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Neural Computing and Applications

, Volume 31, Issue 10, pp 5901–5916 | Cite as

A modified TOPSIS method based on vague parameterized vague soft sets and its application to supplier selection problems

  • Ganeshsree SelvachandranEmail author
  • Xindong Peng
Original Article

Abstract

In this paper, we propose an intuitively straightforward extension of the vague soft set model called the vague parameterized vague soft set (vp-VSS). This model generalizes the vague soft set by including the opinions of an expert or a moderator regarding the values of the membership function for the parameters that are considered, in the form of a vague set. The values provided by the experts indicate the threshold values for the membership functions of the elements, i.e., the minimum values that must be ideally satisfied by all the elements for each parameter. This provides a clear indication to the users of these information, and forms a pertinent component of the model, particularly in the decision-making process. Subsequently, we define some operations for this model and examine its properties. Subsequently, we introduce two algorithms based on a modified TOPSIS approach and a weighted aggregation operator approach, both of which are based on our proposed vp-VSS model. These algorithms are then applied in two multi-attribute decision-making problems involving supplier selection and the evaluation of supplier performance. The performance and utility of these algorithms are compared and contrasted in terms of the computational complexity and discriminative power of the algorithms.

Keywords

Vague soft set TOPSIS Aggregation operator Supplier selection 

Notes

Acknowledgements

The authors would like to express their gratitude to the anonymous reviewers, the editor in charge of this paper, and the Editor-in-Chief for their constructive comments which has helped to improve the quality of this paper. In addition, the first author Ganeshsree Selvachandran would like to gratefully acknowledge the financial assistance received from the Ministry of Education, Malaysia, under Grant No. FRGS/1/2017/STG06/UCSI/03/1 and UCSI University, Kuala Lumpur, Malaysia, under Grant No. Proj-In-FOBIS-014.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

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

References

  1. 1.
    Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353zbMATHGoogle Scholar
  2. 2.
    Molodtsov D (1999) Soft set theory—first results. Comput Math Appl 37(4–5):19–31MathSciNetzbMATHGoogle Scholar
  3. 3.
    Cagman N, Citak F, Enginoglu S (2011) Fuzzy parameterized soft set theory and its applications. Ann Fuzzy Math Inform 2(2):219–226MathSciNetzbMATHGoogle Scholar
  4. 4.
    Cagman N, Citak F, Enginoglu S (2010) Fuzzy parameterized fuzzy soft set theory and its applications. Turk J Fuzzy Syst 1(1):21–35zbMATHGoogle Scholar
  5. 5.
    Alkhazaleh S, Salleh AR, Hassan N (2011) Fuzzy parameterized interval-valued fuzzy soft sets. Appl Math Sci 5(67):3335–3346zbMATHGoogle Scholar
  6. 6.
    Bashir M, Salleh AR (2012) Fuzzy parameterized soft expert set. Abstr Appl Anal 2012:1–15.  https://doi.org/10.1155/2012/258361 MathSciNetzbMATHGoogle Scholar
  7. 7.
    Selvachandran G, Salleh AR (2016) Fuzzy parameterized intuitionistic fuzzy soft expert set theory and its application in decision making. Int J Soft Comput 11(2):52–63zbMATHGoogle Scholar
  8. 8.
    Deli I, Cagman N (2015) Intuitionistic fuzzy parameterized soft set theory and its decision making. Appl Soft Comput 28:109–113Google Scholar
  9. 9.
    Karaaslan F (2016) Intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets with applications in decision making. Ann Fuzzy Math Inform 11(4):607–619MathSciNetzbMATHGoogle Scholar
  10. 10.
    Hwang C-L, Yoon K (1981) Multiple attribute decision making. Methods and applications: a state-of-the-art survey. Springer, BerlinzbMATHGoogle Scholar
  11. 11.
    Mayyas A, Omar MA, Hayajneh MT (2016) Eco-material selection using fuzzy TOPSIS method. Int J Sustain Eng 9(5):292–304Google Scholar
  12. 12.
    Solanki R, Gulati G, Tiwari A, Lohani QMD (2016) A correlation based intuitionistic fuzzy TOPSIS method on supplier selection problem. In: Proceedings of the IEEE international conference on fuzzy systems (FUZZ-IEEE), Vancouver, Canada. http://doi.org/10.1109/CCDC.2010.5499018
  13. 13.
    Eraslan S, Cagman N (2017) A decision making method by combining TOPSIS and grey relation method under fuzzy soft sets. Sigma J Eng Nat Sci 8(1):53–64Google Scholar
  14. 14.
    Chaharsooghi SK, Ashrafi M (2014) Sustainable supplier performance evaluation and selection with neofuzzy TOPSIS method. Int Sch Res Not 2014:1–10.  https://doi.org/10.1155/2014/434168 Google Scholar
  15. 15.
    Ren F, Kong M, Pei Z (2017) A new hesitant fuzzy linguistic TOPSIS method for group multi-criteria linguistic decision making. Symmetry 9(289):1–19Google Scholar
  16. 16.
    Onat NC, Gumus S, Kucukvar M, Tatari O (2016) Application of the TOPSIS and intuitionistic fuzzy approaches for ranking the life cycle sustainability performance of alternative vehicle technologies. Sustain Prod Consum 6:12–25Google Scholar
  17. 17.
    Ye J (2015) An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers. J Intell Fuzzy Syst 28:247–255MathSciNetGoogle Scholar
  18. 18.
    Liang W, Zhang X, Liu M (2015) The maximizing deviation based on interval-valued Pythagorean fuzzy weighted aggregating operator for multiple criteria group decision analysis. Discrete Dyn Nat Soc 2015:1–15.  https://doi.org/10.1155/2015/746572 MathSciNetzbMATHGoogle Scholar
  19. 19.
    Biswas P, Pramanik S, Giri BC (2016) TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment. Neural Comput Appl 27(3):727–737Google Scholar
  20. 20.
    Buyukozkan G, Guleryuz S (2016) Multi-criteria group decision making approach for smart phone selection using intuitionistic fuzzy TOPSIS. Int J Comput Intell Syst 9(4):709–725Google Scholar
  21. 21.
    Yang W, Chen Z, Zhang F (2017) New group decision making method in intuitionistic fuzzy setting based on TOPSIS. Technol Econ Dev Econ 23(3):441–461Google Scholar
  22. 22.
    Gau WL, Buehrer DJ (1993) Vague sets. IEEE Trans Syst Man Cybern 23(2):610–614zbMATHGoogle Scholar
  23. 23.
    Xu W, Ma J, Wang S, Hao G (2010) Vague soft sets and their properties. Comput Math Appl 59:787–794MathSciNetzbMATHGoogle Scholar
  24. 24.
    Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 3(9):589–602MathSciNetzbMATHGoogle Scholar
  25. 25.
    Maji PK, Biswas R, Roy AR (2001) Intuitionistic fuzzy soft sets. J Fuzzy Math 9(3):677–692MathSciNetzbMATHGoogle Scholar
  26. 26.
    Yang X, Lin TY, Yang J, Li Y, Yu D (2009) Combination of interval-valued fuzzy set and soft set. Comput Math Appl 58:521–527MathSciNetzbMATHGoogle Scholar
  27. 27.
    Jiang Y, Tang Y, Chen Q, Liu H, Tang J (2010) Interval-valued intuitionistic fuzzy soft sets and their properties. Comput Math Appl 60:906–918MathSciNetzbMATHGoogle Scholar
  28. 28.
    Shaw K, Shankar R, Yadav SS, Thakur LS (2012) Supplier selection using fuzzy AHP and fuzzy multi-objective linear programming for developing low carbon supply chain. Expert Syst Appl 39(9):8182–8192Google Scholar
  29. 29.
    Rouyendegh BD, Saputro TE (2014) Supplier selection using fuzzy TOPSIS and MCGP: a case study. Proc Soc Behav Sci 116:3957–3970Google Scholar
  30. 30.
    Dargi A, Anjomshoae A, Galankashi MR, Memari A, Tap MBM (2014) Supplier selection: a fuzzy-ANP approach. Proc Comput Sci 31:691–700Google Scholar
  31. 31.
    Kaur P (2014) Selection of vendor based on intuitionistic fuzzy analytical hierarchy process. Adv Oper Res 2014:1–10.  https://doi.org/10.1155/2014/987690 MathSciNetzbMATHGoogle Scholar
  32. 32.
    Kaur P, Rachana KNL (2016) An intuitionistic fuzzy optimization approach to vendor selection problem. Perspect Sci 8:348–350Google Scholar
  33. 33.
    Dweiri F, Kumar S, Khan SA, Jain V (2016) Designing an integrated AHP based decision support system for supplier selection in automotive industry. Expert Syst Appl 62:273–283Google Scholar
  34. 34.
    Junior FRL, Osiro L, Carpinetti LCR (2014) A comparison between fuzzy AHP and fuzzy TOPSIS methods to supplier selection. Appl Soft Comput 21:194–209Google Scholar
  35. 35.
    Wang YM (1997) Using the method of maximizing deviations to make decision for multiindices. Syst Eng Electron 8:21–26Google Scholar
  36. 36.
    Hadi-Venchen A, Mirjaberi M (2014) Fuzzy inferior ratio method for multiple attribute decision making problems. Inf Sci 277:263–272MathSciNetzbMATHGoogle Scholar
  37. 37.
    Peng X, Yang Y (2015) Interval-valued hesitant fuzzy soft sets and their application in decision making. Fundam Inform 141:71–93MathSciNetzbMATHGoogle Scholar
  38. 38.
    Agarwal M, Biswas KK, Hanmandlu M (2013) Generalized intuitionistic fuzzy soft sets with applications in decision-making. Appl Soft Comput 13:3552–3566.  https://doi.org/10.1016/j.asoc.2013.03.015 Google Scholar
  39. 39.
    Zhu K, Zhan J (2016) Fuzzy parameterized fuzzy soft sets and decision making. Int J Mach Learn Cybern 7(6):1207–1212.  https://doi.org/10.1007/s13042-015-0449-z Google Scholar
  40. 40.
    Garg H (2016) A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes. Int J Intell Syst 31(12):1234–1252.  https://doi.org/10.1002/int.21827 Google Scholar
  41. 41.
    Singh P (2015) Correlation coefficients for picture fuzzy sets. J Intell Fuzzy Syst 28:591–604.  https://doi.org/10.3233/IFS-141338 MathSciNetzbMATHGoogle Scholar
  42. 42.
    Yang Y, Tan X, Meng C (2013) The multi-fuzzy soft set and its application in decision making. Appl Math Model 37:4915–4923MathSciNetzbMATHGoogle Scholar
  43. 43.
    Zhang XH (2014) On interval soft sets with applications. Int J Comput Intell Syst 7:186–196Google Scholar
  44. 44.
    Chetia B, Das PK (2011) Application of vague soft sets in students’ evaluation. Adv Appl Sci Res 2(6):418–423Google Scholar
  45. 45.
    Zhang H, Xiong L, Ma W (2015) On interval-valued hesitant fuzzy soft sets. Math Probl Eng 2015:1–17.  https://doi.org/10.1155/2015/254764 MathSciNetzbMATHGoogle Scholar
  46. 46.
    Yager RR (2013) Pythagorean fuzzy subsets. In: Proceedings of the Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, pp 57–61Google Scholar
  47. 47.
    Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers and decision making. Int J Intell Syst 28:436–452Google Scholar
  48. 48.
    Cuong BC (2013) Picture fuzzy sets—first results, Part 1. Seminar “Neuro-fuzzy systems with applications”, Preprint 03/2013, Institute of Mathematics, HanoiGoogle Scholar
  49. 49.
    Cuong BC (2013) Picture fuzzy sets—first results, Part 2. Seminar “Neuro-fuzzy systems with applications”, Preprint 04/2013, Institute of Mathematics, HanoiGoogle Scholar
  50. 50.
    Cuong BC (2014) Picture fuzzy sets. J Comput Sci Cybern 30(4):409–420Google Scholar

Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  1. 1.Department of Actuarial Science and Applied Statistics, Faculty of Business and Information ScienceUCSI UniversityCherasMalaysia
  2. 2.School of Information Science and EngineeringShaoguan UniversityShaoguanChina

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