Advertisement

Applied Intelligence

, Volume 49, Issue 2, pp 496–512 | Cite as

A robust correlation coefficient measure of complex intuitionistic fuzzy sets and their applications in decision-making

  • Harish GargEmail author
  • Dimple Rani
Article
  • 80 Downloads

Abstract

The objective of this work is to present novel correlation coefficient measures for measuring the relationship between the two complex intuitionistic fuzzy sets (CIFSs). In the existing studies of fuzzy and its extension, the uncertainties present in the data are handled with the help of degrees of membership which are the subset of real numbers, and may lose some useful information and hence consequently affect on the decision results. An alternative to these, complex intuitionistic fuzzy set handles the uncertainties with the degrees whose ranges are extended from real subset to the complex subset with unit disc and hence handle the two-dimensional information in a single set. Thus, motivated by this, we develop correlation and weighted correlation coefficients under the CIFS environment in which pairs of the membership degrees represent the two-dimensional information. Also, some of the desirable properties of it are investigated. Further, based on these measures, a multicriteria decision-making approach is presented under the CIFS environment. Two illustrative examples are taken to demonstrate the efficiency of the proposed approach and validate it by comparing their results with the several existing approaches’ results.

Keywords

Intuitionistic fuzzy set Complex intuitionistic fuzzy set Correlation coefficient MCDM Medical diagnosis 

Notes

Acknowledgments

The authors are thankful to the editor and anonymous reviewers for their constructive comments and suggestions that helped us in improving the paper significantly. Also, the author (Dimple Rani) would like to thank the University Grant Commission, New Delhi, India for providing financial support during the preparation of this manuscript.

References

  1. 1.
    Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353CrossRefzbMATHGoogle Scholar
  2. 2.
    Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96CrossRefzbMATHGoogle Scholar
  3. 3.
    Atanassov K, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31:343–349MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Ramot D, Milo R, Fiedman M, Kandel A (2002) Complex fuzzy sets. IEEE Trans Fuzzy Syst 10 (2):171–186CrossRefGoogle Scholar
  5. 5.
    Alkouri A, Salleh A (2012) Complex intuitionistic fuzzy sets, Vol 1482, Ch. 2nd International Conference on Fundamental and Applied Sciences 2012, pp 464–470Google Scholar
  6. 6.
    Garg H, Rani D (2018) Some generalized complex intuitionistic fuzzy aggregation operators and their application to multicriteria decision-making process. Arab J Sci Eng:1–20.  https://doi.org/10.1007/s13369-018-3413-x
  7. 7.
    Arora R, Garg H (2018) Robust aggregation operators for multi-criteria decision making with intuitionistic fuzzy soft set environment. Sci Iran E 25(2):931–942Google Scholar
  8. 8.
    Arora R, Garg H (2018) Prioritized averaging/geometric aggregation operators under the intuitionistic fuzzy soft set environment. Sci Iran 25(1):466–482Google Scholar
  9. 9.
    Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Kaur G, Garg H (2018) Cubic intuitionistic fuzzy aggregation operators. Int J Uncertain Quantif 8 (5):405–427MathSciNetCrossRefGoogle Scholar
  11. 11.
    Wang X, Triantaphyllou E (2008) Ranking irregularities when evaluating alternatives by using some electre methods. Omega - Int J Manag Sci 36:45–63CrossRefGoogle Scholar
  12. 12.
    Kaur G, Garg H (2018) 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 MathSciNetCrossRefGoogle Scholar
  13. 13.
    Kumar K, Garg H (2018) TOPSIS Method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment. Comput Appl Math 37(2):1319–1329MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Garg H, Kumar K (2018) Distance measures for connection number sets based on set pair analysis and its applications to decision making process. Applied Intelligence:1–14.  https://doi.org/10.1007/s10489-018-1152-z  https://doi.org/10.1007/s10489-018-1152-z
  15. 15.
    Kumar K, Garg H (2018) Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making. Appl Intell 48(8):2112–2119CrossRefGoogle Scholar
  16. 16.
    Garg H, Kumar K (2018) An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making. Soft Comput 22(15):4959–4970CrossRefzbMATHGoogle Scholar
  17. 17.
    Garg H (2016) A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems. Appl Soft Comput 38:988–999CrossRefGoogle Scholar
  18. 18.
    Garg H, Kumar K (2018) Improved possibility degree method for ranking intuitionistic fuzzy numbers and their application in multiattribute decision-making. Granular Computing:1–11.  https://doi.org/10.1007/s41066-018-0092-7
  19. 19.
    Gerstenkorn T, Manko J (1991) Correlation of intuitionistic fuzzy sets. Fuzzy Sets Syst 44:39–43MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Hong DH, Hwang SK (1995) Correlation of intuitionistic fuzzy sets in probability spaces. Fuzzy Sets Syst 75:77–81MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Hung WL, Wu JW (2002) Correlation of intuitionistic fuzzy sets by centroid method. Inf Sci 144:219–225MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Bustince H, Burillo P (1995) Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 74:237–244MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Zeng W, Li H (2007) Correlation coefficient of intuitionistic fuzzy sets. J Ind Eng Int 3(5):33–40Google Scholar
  24. 24.
    Garg H (2016) A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes. Int J Intell Syst 31(12):1234–1252CrossRefGoogle Scholar
  25. 25.
    Garg H (2018) Novel correlation coefficients under the intuitionistic multiplicative environment and their applications to decision - making process. Journal of Industrial and Management Optimization:1–19.  https://doi.org/10.3934/jimo.2018018
  26. 26.
    Ye J (2011) Cosine similarity measures for intuitionistic fuzzy sets and their applications. Math Comput Model 53:91–97MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Garg H (2017) An improved cosine similarity measure for intuitionistic fuzzy sets and their applications to decision-making process Hacettepe Journal of Mathematics and Statistics.  https://doi.org/10.15672/HJMS.2017.510
  28. 28.
    Liu B, Shen Y, Mu L, Chen X, Chen L (2016) A new correlation measure of the intuitionistic fuzzy sets. J Intell Fuzzy Syst 30:1019–1028CrossRefzbMATHGoogle Scholar
  29. 29.
    Luo L, Ren H (2016) A new similarity measure of intuitionistic fuzzy set and application in MADM problem. AMSE Ser Adv A 59:204–223Google Scholar
  30. 30.
    Arora R, Garg H (2018) A robust correlation coefficient measure of dual hesistant fuzzy soft sets and their application in decision making. Eng Appl Artif Intell 72:80–92CrossRefGoogle Scholar
  31. 31.
    Ramot D, Friedman M, Langholz G, Kandel A (2003) Complex fuzzy logic. IEEE Trans Fuzzy Syst 11(4):450–461CrossRefGoogle Scholar
  32. 32.
    Greenfield S, Chiclana F, Dick S (2016) Interval-valued complex fuzzy logic. In: IEEE International Conference on Fuzzy Systems(FUZZ), pp 1–6.  https://doi.org/10.1109/FUZZ-IEEE.2016.7737939
  33. 33.
    Alkouri AUM, Salleh AR (2013) Complex Atanassov’s intuitionistic fuzzy relation, Abstract and Applied Analysis 2013. Article ID 287382, pp 18Google Scholar
  34. 34.
    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
  35. 35.
    Rani D, Garg H (2018) Complex intuitionistic fuzzy power aggregation operators and their applications in multi-criteria decision-making. Expert Systems:e12325.  https://doi.org/10.1111/exsy.12325
  36. 36.
    Kumar T, Bajaj RK (2014) On complex intuitionistic fuzzy soft sets with distance measures and entropies, Journal of Mathematics 2014. Article ID 972198, pp 12Google Scholar
  37. 37.
    Garg H (2018) New exponential operational laws and their aggregation operators for interval-valued pythagorean fuzzy multicriteria decision - making. Int J Intell Syst 33(3):653–683CrossRefGoogle Scholar
  38. 38.
    Garg H (2018) Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision-making process. Int J Intell Syst 33(6):1234–1263CrossRefGoogle Scholar
  39. 39.
    Garg H (2017) Distance and similarity measure for intuitionistic multiplicative preference relation and its application. Int J Uncertain Quantif 7(2):117–133CrossRefGoogle Scholar
  40. 40.
    Garg H, Arora R (2018) Dual hesitant fuzzy soft aggregation operators and their application in decision making. Cognitive Computation:1–21.  https://doi.org/10.1007/s12559-018-9569-6

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics, Thapar Institute of Engineering and TechnologyDeemed UniversityPatialaIndia

Personalised recommendations