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TOPSIS Approach for MAGDM Based on Interval-Valued Hesitant Fuzzy N-Soft Environment

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Abstract

Multi-attribute group decision-making (MAGDM) phenomenon is used to handle the information, when a number of attributes of alternatives are evaluated by a group of decision-makers. In this research article, we develop a novel approach called interval-valued hesitant fuzzy N-soft sets (IVHFNSSs) and extend the method of TOPSIS for solving MAGDM problems. In our proposed model, the evaluation information provided by the decision-makers is expressed in the form of ratings, grades and IVHFEs, whereas the information about attribute weights is arbitrary. The model provides us information about the occurrence of ratings or grades in hesitant situation. Moreover, we investigate some useful properties of IVHFNSSs and construct fundamental operations on them. By using the extended TOPSIS method, we describe potential applications of IVHFNSSs in MAGDM. We present our method in an algorithm and a graphical structure.

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References

  1. Akram, M., Adeel, A., Alcantud, J.C.R.: Group decision-making methods based on hesitant \(N\)-soft sets. Expert Syst. Appl. 115, 95–105 (2019)

    Article  Google Scholar 

  2. Akram, M., Adeel, A., Alcantud, J.C.R.: Fuzzy \(N\)-soft sets: a novel model with applications. J. Intell. Fuzzy Syst. 35(4), 4757–4771 (2018)

  3. Alcantud, J.C.R., Laruelle, A.: Dis & approval voting: a characterization. Soc. Choice Welf. 43(1), 1–10 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  4. Alcantud, J.C.R., Santos-García, G.: A new criterion for soft set based decision-making problems under incomplete information. Int. J. Comput. Intell. Syst. 10, 394–404 (2017)

    Article  Google Scholar 

  5. Aruldoss, M., Lakshmi, T.M., Venkatesan, V.P.: A survey on multi-criteria decision-making methods and its applications. Am. J. Inf. Syst. 1(1), 31–43 (2013)

    Google Scholar 

  6. Cao, Q.W., Wu, J.: The extended COWG operators and their application to multiple attributive group decision-making problems with interval numbers. Appl. Math. Model. 35, 2075–2086 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen, N., Xu, Z., Xia, M.: Interval-valued hesitant preference relations and their applications to group decision-making. Knowl. Based Syst. 37, 528–540 (2013)

    Article  Google Scholar 

  8. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Kluwer Academic, New York (1980)

    MATH  Google Scholar 

  9. Dyer, J.S., Fishburn, P.C., Steuer, R.E., Wallenius, J., Zionts, S.: Multiple criteria decision-making, multiattribute utility theory: the next ten years. Manag. Sci. 38, 645–654 (1992)

    Article  MATH  Google Scholar 

  10. Fan, Z.P., Feng, B.: A multiple attributes decision-making method using individual and collaborative attribute data in a fuzzy environment. Inf. Sci. 179, 3603–3618 (2009)

    Article  Google Scholar 

  11. Fatimah, F., Rosadi, D., Hakim, R.B.F., Alcantud, J.C.R.: \(N\)-soft sets and their decision-making algorithms. Soft Comput. 22(12), 3829–3842 (2018)

    Article  MATH  Google Scholar 

  12. Feng, F., Akram, M., Davvaz, B., Fotea, V.L.: Attribute analysis of information systems based on elementary soft implications. Knowl Based Syst. 70, 281–292 (2014)

    Article  Google Scholar 

  13. Hwang, C.L., Yoon, K.: Multiple Attribute Decision-Making: Methods and Applications. Springer, Berlin (1981)

    Book  MATH  Google Scholar 

  14. Jahanshahloo, G.R., Lotfi, F.H., Izadikhah, M.: An algorithmic method to extend TOPSIS for decision-making problems with interval data. Appl. Math. Comput. 175, 1375–1384 (2006)

    MATH  Google Scholar 

  15. Liu, P., Zhang, X.: Research on the supplier selection of supply chain based on entropy weight and improved ELECTRE-III method. Int. J. Prod. Res. 49, 637–646 (2011)

    Article  Google Scholar 

  16. Liu, P., Zhang, L.: An extended multiple criteria decision making method based on neutrosophic hesitant fuzzy information. J. Intell. Fuzzy Syst. 32(6), 4403–4413 (2017)

    Article  MATH  Google Scholar 

  17. Maji, P.K., Biswas, R., Roy, A.R.: Soft set theory. Comput. Math. Appl. 45(4–5), 555–562 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  18. Maji, P.K., Biswas, R., Roy, A.R.: Fuzzy soft sets. J. Fuzzy Math. 9(3), 589–602 (2001)

    MathSciNet  MATH  Google Scholar 

  19. Ma, X., Liu, Q., Zhang, J.: A survey decision making methods based on certain hybrid soft set models. Artif. Intell. Rev. 47(4), 507–530 (2017)

    Article  Google Scholar 

  20. Molodtsov, D.: Soft set theory-first results. Comput. Math. Appl. 37(4–5), 19–31 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  21. Peng, X., Dai, J.: Hesitant fuzzy soft decision making methods based on WASPAS, MABAC and COPRAS with combined weights. J. Intell. Fuzzy Syst. 33(2), 1313–1325 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  22. Peng, X., Yang, Y.: Approaches to interval-valued intuitionistic hesitant fuzzy soft sets based decision making. Ann. Fuzzy Math. Inform. 10(4), 657–680 (2015)

    MathSciNet  MATH  Google Scholar 

  23. Peng, X., Yang, Y.: Interval-valued hesitant fuzzy soft sets and their application in decision-making. Fundamenta Informaticae 141(1), 71–93 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  24. Stewart, T.J.: A critical survey on the status of multiple criteria decision making theory and practice. Omega 20, 569–586 (1992)

    Article  Google Scholar 

  25. Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25(6), 529–539 (2010)

    MATH  Google Scholar 

  26. Torra, V., Narukawa, Y.: On hesitant fuzzy sets and decisions. In: IEEE International Conference on Fuzzy Systems, 1378–1382 (2009)

  27. Wang, J.Q., Han, Z.Q., Zhang, H.Y.: Multi-criteria group decision-making method based on intuitionistic interval fuzzy information. Group Decis. Negot. 23, 715–733 (2014)

    Article  Google Scholar 

  28. Wang, F., Li, X., Chen, X.: Hesitant fuzzy soft set and its applications in multicriteria decision-making. J. Appl. Math.. 2014 Article ID 643785, https://doi.org/10.1155/2014/643785 (2014)

  29. Wang, J.Q., Li, X.E., Chen, X.H.: Hesitant fuzzy soft sets with application in multicriteria group decision-making problems. Sci. World J.. 2015 Article ID 806983, https://doi.org/10.1155/2015/806983 (2015)

  30. Xia, M., Xu, Z.S.: Hesitant fuzzy information aggregation in decision-making. Int. J. Approx. Reason. 52, 395–407 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  31. Xia, M., Xu, Z., Chen, N.: Some hesitant fuzzy aggregation operators with their application in group decision-making. Group Decis. Negot. 22(2), 259–297 (2013)

    Article  Google Scholar 

  32. Xu, Z., Zhang, X.: Hesitant fuzzy multi-attribute decision-making based on TOPSIS with incomplete weight information. Knowl. Based Syst. 52, 53–64 (2013)

    Article  Google Scholar 

  33. Wu, Z.B., Chen, Y.H.: The maximizing deviation method for group multiple attribute decision-making under linguistic environment. Fuzzy Sets Syst. 158, 1608–1617 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  34. Yue, Z.L.: An extended TOPSIS for determining weights of decision-makers with interval numbers. Knowl. Based Syst. 24, 146–153 (2011)

    Article  Google Scholar 

  35. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  MATH  Google Scholar 

  36. Zafar, F., Akram, M.: A novel decision-making method based on rough fuzzy information. Int. J. Fuzzy Syst. 20(3), 1000–1014 (2018)

    Article  MathSciNet  Google Scholar 

  37. Zhu, B., Xu, Z.S., Xu, J.P.: Deriving a ranking from hesitant fuzzy preference relations under group decision-making. IEEE Trans. Cybern. 44(8), 1328–1337 (2014)

    Article  Google Scholar 

  38. Zou, Y., Xiao, Z.: Data analysis approaches of soft sets under incomplete information. Knowl. Based Syst. 21(8), 941–945 (2008)

    Article  Google Scholar 

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Acknowledgements

The authors are grateful to an associate editor and anonymous referees for their valuable comments.

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  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan

    Muhammad Akram & Arooj Adeel

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  1. Muhammad Akram
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  2. Arooj Adeel
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Correspondence to Muhammad Akram.

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Akram, M., Adeel, A. TOPSIS Approach for MAGDM Based on Interval-Valued Hesitant Fuzzy N-Soft Environment. Int. J. Fuzzy Syst. 21, 993–1009 (2019). https://doi.org/10.1007/s40815-018-0585-1

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  • DOI: https://doi.org/10.1007/s40815-018-0585-1

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