Advertisement

Improved possibility degree method for ranking intuitionistic fuzzy numbers and their application in multiattribute decision-making

  • Harish Garg
  • Kamal Kumar
Original Paper

Abstract

In the present paper, we define an improved possibility degree method to rank the different intuitionistic fuzzy numbers (IFNs). To achieve it, we first present some shortcomings of the existing possibility degree method and score function of IFNs. The existing shortcomings are overcome by proposing a new possibility degree measure for IFNs. The desirable properties of it are analyzed in details. Afterward, based on proposed possibility degree measure, a decision-making approach presents to solve the multiattribute decision-making (MADM) problem under the intuitionistic fuzzy set environment. Finally, a real-life case is studied to manifest the practicability and feasibility of the proposed decision-making method.

Keywords

Multiattribute decision-making Possibility degree measure Intuitionistic fuzzy set Informative measures 

References

  1. Arora R, Garg H (2018) Prioritized averaging/geometric aggregation operators under the intuitionistic fuzzy soft set environment. Scientia Iranica 25(1):466–482.  https://doi.org/10.24200/SCI.2017.4410
  2. Atanassov K, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31:343–349MathSciNetCrossRefzbMATHGoogle Scholar
  3. Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96CrossRefzbMATHGoogle Scholar
  4. Chen SM, Chang CH (2015) A novel similarity measure between atanassov’s intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition. Inf Sci 291:96–114CrossRefGoogle Scholar
  5. Chen SM, Randyanto Y (2013) A novel similarity measure between intuitionistic fuzzy sets and its applications. Int J Pattern Recognit Artif Intell 27(7):1350021(34pages)Google Scholar
  6. Chen SM, Cheng SH, Chiou CH (2016a) Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology. Inform Fusion 27:215–227CrossRefGoogle Scholar
  7. Chen SM, Cheng SH, Lan TC (2016b) A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Inf Sci 343–344:15–40MathSciNetCrossRefGoogle Scholar
  8. Dammak F, Baccour L, Alimi AM (2016) An exhaustive study of possibility measures of interval-valued intuitionistic fuzzy sets and application to multicriteria decision making. Adv Fuzzy Syst 2016:10 (Article ID 9185,706)Google Scholar
  9. Gao F (2013) Possibility degree and comprehensive priority of interval numbers. Syst Eng Theory Pract 33(8):2033–2040Google Scholar
  10. Garg H (2016a) Generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm and their application to decision making. Comput Ind Eng 101:53–69CrossRefGoogle Scholar
  11. Garg H (2016b) A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems. Appl Soft Comput 38:988–999.  https://doi.org/10.1016/j.asoc.2015.10.040 CrossRefGoogle Scholar
  12. Garg H (2016c) Some series of intuitionistic fuzzy interactive averaging aggregation operators. SpringerPlus 5(1):999.  https://doi.org/10.1186/s40064-016-2591-9
  13. Garg H (2017a) Distance and similarity measure for intuitionistic multiplicative preference relation and its application. Int J Uncertain Quantif 7(2):117–133CrossRefGoogle Scholar
  14. Garg H (2017b) Novel intuitionistic fuzzy decision making method based on an improved operation laws and its application. Eng Appl Artif Intell 60:164–174CrossRefGoogle Scholar
  15. Garg H (2018) Some arithmetic operations on the generalized sigmoidal fuzzy numbers and its application. Granul Comput 3(1):9–25.  https://doi.org/10.1007/s41066-017-0052-7 CrossRefGoogle Scholar
  16. Garg H, Agarwal N, Tripathi A (2017) Generalized intuitionistic fuzzy entropy measure of order \(\alpha\) and degree \(\beta\) and its applications to multi-criteria decision making problem. Int J Fuzzy Syst Appl 6(1):86–107CrossRefGoogle Scholar
  17. He Y, Chen H, Zhau L, Liu J, Tao Z (2014) Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making. Inf Sci 259:142–159MathSciNetCrossRefzbMATHGoogle Scholar
  18. Jamkhaneh EB, Garg H (2017) Some new operations over the generalized intuitionistic fuzzy sets and their application to decision-making process. Granul Comput.  https://doi.org/10.1007/s41066-017-0059-0
  19. Joshi D, Kumar S (2014) Intuitionistic fuzzy entropy and distance measure based topsis method for multi-criteria decision making. Egypt Inform J 15(2):97–104CrossRefGoogle Scholar
  20. Kaur G, Garg H (2018a) Cubic intuitionistic fuzzy aggregation operators. Int J Uncertain Quantif.  https://doi.org/10.1615/Int.J.UncertaintyQuantification.2018020471
  21. Kaur G, Garg H (2018b) Multi attribute decision-making based on bonferroni mean operators under cubic intuitionistic fuzzy set environment. Entropy 20(1):65.  https://doi.org/10.3390/e20010065 CrossRefGoogle Scholar
  22. Kumar K, Garg H (2016) TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment. Comput Appl Math.  https://doi.org/10.1007/s40314-016-0402-0
  23. Kumar K, Garg H (2017) Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making. Appl Intell.  https://doi.org/10.1007/s10489-017-1067-0
  24. Pedrycz W, Chen SM (2011) Granular computing and intelligent systems: design with information granules of higher order and higher type. Springer, HeidelbergCrossRefGoogle Scholar
  25. Pedrycz W, Chen SM (2015) Granular computing and decision-making: interactive and iterative approaches. Springer, Heidelberg, GermanyCrossRefGoogle Scholar
  26. Rani D, Garg H (2017) Distance measures between the complex intuitionistic fuzzy sets and its applications to the decision-making process. Int J Uncertain Quantif 7(5):423–439MathSciNetCrossRefGoogle Scholar
  27. Singh S, Garg H (2017) Distance measures between type-2 intuitionistic fuzzy sets and their application to multicriteria decision-making process. Appl Intell 46(4):788–799CrossRefGoogle Scholar
  28. Wan S, Dong J (2014) A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decision making. J Comput Syst Sci 80(1):237–256MathSciNetCrossRefzbMATHGoogle Scholar
  29. Wan SP, Xu GL, Wang F, Dong JY (2015) A new method for atanassov’s interval-valued intuitionistic fuzzy magdm with incomplete attribute weight information. Inf Sci 316:329–347CrossRefGoogle Scholar
  30. Wang W, Liu X (2012) Intuitionistic fuzzy information aggregation using einstein operations. IEEE Trans Fuzzy Syst 20(5):923–938CrossRefGoogle Scholar
  31. Wang W, Liu X (2013) Interval-valued intuitionistic fuzzy hybrid weighted averaging operator based on einstein operation and its application to decision making. J Intell Fuzzy Syst 25(2):279–290MathSciNetzbMATHGoogle Scholar
  32. Wang X, Triantaphyllou E (2008) Ranking irregularities when evaluating alternatives by using some electre methods. Omega Int J Manag Sci 36:45–63CrossRefGoogle Scholar
  33. Wei CP, Tang X (2010) Possibility degree method for ranking intuitionistic fuzzy numbers. In: 3rd IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology (WI-IAT ’10), pp 142–145Google Scholar
  34. Wei G (2010) Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making. Appl Soft Comput 10:423–431CrossRefGoogle Scholar
  35. Xu ZS (2007a) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187CrossRefGoogle Scholar
  36. Xu ZS (2007b) Some similarity meeasures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optim Decis Mak 6:109–121MathSciNetCrossRefzbMATHGoogle Scholar
  37. Xu ZS, Da QL (2003) Possibility degree method for ranking interval numbers and its application. J Syst Eng 18:67–70Google Scholar
  38. Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433MathSciNetCrossRefzbMATHGoogle Scholar
  39. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353CrossRefzbMATHGoogle Scholar
  40. Zhang X, Yue G, Teng Z (2009) Possibility degree of interval-valued intuitionistic fuzzy numbers and its application. In: Proceedings of the international symposium on information processing, pp 33–36Google Scholar
  41. Zhao H, Xu Z, Ni M, Liu S (2010) Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst 25(1):1–30CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsThapar Institute of Engineering and Technology (Deemed University)PatialaIndia

Personalised recommendations