Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

A new approach to construct similarity measure for intuitionistic fuzzy sets

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The intuitionistic fuzzy set (IFS), as a generation of Zadeh’s fuzzy set, can express and process uncertainty much better. Similarity measures between IFSs are used to indicate the similarity degree between the information carried by IFSs. Although several similarity measures for IFSs have been proposed in previous studies, some of them cannot satisfy the axioms of similarity, or provide counterintuitive cases. In this paper, we first review several widely used similarity measures and then propose a new similarity measures. As the consistency of two IFSs, the proposed similarity measure is defined based on the direct operation on the membership function, non-membership function, hesitation function and the upper bound of membership function of two IFS, rather than based on the distance measure or the relationship of membership and non-membership functions. It proves that the proposed similarity measure satisfies the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns. Experiments on medical diagnosis and cluster analysis are carried out to illustrate the applicability of the proposed similarity measure in practice.

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

Similar content being viewed by others

Explore related subjects

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

References

  • Atanassov KT (1986) Intuitionistic fuzzy-sets. Fuzzy Set Syst 20:87–96

    Article  MATH  Google Scholar 

  • Balasubramaniam P, Ananthi VP (2014) Image fusion using intuitionistic fuzzy sets. Inf Fusion 20(1):21–30

    Article  Google Scholar 

  • Boran FE, Akay D (2014) A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition. Inf Sci 255:45–57

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Chen TY (2007) A note on distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets Syst 158:2523–2525

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Grzegorzewski P (2004) Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets Syst 148:319–328

    Article  MathSciNet  MATH  Google Scholar 

  • Hong DH, Kim C (1999) A note on similarity measures between vague sets and between elements. Inf Sci 115:83–96

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Hwang CM, Yang MS, Hung WL, Lee MG (2012) A similarity measure of intuitionistic fuzzy sets based on the Sugeno integral with its application to pattern recognition. Inf Sci 189:93–109

    Article  MathSciNet  MATH  Google Scholar 

  • Li DF (2004) Some measures of dissimilarity in intuitionistic fuzzy structures. J Comput Syst Sci 68:115–122

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Li J, Deng G (2012) The relationship between similarity measure and entropy of intuitionistic fuzzy sets. Inf Sci 188:314–321

    Article  MathSciNet  MATH  Google Scholar 

  • Li F, Xu Z (2001) Similarity measures between vague sets. J Softw 12:922–927

    Google Scholar 

  • Li Y, Chi Z, Yan D (2002) Similarity measures between vague sets and vague entropy. J Comput Sci 29:129–132

    Google Scholar 

  • Li Y, Olson DL, Qin Z (2007) Similarity measures between intuitionistic fuzzy (vague) sets: a comparative analysis. Pattern Recognit Lett 28:278–285

    Article  Google Scholar 

  • Liang ZZ, Shi PF (2003) Similarity measures on intuitionistic fuzzy sets. Pattern Recognit Lett 24:2687–2693

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Ngan SC (2016) An activation detection based similarity measure for intuitionistic fuzzy sets. Expert Syst Appl 60(1):62–80

    Article  Google Scholar 

  • Own CM (2009) Switching between type-2 fuzzy sets and intuitionistic fuzzy sets: an application in medical diagnosis. Appl Intell 31(3):283–291

    Article  Google Scholar 

  • Papakostas GA (2013) Distance and similarity measures between intuitionistic fuzzy sets: a comparative analysis from a pattern recognition point of view. Pattern Recognit Lett 34:1609–1622

    Article  Google Scholar 

  • Szmidt E (2014) Distances and similarities in intuitionistic fuzzy sets. Springer, New York

    Book  MATH  Google Scholar 

  • Szmidt E, Kacprzyk J (2000) Distances between intuitionistic fuzzy sets. Fuzzy Set Syst 114:505–518

    Article  MathSciNet  MATH  Google Scholar 

  • Szmidt E, Kacprzyk J (2002) Using intuitionistic fuzzy sets in group decision making. Control Cybern 31:1055–1057

    MATH  Google Scholar 

  • Szmidt E, Kacprzyk J (2004) A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. In: ICAISC, pp 388–393

  • Vlachos IK, Sergiadis GD (2007) Intuitionistic fuzzy information-application to pattern recognition. Pattern Recognit Lett 28:197–206

    Article  Google Scholar 

  • Wang W, Xin X (2005) Distance measure between intuitionistic fuzzy sets. Pattern Recognit Lett 26:2063–2069

    Article  Google Scholar 

  • Wei CP, Wang P, Zhang YZ (2011) Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Inf Sci 181:4273–4286

    Article  MathSciNet  MATH  Google Scholar 

  • Xia M, Xu Z (2010) Some new similarity measures for intuitionistic fuzzy values and their application in group decision making. J Syst Sci Syst Eng 19:430–452

    Article  Google Scholar 

  • Xu Z (2007) Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making. Fuzzy Optim Decis Mak 6:109–121

    Article  MathSciNet  MATH  Google Scholar 

  • Xu Z, Chen J (2008) An overview of distance and similarity measures of intuitionistic fuzzy sets. Int J Uncertain Fuzziness 16:529–555

    Article  MathSciNet  MATH  Google Scholar 

  • Xu Z, Yager RR (2009) Intuitionistic and interval-valued intuitionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group. Fuzzy Optim Decis Mak 8:123–139

    Article  MathSciNet  MATH  Google Scholar 

  • Xu Z, Chen J, Wu J (2008) Clustering algorithm for intuitionistic fuzzy sets. Inf Sci 178:3775–3790

    Article  MathSciNet  MATH  Google Scholar 

  • Ye J (2011) Cosine similarity measures for intuitionistic fuzzy sets and their applications. Math Comput Model 53:91–97

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  • Zeng W, Guo P (2008) Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship. Inf Sci 178:1334–1342

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang H, Yu L (2013) New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets. Inf Sci 245:181–196

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This study was funded by National Natural Science Foundation of China (Grant Nos. 61703426, 61273275, 60975026, 61573375 and 61503407).

Author information

Authors and Affiliations

  1. Air Force Engineering University, Xi’an, 710051, People’s Republic of China

    Yafei Song, Xiaodan Wang, Wen Quan & Wenlong Huang

Authors
  1. Yafei Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaodan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wen Quan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wenlong Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yafei Song.

Ethics declarations

Conflict of interest

All authors declare that they have no conflict of interest.

Human participants

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Communicated by V. Loia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Song, Y., Wang, X., Quan, W. et al. A new approach to construct similarity measure for intuitionistic fuzzy sets. Soft Comput 23, 1985–1998 (2019). https://doi.org/10.1007/s00500-017-2912-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-017-2912-0

Keywords

Search

Navigation