar
  13. Chen, S. M., & Tan, J. M. (1994). Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems, 67(2), 163–172.CrossRefGoogle Scholar
  14. Das, S., & Kar, S. (2014). Group decision making in medical system: An intuitionistic fuzzy soft set approach. Applied Soft Computing, 24, 196–211.CrossRefGoogle Scholar
  15. Deli, I., & Cagman, N. (2015). Intuitionistic fuzzy parameterized soft set theory and its decision making. Applied Soft Computing, 28, 109–113.CrossRefGoogle Scholar
  16. Fuller, R., & Majlender, P. (2003). On obtaining minimal variability OWA operator weights. Fuzzy Sets and Systems, 136(2), 203–215.CrossRefGoogle Scholar
  17. Ghorbani, M., Arabzad, S. M., & Shahin, A. (2013). A novel approach for supplier selection based on the Kano model and fuzzy MCDM. International Journal of Production Research, 51(18), 5469–5484.CrossRefGoogle Scholar
  18. Govindan, K., & Sivakumar, R. (2016). Green supplier selection and order allocation in a low-carbon paper industry: integrated multi-criteria heterogeneous decision-making and multi-objective linear programming approaches. Annals of Operations Research, 238(1–2), 243–276.CrossRefGoogle Scholar
  19. Kar, A. K. (2015). A hybrid group decision support system for supplier selection using analytic hierarchy process, fuzzy set theory and neural network. Journal of Computational Science, 6, 23–33.CrossRefGoogle Scholar
  20. Karsak, E. E., & Dursun, M. (2014). An integrated supplier selection methodology incorporating QFD and DEA with imprecise data. Expert Systems with Applications, 41(16), 6995–7004.CrossRefGoogle Scholar
  21. Kim, D. Y., & Wagner, S. M. (2012). Supplier selection problem revisited from the perspective of product configuration. International Journal of Production Research, 50(11), 2864–2876.CrossRefGoogle Scholar
  22. Li, Z. W., & Xie, T. S. (2014). The relationship among soft sets, soft rough sets and topologies. Soft Computing, 18(4), 717–728.CrossRefGoogle Scholar
  23. Lima, F. R., Osiro, L., & Carpinetti, L. C. R. (2014). A comparison between fuzzy AHP and fuzzy TOPSIS methods to supplier selection. Applied Soft Computing, 21, 194–209.CrossRefGoogle Scholar
  24. Maji, P. K., Biswas, R., & Roy, A. R. (2003). Soft set theory. Computers & Mathematics with Applications, 45(4–5), 555–562.CrossRefGoogle Scholar
  25. Mamat, R., Herawan, T., & Denis, M. M. (2013). MAR: Maximum attribute relative of soft set for clustering attribute selection. Knowledge-Based Systems, 52, 11–20.CrossRefGoogle Scholar
  26. Mianabadi, H., Sheikhmohammady, M., Mostert, E., & Van de Giesen, N. (2014). Application of the ordered weighted averaging (OWA) method to the Caspian Sea conflict. Stochastic Environmental Research and Risk Assessment, 28(6), 1359–1372.Google Scholar
  27. Molodtsov, D. (1999). Soft set theory—first results. Computers & Mathematics with Applications, 37(4–5), 19–31.CrossRefGoogle Scholar
  28. O’Hagan, M. (1988). Aggregating template or rule antecedents in real time expert systems with fuzzy set logic. In Proceedings of the 22th Annual IEEE Asilomar Conference on Signals, Systems, Computers Pacific Grove, CA, USA, pp. 681-689.Google Scholar
  29. Peric, T., Babic, Z., & Veza, I. (2013). Vendor selection and supply quantities determination in a bakery by AHP and fuzzy multi-criteria programming. International Journal of Computer Integrated Manufacturing, 26(9), 816–829.CrossRefGoogle Scholar
  30. Rezaei, J., Fahim, P. B. M., & Tavasszy, L. (2014). Supplier selection in the airline retail industry using a funnel methodology: Conjunctive screening method and fuzzy AHP. Expert Systems with Applications, 41(18), 8165–8179.CrossRefGoogle Scholar
  31. Saeidi, R. G., Oukil, A., Amin, G. R., & Raissi, S. (2015). Prioritization of textile fabric defects using ordered weighted averaging operator. International Journal of Advanced Manufacturing Technology, 76(5–8), 745–752.CrossRefGoogle Scholar
  32. Schoenherr, T., Modi, S. B., Benton, W. C., Carter, C. R., Choi, T. Y., Larson, P. D., et al. (2012). Research opportunities in purchasing and supply management. International Journal of Production Research, 50(16), 4556–4579.CrossRefGoogle Scholar
  33. Sheikhalishahi, M., & Torabi, S. A. (2014). Maintenance supplier selection considering life cycle costs and risks: a fuzzy goal programming approach. International Journal of Production Research, 52(23), 7084–7099.CrossRefGoogle Scholar
  34. Singh, S. K., & Yadav, S. P. (2016). A new approach for solving intuitionistic fuzzy transportation problem of type-2. Annals of Operations Research, 243(1–2), 349–363.CrossRefGoogle Scholar
  35. Suo, M. Q., Li, Y. P., & Huang, G. H. (2012). Multicriteria decision making under uncertainty: An advanced ordered weighted averaging operator for planning electric power systems. Engineering Applications of Artificial Intelligence, 25(1), 72–81.CrossRefGoogle Scholar
  36. Wang, F., Zeng, S. L., & Zhang, C. H. (2013). A method based on intuitionistic fuzzy dependent aggregation operators for supplier selection, Mathematical Problems in Engineering. Article ID: 481202.Google Scholar
  37. Wang, X., Dang, Y. G., & Hou, D. Q. (2014). Multiattribute grey target decision method based on soft set theory. Mathematical Problems in Engineering. Article ID 307586.Google Scholar
  38. Wu, C. M., Hsieh, C. L., & Chang, K. L. (2013). A hybrid multiple criteria decision making model for supplier selection. Mathematical Problems in Engineering Article ID: 324283.Google Scholar
  39. Xiao, Z., Gong, K., & Zou, Y. (2009). A combined forecasting approach based on fuzzy soft sets. Journal of Computational and Applied Mathematics, 228(1), 326–333.CrossRefGoogle Scholar
  40. Xu, W., Xiao, Z., Dang, X., Yang, D. L., & Yang, X. L. (2014). Financial ratio selection for business failure prediction using soft set theory. Knowledge-Based Systems, 63, 59–67.CrossRefGoogle Scholar
  41. Xu, Z. S. (2007). Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems, 15(6), 1179–1187.CrossRefGoogle Scholar
  42. Xu, Z. S., & Da, W. L. (2002). The ordered weighted geometric averaging operators. International Journal of Intelligent Systems, 17(7), 709–716.CrossRefGoogle Scholar
  43. Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems, Man and Cybernetics, 18(1), 183–190.CrossRefGoogle Scholar
  44. You, X. Y., You, J. X., Liu, H. C., & Zhen, L. (2015). Group multi-criteria supplier selection using an extended VIKOR method with interval 2-tuple linguistic information. Expert Systems with Applications, 42(4), 1906–1916.CrossRefGoogle Scholar
  45. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.CrossRefGoogle Scholar
  46. Zarghami, M., Szidarovszky, F., & Ardakanian, R. (2008). Sensitivity analysis of the OWA operator. IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics, 38(2), 547–552.CrossRefGoogle Scholar
  47. Zeng, S. Z., Merigo, J. M., Palacios-Marques, D., Jin, H. H., & Gu, F. J. (2017). Intuitionistic fuzzy induced ordered weighted averaging distance operator and its application to decision making. Journal of Intelligent and Fuzzy Systems, 32(1), 11–22.CrossRefGoogle Scholar
  48. Zeng, S. Z., Palacios-Marques, D., & Zhu, F. C. (2016). A new model for interactive group decision making with intuitionistic fuzzy preference relations. Informatica, 27(4), 911–928.CrossRefGoogle Scholar
  49. Zeng, S. Z., Su, W. H., & Zhang, C. H. (2016). Intuitionistic fuzzy generalized probabilistic ordered weighted averaging operator and its application to group decision making. Technological and Economic Development of Economy, 22(2), 177–193.CrossRefGoogle Scholar
  50. Zhang, Z. M., Wang, C., Tian, D. Z., & Li, K. (2014). A novel approach to interval-valued intuitionistic fuzzy soft set based decision making. Applied Mathematical Modelling, 38(4), 1255–1270.CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Management SciencesR.O.C. Military AcademyKaohsiungTaiwan

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