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TOPSIS Method for Developing Supplier Selection with Probabilistic Linguistic Information

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Abstract

In this paper, we investigate the probabilistic linguistic multiple attribute group decision-making (MAGDM) with incomplete weight information. In this method, the linguistic term sets (LTSs) is converted into probabilistic linguistic term sets (PLTSs). For deriving the weight information of the attribute, an optimization model is built on the basis of the fundamental idea of conventional TOPSIS method, by which the attribute weights can be decided. In addition, the optimal alternative(s) is decided by computing the shortest distance from the probabilistic linguistic positive ideal solution (PLPIS) and on the other side the farthest distance of the probabilistic linguistic negative ideal solution (PLNIS). The method has precise trait in probabilistic linguistic information processing. The information distortion and losing was avoided which happen formerly in the probabilistic linguistic information processing. In the end, a case study for green supplier selection is given to demonstrate the merits of the developed method. The results display that the approach is uncomplicated, valid and simple to compute.

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References

  1. Hwang, C.L., Yoon, K.: Multiple attribute decision making methods and applications. Springer, Berlin (1981)

    MATH  Google Scholar 

  2. Lai, Y.J., Liu, T.Y., Hwang, C.L.: Topsis for MODM. Eur. J. Oper. Res. 76, 486–500 (1994)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  4. Wang, Y.M., Elhag, T.M.S.: Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment. Expert Syst. Appl. 31, 309–319 (2006)

    Google Scholar 

  5. Taleizadeh, A.A., Niaki, S.T.A., Aryanezhad, M.B.: A hybrid method of Pareto, TOPSIS and genetic algorithm to optimize multi-product multi-constraint inventory control systems with random fuzzy replenishments. Math. Comput. Modell. 49, 1044–1057 (2009)

    MathSciNet  MATH  Google Scholar 

  6. Wei, G.W.: Extension of TOPSIS method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information. Knowl. Inf. Syst. 25, 623–634 (2010)

    Google Scholar 

  7. Chen, Y., Li, K.W., Liu, S.F.: An OWA-TOPSIS method for multiple criteria decision analysis. Expert Syst. Appl. 38, 5205–5211 (2011)

    Google Scholar 

  8. Baky, I.A.: Interactive TOPSIS algorithms for solving multi-level non-linear multi-objective decision-making problems. Appl. Math. Modell. 38, 1417–1433 (2014)

    MathSciNet  MATH  Google Scholar 

  9. Lan, J.B., Yang, M., Hu, M.M., Liu, F.: Multi-attribute group decision making based on hesitant fuzzy sets, TOPSIS method and fuzzy preference relations. Technol. Econ. Dev. Econ. 24, 2295–2317 (2018)

    Google Scholar 

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

    Google Scholar 

  11. Wang, L.N., Wang, H., Xu, Z.S., Ren, Z.L.: The interval-valued hesitant Pythagorean fuzzy set and its applications with extended TOPSIS and Choquet integral-based method. Int. J. Intell. Syst. 34, 1063–1085 (2019)

    Google Scholar 

  12. Tang, H.M., Shi, Y., Dong, P.W.: Public blockchain evaluation using entropy and TOPSIS. Expert Syst. Appl. 117, 204–210 (2019)

    Google Scholar 

  13. Lu, J.P., Wei, C., Wu, J., Wei, G.W.: TOPSIS method for probabilistic linguistic MAGDM with entropy weight and its application to supplier selection of new agricultural machinery products. Entropy 21, 953 (2019)

    MathSciNet  Google Scholar 

  14. Abdullah, S., Amin, N.U.: Analysis of S-box image encryption based on generalized fuzzy soft expert set. Nonlinear Dyn. 79, 1679–1692 (2015)

    Google Scholar 

  15. Wang, J., Gao, H., Wei, G.W.: Some 2-tuple linguistic neutrosophic number Muirhead mean operators and their applications to multiple attribute decision making. J. Exp. Theor. Artif. Intell. 31, 409–439 (2019)

    Google Scholar 

  16. Wang, J., Lu, J.P., Wei, G.W., Lin, R., Wei, C.: Models for MADM with single-valued neutrosophic 2-tuple linguistic muirhead mean operators. Mathematics 7, 442 (2019)

    Google Scholar 

  17. Zhang, S.Q., Gao, H., Wei, G.W., Wei, Y., Wei, C.: Evaluation based on distance from average solution method for multiple criteria group decision making under picture 2-tuple linguistic environment. Mathematics 7, 243 (2019)

    Google Scholar 

  18. Deng, X.M., Gao, H.: TODIM method for multiple attribute decision making with 2-tuple linguistic Pythagorean fuzzy information. J. Intell. Fuzzy Syst. 37, 1769–1780 (2019)

    Google Scholar 

  19. Lu, J.P., Wei, C.: TODIM method for performance appraisal on social-integration-based rural reconstruction with interval-valued intuitionistic fuzzy information. J. Intell. Fuzzy Syst. 37, 1731–1740 (2019)

    Google Scholar 

  20. Rodriguez, R.M., Martinez, L., Herrera, F.: Hesitant fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 20, 109–119 (2012)

    Google Scholar 

  21. Liao, H.C., Xu, Z.S., Zeng, X.J.: Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Trans. Fuzzy Syst. 23, 1343–1355 (2015)

    Google Scholar 

  22. Gou, X.J., Xu, Z.S., Liao, H.C.: Hesitant fuzzy linguistic entropy and cross-entropy measures and alternative queuing method for multiple criteria decision making. Inf. Sci. 388, 225–246 (2017)

    Google Scholar 

  23. Wei, G.W.: The generalized dice similarity measures for multiple attribute decision making with hesitant fuzzy linguistic information. Econ. Res. 32, 1498–1520 (2019)

    Google Scholar 

  24. Lin, M.W., Xu, Z.S., Zhai, Y.L., Yao, Z.Q.: Multi-attribute group decision-making under probabilistic uncertain linguistic environment. J. Oper. Res. Soc. 69, 157–170 (2018)

    Google Scholar 

  25. Pang, Q., Wang, H., Xu, Z.S.: Probabilistic linguistic term sets in multi-attribute group decision making. Inf. Sci. 369, 128–143 (2016)

    Google Scholar 

  26. Liang, D.C., Kobina, A., Quan, W.: Grey relational analysis method for probabilistic linguistic multi-criteria group decision-making based on geometric Bonferroni mean. Int. J. Fuzzy Syst. 20, 2234–2244 (2018)

    Google Scholar 

  27. Wei, G.W., Wang, R., Wang, J., Wei, C., Zhang, Y.: Methods for evaluating the technological innovation capability for the high-tech enterprises with generalized interval neutrosophic number Bonferroni mean operators. IEEE Access 7, 86473–86492 (2019)

    Google Scholar 

  28. Lin, M.W., Chen, Z.Y., Liao, H.C., Xu, Z.S.: ELECTRE II method to deal with probabilistic linguistic term sets and its application to edge computing. Nonlinear Dyn. 96, 2125–2143 (2019)

    Google Scholar 

  29. Chen, S.X., Wang, J.Q., Wang, T.L.: Cloud-based ERP system selection based on extended probabilistic linguistic MULTIMOORA method and Choquet integral operator. Comput. Appl. Math. 38, 88 (2019)

    MathSciNet  MATH  Google Scholar 

  30. Wu, X.L., Liao, H.C., Xu, Z.S., Hafezalkotob, A., Herrera, F.: Probabilistic linguistic MULTIMOORA: a multicriteria decision making method based on the probabilistic linguistic expectation function and the improved Borda rule. IEEE Trans. Fuzzy Syst. 26, 3688–3702 (2018)

    Google Scholar 

  31. Feng, X.Q., Liu, Q., Wei, C.P.: Probabilistic linguistic QUALIFLEX approach with possibility degree comparison. J. Intell. Fuzzy Syst. 36, 719–730 (2019)

    Google Scholar 

  32. Liao, H.C., Jiang, L.S., Lev, B., Fujitac, H.: Novel operations of PLTSs based on the disparity degrees of linguistic terms and their use in designing the probabilistic linguistic ELECTRE III method. Appl. Soft Comput. 80, 450–464 (2019)

    Google Scholar 

  33. Xu, Z.S.: Deviation measures of linguistic preference relations in group decision making. Omega-Int. J. Manag. Sci. 33, 249–254 (2005)

    Google Scholar 

  34. Gou, X.J., Xu, Z.S., Liao, H.C.: Multiple criteria decision making based on Bonferroni means with hesitant fuzzy linguistic information. Soft Comput. 21, 6515–6529 (2017)

    MATH  Google Scholar 

  35. Mao, X.B., Wu, M., Dong, J.Y., Wan, S.P., Jin, Z.: A new method for probabilistic linguistic multi-attribute group decision making: application to the selection of financial technologies. Appl. Soft Comput. 77, 155–175 (2019)

    Google Scholar 

  36. Kim, S.H., Ahn, B.S.: Interactive group decision making procedure under incomplete information. Eur. J. Oper. Res. 116, 498–507 (1999)

    MATH  Google Scholar 

  37. Li, Z.X., Gao, H., Wei, G.W.: Methods for multiple attribute group decision making based on intuitionistic fuzzy dombi hamy mean operators. Symmetry 10, 574 (2018)

    MATH  Google Scholar 

  38. Wang, J., Gao, H., Wei, G.W., Wei, Y.: Methods for multiple-attribute group decision making with q-Rung interval-valued orthopair fuzzy information and their applications to the selection of green suppliers. Symmetry 11, 56 (2019)

    MATH  Google Scholar 

  39. Gao, H.: Pythagorean fuzzy Hamacher Prioritized aggregation operators in multiple attribute decision making. J. Intell. Fuzzy Syst. 35, 2229–2245 (2018)

    Google Scholar 

  40. Li, Z.X., Lu, M.: Some novel similarity and distance and measures of Pythagorean fuzzy sets and their applications. J. Intell. Fuzzy Syst. 37, 1781–1799 (2019)

    Google Scholar 

  41. Wang, R.: Research on the application of the financial investment risk appraisal models with some interval number muirhead mean operators. J. Intell. Fuzzy Syst. 37, 1741–1752 (2019)

    Google Scholar 

  42. Wei, G.W., Wang, J., Lu, M., Wu, J., Wei, C.: Similarity measures of spherical fuzzy sets based on cosine function and their applications. IEEE Access 7, 159069–159080 (2019)

    Google Scholar 

  43. Wei, G.W., Zhang, S.Q., Lu, J.P., Wu, J., Wei, C.: An extended bidirectional projection method for picture fuzzy MAGDM and its application to safety assessment of construction project. IEEE Access 7, 166138–166147 (2019)

    Google Scholar 

  44. Lu, J.P., Tang, X.Y., Wei, G.W., Wei, C., Wei, Y.: Bidirectional project method for dual hesitant Pythagorean fuzzy multiple attribute decision-making and their application to performance assessment of new rural construction. Int. J. Intell. Syst. 34, 1920–1934 (2019)

    Google Scholar 

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

    Google Scholar 

  46. Wu, L.P., Wang, J., Gao, H.: Models for competiveness evaluation of tourist destination with some interval-valued intuitionistic fuzzy Hamy mean operators. Int. J. Intell. Syst. 36, 5693–5709 (2019)

    Google Scholar 

  47. Wei, G.W., Wu, J., Wei, C., Wang, J., Lu, J.P.: Models for MADM with 2-tuple linguistic neutrosophic Dombi Bonferroni mean operators. IEEE Access 71, 108878–108905 (2019)

    Google Scholar 

  48. Zhang, Y.X., Xu, Z.S., Liao, H.C.: Water security evaluation based on the TODIM method with probabilistic linguistic term sets. Soft Comput. 23, 6215–6230 (2019)

    Google Scholar 

  49. Tang, X.Y., Wei, G.W.: Dual hesitant Pythagorean fuzzy Bonferroni mean operators in multi-attribute decision making. Arch. Control Sci. 29, 339–386 (2019)

    MathSciNet  MATH  Google Scholar 

  50. Tang, X.Y., Wei, G.W., Gao, H.: Models for multiple attribute decision making with interval-valued pythagorean fuzzy muirhead mean operators and their application to green suppliers selection. Informatica 30, 153–186 (2019)

    Google Scholar 

  51. Deng, X.M., Wang, J., Wei, G.W.: Some 2-tuple linguistic Pythagorean Heronian mean operators and their application to multiple attribute decision-making. J. Exp. Theor. Artif. Intell. 31, 555–574 (2019)

    Google Scholar 

  52. Wei, G.W.: 2-tuple intuitionistic fuzzy linguistic aggregation operators in multiple attribute decision making. Iran. J. Fuzzy Syst. 16, 159–174 (2019)

    MathSciNet  MATH  Google Scholar 

  53. Liu, Z.M., Liu, P.D., Liang, X.: Multiple attribute decision-making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q-rung orthopair fuzzy environment. Int. J. Intell. Syst. 33, 1900–1928 (2018)

    Google Scholar 

  54. Liu, P.D., Liu, W.Q.: Multiple-attribute group decision-making based on power Bonferroni operators of linguistic q-rung orthopair fuzzy numbers. Int. J. Intell. Syst. 34, 652–689 (2019)

    Google Scholar 

  55. Liu, P.D., Teng, F.: Probabilistic linguistic TODIM method for selecting products through online product reviews. Inf. Sci. 485, 441–455 (2019)

    Google Scholar 

  56. Zhang, S.Q., Wei, G.W., Gao, H., Wei, C., Wei, Y.: EDAS method for multiple criteria group decision making with picture fuzzy information and its application to green suppliers selections. Technol. Econ. Dev. Econ. 26, 1123–1138 (2019)

    Google Scholar 

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Acknowledgements

The work was supported by the National Natural Science Foundation of China under Grant No. 71571128 and the Humanities and Social Sciences Foundation of Ministry of Education of the People’s Republic of China (No. 19YJA630056).

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Authors and Affiliations

  1. School of Mathematical Sciences, Sichuan Normal University, Chengdu, 610101, People’s Republic of China

    Fan Lei

  2. School of Business, Sichuan Normal University, Chengdu, 610101, People’s Republic of China

    Guiwu Wei & Hui Gao

  3. School of Statistics, Southwestern University of Finance and Economics, Chengdu, 611130, People’s Republic of China

    Jiang Wu & Cun Wei

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  1. Fan Lei
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  2. Guiwu Wei
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  3. Hui Gao
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  4. Jiang Wu
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  5. Cun Wei
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Correspondence to Guiwu Wei.

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Lei, F., Wei, G., Gao, H. et al. TOPSIS Method for Developing Supplier Selection with Probabilistic Linguistic Information. Int. J. Fuzzy Syst. 22, 749–759 (2020). https://doi.org/10.1007/s40815-019-00797-6

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