article

Similarity measures on intuitionistic fuzzy sets

Authors:

Pengfei ShiAuthors Info & Claims

Pattern Recognition Letters, Volume 24, Issue 15

Pages 2687 - 2693

https://doi.org/10.1016/S0167-8655(03)00111-9

Published: 01 November 2003 Publication History

Abstract

Intuitionistic fuzzy sets (IFSs), proposed by Atanassov, have gained attention from researchers for their applications in various fields. Then similarity measures between IFSs were developed. In this paper, firstly, some existing measures of similarity are reviewed. Then some examples are applied to show that some existing similarity measures are not always effective in some cases. At the same time, several new similarity measures are proposed and the relationships between some similarity measures are proved. Finally a comparison is made to show the proposed similarity measures are more reasonable than some existing similarity measures in general cases. Therefore, the proposed similarity measures can provide a useful way for measuring IFSs more effectively.

References

[1]

Atanassov, K., 1986. Intuitionistic fuzzy sets. Fuzzy Sets Systems 20 (1), 87-96.

Digital Library

[2]

Atanassov, K., 1989. More on intuitionistic fuzzy sets. Fuzzy Sets Systems 33 (1), 37-46.

Digital Library

[3]

Atanassov, K., 1994a. Operators over interval valued intuitionistic fuzzy sets. Fuzzy Sets Systems 64 (2), 159-174.

Digital Library

[4]

Atanassov, K., 1994b. New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets Systems 61 (2), 137-142.

Digital Library

[5]

Atanassov, K., 1995. Remarks on the intuitionistic fuzzy sets. Fuzzy Sets Systems 75 (3), 401-402.

Digital Library

[6]

Atanassov, K., 1999. Intuitionistic Fuzzy Sets. Theory and Applications. Physica-Verlag, Heidelberg, New York.

[7]

Bustince, H., Burillo, P., 1996. Vague sets are intuitionistic fuzzy sets. Fuzzy Sets Systems 79 (3), 403-405.

Digital Library

[8]

Chen, S.M., 1988. A new approach to handling fuzzy decision making problems. IEEE Trans. Systems Man Cybernet. 18 (6), 1012-1016.

[9]

Chen, S.M., 1994. A weighted fuzzy reasoning algorithm for medical diagnosis. Decis. Support Systems, 37-43.

Digital Library

[10]

Chen, S.M., 1995. A comparison of similarity measures of fuzzy values. Fuzzy Sets Systems 72 (1), 79-89.

Digital Library

[11]

Chen, S.M., Tan, J.M., 1994. Handling multi-criteria fuzzy decision-making problems based on vague sets. Fuzzy Sets Systems 67 (2), 163-172.

[12]

De, S.K., Biswas, A., Roy, R., 2000. Some operations on intuitionistic fuzzy sets. Fuzzy Sets System 114 (3), 477-484.

[13]

De, S.K., Biswas, A., Roy, R., 2001. An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Systems 117 (2), 209-213.

Digital Library

[14]

Gau, W.L., Buehere, D.J., 1993. Vague sets. IEEE Trans. Systems Man Cybernet. 23 (2), 610-614.

[15]

Hyung, L.K., Song, Y.S., Lee, K.M., 1994. Similarity measures between fuzzy sets and between elements. Fuzzy Sets Systems 62 (3), 291-293.

Digital Library

[16]

Li, D., Cheng, C., 2002. New similarity measures of intuitionistic fuzzy sets and application to pattern recognition. Pattern Recognition Lett. 23 (1-3), 221-225.

Digital Library

[17]

Pappis, C.P., Karacatilides, N.I., 1993. A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets Systems 56 (2), 171-174.

Digital Library

[18]

Santini, S., Jain, R., 1999. Similarity measures. IEEE Trans. PAMI 21 (9), 871-883.

Digital Library

[19]

Szmidt, E., Kacprzyk, J., 2000. Distances belween intuitionistic fuzzy sets. Fuzzy Sets Systems 114 (3), 505-518.

[20]

Taranli, N., Coker, D., 2001. Fuzzy connectedness in intuitionistic fuzzy topological spaces. Fuzzy Sets Systems 116 (3), 369-375.

[21]

Wang, W.-J., 1997. New similarity measures on fuzzy sets and on elements. Fuzzy Sets Systems 85 (3), 305-309.

[22]

Zadeh, L.A., 1965. Fuzzy sets. Inform. Control 8, 338-353.

[23]

Zwich, R., Larlstein, E., Budescu, D., 1987. Measures of similarity among fuzzy sets: A comparative analysis. Internet J. Approx. Reason 1, 221-242.

Cited By

Huang WZhang FWang SKong F(2024)A novel knowledge-based similarity measure on intuitionistic fuzzy sets and its applications in pattern recognitionExpert Systems with Applications: An International Journal10.1016/j.eswa.2024.123835249:PCOnline publication date: 17-Jul-2024
https://dl.acm.org/doi/10.1016/j.eswa.2024.123835
Vishnukumar PEdwin Antony Raj MSivaraman G(2024)A novel similarity measure based on new accuracy function on interval-valued intuitionistic fuzzy number and its application to multicriteria decision-making problemNeural Computing and Applications10.1007/s00521-023-09313-236:10(5183-5195)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s00521-023-09313-2
Luo MWang L(2024)A novel similarity measure for intuitionistic fuzzy sets and its application to pattern recognitionSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-023-09474-128:7-8(6207-6217)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s00500-023-09474-1
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Index Terms

Similarity measures on intuitionistic fuzzy sets
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
      1. Probabilistic reasoning
      2. Vagueness and fuzzy logic

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Published In

cover image Pattern Recognition Letters

Pattern Recognition Letters Volume 24, Issue 15

November 2003

381 pages

ISSN:0167-8655

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Publisher

Elsevier Science Inc.

United States

Publication History

Published: 01 November 2003

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Cited By

Huang WZhang FWang SKong F(2024)A novel knowledge-based similarity measure on intuitionistic fuzzy sets and its applications in pattern recognitionExpert Systems with Applications: An International Journal10.1016/j.eswa.2024.123835249:PCOnline publication date: 17-Jul-2024
https://dl.acm.org/doi/10.1016/j.eswa.2024.123835
Vishnukumar PEdwin Antony Raj MSivaraman G(2024)A novel similarity measure based on new accuracy function on interval-valued intuitionistic fuzzy number and its application to multicriteria decision-making problemNeural Computing and Applications10.1007/s00521-023-09313-236:10(5183-5195)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s00521-023-09313-2
Luo MWang L(2024)A novel similarity measure for intuitionistic fuzzy sets and its application to pattern recognitionSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-023-09474-128:7-8(6207-6217)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s00500-023-09474-1
Dutta PTalukdar P(2023)An Advanced Entropy Measure of IFSs via Similarity MeasureInternational Journal of Fuzzy System Applications10.4018/IJFSA.31971212:1(1-23)Online publication date: 10-Mar-2023
https://dl.acm.org/doi/10.4018/IJFSA.319712
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Ashraf SAttaullah Naeem MKhan ARehman NPandit M(2023)Novel Information Measures for Fermatean Fuzzy Sets and Their Applications to Pattern Recognition and Medical DiagnosisComputational Intelligence and Neuroscience10.1155/2023/92732392023Online publication date: 1-Jan-2023
https://dl.acm.org/doi/10.1155/2023/9273239
Wu XZhu ZChen CChen GLiu P(2023)A Monotonous Intuitionistic Fuzzy TOPSIS Method Under General Linear Orders via Admissible Distance MeasuresIEEE Transactions on Fuzzy Systems10.1109/TFUZZ.2022.320543531:5(1552-1565)Online publication date: 1-May-2023
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Dutta PBanik A(2023)Crime linkage and psychological profiling of offenders under intuitionistic fuzzy environment using a novel resemblance measureArtificial Intelligence Review10.1007/s10462-023-10538-956:Suppl 1(893-936)Online publication date: 11-Jul-2023
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Saikia BDutta PTalukdar P(2023)An advanced similarity measure for Pythagorean fuzzy sets and its applications in transportation problemArtificial Intelligence Review10.1007/s10462-023-10421-756:11(12689-12724)Online publication date: 23-Mar-2023
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Attaullah Ullah SDrissi RAl-Duais F(2023)A new type of cosine similarity measures based on intuitionistic hesitant fuzzy rough sets for the evaluation of volatile currency: evidence from the Pakistan economyKnowledge and Information Systems10.1007/s10115-023-01909-365:11(4741-4758)Online publication date: 1-Nov-2023
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