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A Fuzzy Multi-objective Linear Programming Model Based on Interval-valued Intuitionistic Fuzzy Sets for Supplier Selection

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Abstract

Nowadays, companies are paying more attention to supply chain management in order to achieve success in the competitions and keep the customers satisfied. Therefore, supplier selection is of prime importance in a supply chain which has a key role in determining the success or failure of a business. In this paper, fuzzy multi-objective linear programming model with group decision making is presented. Firstly, linguistic variables in the form of interval-valued intuitionistic fuzzy numbers and group decisions are defined. By using TOPSIS method, the weight of each criterion (objective) and weight of each constraint are determined. Then, with defining membership functions of the objectives and membership functions of suppliers’ constraints and using the achieved weights from the previous phase, the supplier selection problem will be converted to fuzzy multi-objective linear programming model which determines the appropriate ordering quantities for each supplier. Finally, two numerical examples for supplier selection are used to demonstrate the practicality and effectiveness of the proposed approach.

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References

  1. Gong, Y.: Fuzzy multi-attribute group decision making method based on interval type-2 fuzzy sets and applications to global supplier selection. Int. J. Fuzzy Syst. 15(4), 392 (2013)

    MathSciNet  Google Scholar 

  2. Tao, Z., Chen, H., Zhou, L., Liu, J.: A generalized multiple attributes group decision making approach based on intuitionistic fuzzy sets. Int. J. Fuzzy Syst. 16(2), 184 (2014)

    MathSciNet  Google Scholar 

  3. Y. He and Z. He Extensions of Atanassov’s Intuitionistic fuzzy interaction bonferroni means and their application to multiple attribute decision making. IEEE Trans. Fuzzy Syst. doi: 10.1109/TFUZZ.2015.2460750

  4. He, Y., Chen, H., Zhou, L., Liu, J., Tao, Z.: Generalized interval-valued atanassov’s intuitionistic fuzzy power operators and their application to group decision making. Int. J. Fuzzy Syst. 15(4), 401–411 (2013)

    MathSciNet  Google Scholar 

  5. Peng, B., Ye, C., Zeng, S.: Some intuitionistic fuzzy weighted geometric distance measures and their application to group decision making. Int. J. Uncertain. Fuzziness Knowl. Syst. 22(5), 699–715 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Izadikhah, M.: Group decision making process for supplier selection with TOPSIS method under interval-valued intuitionistic fuzzy numbers. Adv. Fuzzy Syst. 2, 2012 (2012)

    MathSciNet  MATH  Google Scholar 

  7. Yucel, A., Guneri, A.F.: A weighted additive fuzzy programming approach for multi-criteria supplier selection. Expert Syst. Appl. 38(5), 6281–6286 (2011)

    Article  Google Scholar 

  8. Choi, J., Bai, S.X., Geunes, J., Romeijn, H.E.: Manufacturing delivery performance for supply chain management. Math. Comput. Model. 45(1–2), 11–20 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Liu, F.H.F., Hai, H.L.: The voting analytic hierarchy process method for selecting supplier. Int. J. Prod. Econ. 97(3), 308–317 (2005)

    Article  Google Scholar 

  10. Narasimhan, R.: An analytic approach to supplier selection. J. Purch. Mater. Manag. 1, 27–32 (1983)

    Google Scholar 

  11. Barbarosoglu, G., Yazgac, T.: An application of the analytic hierarchy process to the supplier selection problem. Prod. Invent. Manag. 38, 14–21 (1997)

    Google Scholar 

  12. Jahanshahloo, G.R., Lotfi, F.H., Izadikhah, M.: Extension of the TOPSIS for decision-making problems with fuzzy data. Appl. Math. Comput. 181(2), 1541–1551 (2006)

    Article  MATH  Google Scholar 

  13. Boran, F.E., Genc, S., Kurt, M., Akay, D.: A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst. Appl. 36(8), 11363–11368 (2009)

    Article  Google Scholar 

  14. Zhang, D., Zhang, J., Yu, B.: Supplier selection using MCDM approach based on Vague Set. Workshop Intell. Inform. Technol. Appl. 36, 311–314 (2007)

    Google Scholar 

  15. Faez, F., Ghodsypour, S.H., O’Brien, C.: Vendor selection and order allocation using an integrated fuzzy case-based reasoning and mathematical programming model. Int. J. Prod. Econ. 21(2), 395–408 (2009)

    Article  Google Scholar 

  16. Chen, T.Y., Wang, H.P., Lu, Y.Y.: A multi criteria group decision making approach based on interval- valued intuitionistic fuzzy sets: a comparative perspective. Expert Syst. Appl. 38(6), 7647–7658 (2011)

    Article  Google Scholar 

  17. Amid, A., Ghodsypour, S.H., O’Brien, C.: A weighted max–min model for fuzzy multi-objective supplier selection in a supply chain. Prod. Econ. 131(1), 139–145 (2011)

    Article  Google Scholar 

  18. Chen, C.T.: Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst. 114(1), 1–9 (2000)

    Article  MATH  Google Scholar 

  19. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–356 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  20. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-I. Inf. Sci. 8(3), 199–249 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  21. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  22. Atanassov, K.T., Gargov, G.: Interval valued ntuitionistic fuzzy sets. Fuzzy Sets Syst. 31(3), 343–349 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  23. Xiao, Z., Wei, G.: Application interval-valued intuitionistic fuzzy set to select supplier. Proc. Fifth Int. Conf. Fuzzy Syst. Knowl. Discov 3, 351–355 (2008)

    Google Scholar 

  24. Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall, Englewood Cliffs (1995)

    MATH  Google Scholar 

  25. Weber, C.A., Current, J.R.: A multi objective approach to vendor selection. J. Operat. Res. 68(2), 173–184 (1993)

    Article  MATH  Google Scholar 

  26. Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1(1), 45–55 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  27. Tiwari, R.N., Dharmar, S., Rao, J.R.: Fuzzy goal programming-an additive model. Fuzzy Sets Syst. 24(1), 27–34 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  28. Kobashikawa, C., Dong, F., Hirota, K.: Two techniques to process conflicting subjective probabilities in individual decision making. Int. J. Fuzzy Syst. 11(2), 87–96 (2009)

    MathSciNet  Google Scholar 

  29. Li, L.G., Peng, D.H.: Interval-valued hesitant fuzzy Hamacher synergetic weighted aggregation operators and their application to shale gas areas selection. Math. Probl. Eng. 2014, 25 (2014)

    MathSciNet  Google Scholar 

  30. Zimmermann, H.J.: Fuzzy Set Theory and Its Applications, 4nd edn. Kluwer, Boston (2001)

    Book  Google Scholar 

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Authors and Affiliations

  1. Kerman Graduate University of Advanced Technology, Kerman, Iran

    Afsane Afzali

  2. Department of Computer Science, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

    Marjan Kuchaki Rafsanjani

  3. Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

    Arsham Borumand Saeid

Authors
  1. Afsane Afzali
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  2. Marjan Kuchaki Rafsanjani
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  3. Arsham Borumand Saeid
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Correspondence to Arsham Borumand Saeid.

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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, 864–874 (2016). https://doi.org/10.1007/s40815-016-0201-1

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