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Diverse Ranking Approach in MCDM Based on Trapezoidal Intuitionistic Fuzzy Numbers

  • Zamali TarmudiEmail author
  • Norzanah Abd Rahman
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 942)

Abstract

Intuitionistic fuzzy set (IFS) is a generalization of the fuzzy set that is characterized by the membership and non-membership function. It is proven that IFS improves the drawbacks in fuzzy set since it is designed to deal with the uncertainty aspects. In spite of this advantage, the selection of the ranking approach is still one of the fundamental issues in IFS operations. Thus, this paper intends to compare three ranking approaches of the trapezoidal intuitionistic fuzzy numbers (TrIFN). The ranking approaches involved are; expected value-based approach, centroid-based approach, and score function-based approach. To achieve the objective, one numerical example in prioritizing the alternatives using intuitionistic fuzzy multi-criteria decision making (IF-MCDM) are provided to illustrate the comparison of these ranking approaches. Based on the comparison, it was found that the alternatives MCDM problems can be ranked easily in efficient and accurate manner.

Keywords

Intuitionistic fuzzy set Trapezoidal intuitionistic fuzzy numbers Multi-criteria decision-making Ranking approach 

Notes

Acknowledgements

This research was supported by grant of Fundamental Research Grant Scheme (FRGS) from Ministry of Education (formerly known as Ministry of Higher Education (MOHE) Malaysia and Universiti Teknologi MARA (UiTM), Malaysia, reference no.: 600-IRMI/FRGS 5/3(84/2016).

References

  1. 1.
    Mitchell, H.B.: Ranking intuitionistic fuzzy numbers. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 12(3), 377–386 (2004)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Nayagam, V.L.G., Venkateswari, G., Sivaraman, G.: Modified ranking of intuitionistic fuzzy numbers. NFIS 17(1), 5–22 (2011)zbMATHGoogle Scholar
  3. 3.
    Kakarontzas, G., Gerogiannis, V.C.: An intuitionistic fuzzy approach for ranking web services under evaluation uncertainty. In: IEEE International Conference on Services Computing, pp. 742–745 (2015)Google Scholar
  4. 4.
    Shen, L., Wang, H., Feng, X.: Ranking methods of intuitionistic fuzzy numbers in multicriteria decision making. In: 3rd International Conference on Information Management Innovation Management and Industrial Engineering, pp. 143–146 (2010)Google Scholar
  5. 5.
    Biswas, A., De, A.K.: An efficient ranking technique for intuitionistic fuzzy numbers with its application in chance constrained bilevel programming. Adv. Fuzzy Syst. 2016, 1–12 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Li, D.F., Nan, J.X., Zhang, M.J.: A ranking method of triangular intuitionistic fuzzy numbers and application to decision making. Int. J. Comput. Intell. Syst. 3(5), 522–530 (2010)CrossRefGoogle Scholar
  7. 7.
    De, P.K., Das, D.: Ranking of trapezoidal intuitionistic fuzzy numbers. In: 12th International Conference on Intelligent Systems Design and Applications (ISDA), pp. 184–188 (2012)Google Scholar
  8. 8.
    De, P.K., Das, D.: A study on ranking of trapezoidal intuitionistic fuzzy numbers. Int. J. Comput. Inf. Syst. Ind. Manag. Appl. 6, 437–444 (2014)Google Scholar
  9. 9.
    Rezvani, S.: Ranking method of trapezoidal intuitionistic fuzzy numbers. Ann. Fuzzy Math. Inform. 5(3), 515–523 (2012)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Kumar, A., Kaur, M.: A ranking approach for intuitionistic fuzzy numbers and its application. J. Appl. Res. Technol. 11, 381–396 (2013)CrossRefGoogle Scholar
  11. 11.
    Roseline, S.S., Amirtharaj, E.C.H.: A new ranking of intuitionistic fuzzy numbers. Indian J. Appl. Res. 3, 1–2 (2013)CrossRefGoogle Scholar
  12. 12.
    Nehi, H.M.: A new ranking method for intuitionistic fuzzy numbers. Int. J. Fuzzy Syst. 12(1), 80–86 (2010)MathSciNetGoogle Scholar
  13. 13.
    Grzegrorzewski, P.: The hamming distance between intuitionistic fuzzy sets. In: Proceedings of the IFSA 2003 World Congress, Istanbul, pp. 35–38 (2013)Google Scholar
  14. 14.
    Zeng, X.-T., Li, D.-F., Yu, G.-F.: A value and ambiguity-based ranking method of trapezoidal intuitionistic fuzzy numbers and application to decision making. Sci. World J. 2014, 1–8 (2014)CrossRefGoogle Scholar
  15. 15.
    Li, D.-F., Yang, J.: A difference-index based ranking method of trapezoidal intuitionistic fuzzy numbers and application to multiattribute decision making. Math. Comput. Appl. 20(1), 25–38 (2015)MathSciNetGoogle Scholar
  16. 16.
    Keikha, A., Nehi, H.M.: Operation and ranking methods for intuitionistic fuzzy numbers, a review and new method. Int. J. Intell. Syst. Appl. 1, 35–48 (2016)zbMATHGoogle Scholar
  17. 17.
    Prakash, A.A., Suresh, M., Vengataasalam, S.: A new ranking of intuitionistic fuzzy numbers using a centroid concept. Math. Sci. 10, 177–184 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Das, S., Guha, D.: A centroid-based ranking method of trapezoidal intuitionistic fuzzy numbers and its application to MCDM problems. Fuzzy Inf. Eng. 8, 41–74 (2016)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Velu, L.G.N., Selvaraj, J., Ponnialagan, D.: A new ranking principle for ordering trapezoidal intuitionistic fuzzy numbers. Complexity 2017, 1–24 (2017)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Ye, J.: Expected value method for intuitionistic trapezoidal fuzzy multicriteria decision-making problems. Expert Syst. Appl. 38, 11730–11734 (2011)CrossRefGoogle Scholar
  21. 21.
    Atanassov, K.T.: Intuitionistic fuzzy set. Fuzzy Sets Syst. 20, 87–96 (1996)CrossRefGoogle Scholar
  22. 22.
    Nehi, H.M., Maleki, H.R.: Intuitionistic fuzzy numbers and it’s applications in fuzzy optimization problem. In: Proceedings of the 9th WSEAS International Conference on Systems, Athen, Greece, pp. 1–5 (2015)Google Scholar
  23. 23.
    Nikjoo, A.V., Saeedpoor, M.: An intuitionistic fuzzy DEMATEL methodology for prioritising the components of SWOT matrix in the Iranian insurance industry. Int. J. Oper. Res. 20(4), 439–452 (2014)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Vafadarnikjoo, A., Mobin, M., Allahi, S., Rastegari, A.: A hybrid approach of intuitionistic fuzzy set theory and DEMATEL method to prioritize selection criteria of bank. Int. J. Comput. Intell. Syst. 8(4), 637–666 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Faculty of Computer and Mathematical SciencesUniversiti Teknologi MARA (Johor Branch)SegamatMalaysia
  2. 2.Faculty of Computer and Mathematical SciencesUniversiti Teknologi MARA (Sabah Branch)Kota KinabaluMalaysia

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