Skip to main content
Springer Nature Link
Log in

An Atanassov’s intuitionistic fuzzy multi-attribute group decision making method based on entropy and similarity measure

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

In this paper, we propose a new similarity measure for Atanassov’s intuitionistic fuzzy sets by the relationship between entropy and similarity measure. With respect to multi-attribute group decision making problem, we then give an approach to derive the relative importance weights of experts. This approach takes into account decision information from three aspects: the uncertainty degrees of individual expert’s assessing information for alternatives, the similarity degree of the assessing information for alternatives provided by individual expert, and the similarity degree of the individual expert’s assessing information to all the others’. Finally, we establish a method for handling multi-attribute group decision making problem with Atanassov’s intuitionistic fuzzy information, and adopt an illustrative example to demonstrate its rationality and effectiveness.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Abo-Tabl EA (2012) Rough sets and topological spaces based on similarity. Int J Mach Learn Cybern. doi:10.1007/s13042-012-0107-7

  2. Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96

    Article  MATH  MathSciNet  Google Scholar 

  3. Beliakov G, Bustince H et al (2011) On averaging operators for Atanassov’s intuitionistic fuzzy sets. Inf Sci 181:1116–1124

    Article  MATH  MathSciNet  Google Scholar 

  4. Burillo P, Bustince H (1996) Vague sets are intuitionistic sets. Fuzzy Sets Syst 79:403–405

    Article  MATH  MathSciNet  Google Scholar 

  5. Burillo P, Bustince H (1996) Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst 78:305–316

    Article  MATH  MathSciNet  Google Scholar 

  6. Chen SM (1995) Measures of similarity between vague sets. Fuzzy Sets Syst 74:217–223

    Article  MATH  Google Scholar 

  7. Chen SM, Tan JM (1994) Handling multi-criteria fuzzy decision making problems based on vague set theory. Fuzzy Sets Syst 67(2):163–172

    Article  MATH  MathSciNet  Google Scholar 

  8. Cornelis C, Atanassov K, Kerre EE (2003) Intuitionistic fuzzy sets and interval-valued fuzzy sets: a critical comparison. In: Proceedings of third European conference on fuzzy logic and Technology (EUSFLAT’03), Zittau, Germany, pp 159–163

  9. De SK, Biswas R, Roy AR (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Syst 117(2):209–213

    Article  MATH  MathSciNet  Google Scholar 

  10. Deschrijver G, Kerre EE (2003) On the relationship between some extensions of fuzzy set theory. Fuzzy Sets Syst 133:227–235

    Article  MATH  MathSciNet  Google Scholar 

  11. Gau WL, Buehrer DJ (1993) Vague sets. IEEE Trans Syst Man Cybern 23(2):610–614

    Article  MATH  Google Scholar 

  12. Hong DH, Choi CH (2000) Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 114:103–113

    Article  MATH  Google Scholar 

  13. Hung WL, Yang MS (2004) Similarity measures of intuitionistic fuzzy sets based on Huasdorff distance. Pattern Recognit Lett 25:1603–1611

    Article  Google Scholar 

  14. Li DF, Cheng CT (2002) New similarity measure of intuitionistic fuzzy sets and application to pattern recongnitions. Pattern Recognit Lett 23:221–225

    Article  MATH  MathSciNet  Google Scholar 

  15. Li YH, Olson DL, Zeng Q (2007) Similarity measures between intuitionistic fuzzy (vague) set: a comparative analysis. Pattern Recognit Lett 28:278–285

    Article  Google Scholar 

  16. Li DF, Wang YC, Liu S, Shan F (2009) Fractional programming methodology for multi-attribute group decision-making using IFS. Appl Soft Comput 9:219–225

    Article  Google Scholar 

  17. Li F, Xu ZY (2001) Similarity measures between vague sets. Software (in Chinese) 12(6):922–927

    Google Scholar 

  18. Mitchell HB (2003) On the Dengfeng-Chuntain similarity measure and its application to pattern recognition. Pattern Recognit Lett 24:3101–3104

    Article  Google Scholar 

  19. Pal N R, Bustince H et al (2013) Uncertainties with Atanassovs intuitionistic fuzzy sets: fuzziness and lack of knowledge. Inf Sci 228:61–74

    Google Scholar 

  20. Pearl PG, Yan H (2012) A hierarchical multilevel thresholding method for edge information extraction using fuzzy entropy. Int J Mach Learn Cybern 3(4):297–305

    Article  Google Scholar 

  21. Szmidt E, Kacprzyk J (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst 118(3):467–477

    Article  MATH  MathSciNet  Google Scholar 

  22. Szmidt E, Kacprzyk J (2005) New measures of entropy for intuitionistic fuzzy sets. Ninth Int Conf IFSs Sofia 11(2):12–20

    Google Scholar 

  23. Vlachos IK, Sergiadis GD (2007) Intuitionistic fuzzy information—applications to pattern recognition. Pattern Recognit Lett 28:197–206

    Article  Google Scholar 

  24. Vlachos IK, Sergiadis GD (2007) Subsethood, entropy, and cardinality for interval-valued fuzzy sets: an algebraic derivation. Fuzzy Sets Syst 158:1384–1396

    Article  MATH  MathSciNet  Google Scholar 

  25. Wan SP (2010) Determination of experts’ weights based on vague sets for multi-attribute group decision-making. Commun Appl Math Comput 24(1):45–52

    MATH  MathSciNet  Google Scholar 

  26. Wang XZ, Dong CR (2009) Improving generalization of fuzzy if-then rules by maximizing fuzzy entropy. IEEE Trans Fuzzy Syst 17(3):556–567

    Article  Google Scholar 

  27. Wang XZ, He YL, Wang DD (2013) Non-Naive Bayesian classifiers for classification problems with continuous attributes. IEEE Trans Cybern. doi:10.1109/TCYB.2013.2245891

  28. Wei CP, Gao ZH, Guo TT (2012) An intuitionistic fuzzy entropy measure based on the trigonometric function. Control Decis (in Chinese) 27(4):571–574

    MATH  MathSciNet  Google Scholar 

  29. Wei CP, Liang X, Zhang YZ (2012) A comparative analysis and improvement of entropy measures for intuitionistic fuzzy sets. J Syst Sci Math Sci 32(11):1437–1448

    MATH  MathSciNet  Google Scholar 

  30. Wei CP, Tang XJ (2011) An intuitionistic fuzzy group decision making approach based on entropy and similarity measures. Int J Inf Technol Decis Mak 10(6):1111–1130

    Article  MATH  Google Scholar 

  31. Wei CP, Wang P, Zhang YZ (2011) Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Inf Sci 182(19):4273–4286

    Article  MathSciNet  Google Scholar 

  32. Xia MM, Xu ZS (2011) Some new similarity measures for intuitionistic fuzzy values and their application in group decision making. J Syst Sci Syst Eng 19(4):430–452

    Article  Google Scholar 

  33. Xia MM, Xu ZS (2012) Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment. Inf Fusion 13(1):31–47

    Article  MathSciNet  Google Scholar 

  34. Xu ZS (2010) A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making. Group Decis Negot 19:57–76

    Article  Google Scholar 

  35. Xu ZS (2008) An overview of distance and similarity measures of intuitionistic sets. Int J Uncertain Fuzziness Knowl-Based Syst 16(4):529–555

    Article  MATH  Google Scholar 

  36. Xu ZS (2011) Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowl-Based Syst 24:749–760

    Article  Google Scholar 

  37. Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187

    Article  Google Scholar 

  38. Xu ZS (2007) On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognitions. J Southeast Univ (English Ed) 23(1):139–143

    MATH  MathSciNet  Google Scholar 

  39. Xu ZS (2007) Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control Decis 22(2):215–219

    Google Scholar 

  40. Xu ZS (2007) Multi-person multi-attribute decision making models under intuitionistic fuzzy environment. Fuzzy Optim Decis Mak 6(3):221–236

    Article  MATH  MathSciNet  Google Scholar 

  41. Xu ZS (2007) Multiple attribute decision making with intuitionistic fuzzy preference information. Syst Eng-Theory Pract 27(11):62–71

    Article  Google Scholar 

  42. Xu ZS (2010) Choquet integrals of weighted intuitionistic fuzzy information. Inf Sci 180:726–736

    Article  MATH  Google Scholar 

  43. Xu ZS, Cai XQ (2010) Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information. Int J Intell Syst 25:489–513

    MATH  MathSciNet  Google Scholar 

  44. Xu ZS, Hu H (2010) Projection models for intuitionistic fuzzy multiple attribute decision making. Int J Inf Technol Decis Mak 9(2):267–280

    Article  MATH  Google Scholar 

  45. Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35(4):417–433

    Article  MATH  MathSciNet  Google Scholar 

  46. Xu ZS, Yager RR (2008) Dynamic intuitionistic fuzzy multi-attribute decision making. Int J Approx Reason 48:246–262

    Article  MATH  MathSciNet  Google Scholar 

  47. Ye J (2010) Two effective measures of intuitionistic fuzzy entropy. Comput Lett 87(1–2):55–62

    Article  MATH  MathSciNet  Google Scholar 

  48. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–356

    Article  MATH  MathSciNet  Google Scholar 

  49. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8:199–249

    MATH  MathSciNet  Google Scholar 

  50. Zeng WY, Li HX (2006) Relationship between similarity measure and entropy of interval-valued fuzzy sets. Fuzzy Sets Syst 157:1477–1484

    Article  MATH  MathSciNet  Google Scholar 

  51. Zhang QS, Jiang SY (2008) A note on information entropy measures for vague sets and its application. Inf Sci 178:4184–4191

    Article  MATH  Google Scholar 

  52. Zhang HY, Zhang WX, Mei CL (2009) Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure. Knowl-Based Syst 22:449–454

    Article  Google Scholar 

Download references

Acknowledgments

The work was partly supported by the National Natural Science Foundation of China (71171187, 71271050), Ministry of Education Foundation of Humanities and Social Sciences (10YJC630269).

Author information

Authors and Affiliations

  1. School of Business Administration, Northeastern University, Shenyang, Liaoning, 110819, China

    Xia Liang

  2. Institute of Operations Research, Qufu Normal University, Rizhao, Shandong, 276826, China

    Cuiping Wei

Authors
  1. Xia Liang
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Cuiping Wei
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Cuiping Wei.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liang, X., Wei, C. An Atanassov’s intuitionistic fuzzy multi-attribute group decision making method based on entropy and similarity measure. Int. J. Mach. Learn. & Cyber. 5, 435–444 (2014). https://doi.org/10.1007/s13042-013-0178-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-013-0178-0

Keywords