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A New Similarity Measure for Picture Fuzzy Sets and Its Application to Multi-Attribute Decision Making
Volume 32, Issue 3 (2021), pp. 543–564
Pub. online: 29 April 2021      Type: Research Article      Open accessOpen Access
Received
1 July 2020
Accepted
1 April 2021
Published
29 April 2021

Abstract

As an extension of intuitionistic fuzzy sets, picture fuzzy sets can deal with vague, uncertain, incomplete and inconsistent information. The similarity measure is an important technique to distinguish two objects. In this study, a similarity measure between picture fuzzy sets based on relationship matrix is proposed. The new similarity measure satisfies the axiomatic definition of similarity measure. It can be testified from a numerical experiment that the new similarity measure is more effective. Finally, we apply the proposed similarity measure to multiple-attribute decision making.

References

 
Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96.
 
Bustince, H., Barrenechea, E., Pagola, M. (2007). Image thresholding using restricted equivalence functions and maximizing the measures of similarity. Fuzzy Sets and Systems, 158, 496–516.
 
Chen, S.M., Chang, C.H. (2015). A novel similarity measure between Atanassov’s intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition. Information Sciences, 291, 96–114.
 
Chen, S.M., Cheng, S.H., Chiou, C.H. (2016). Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology. Information Fusion, 27, 215–227.
 
Chu, C.H., Hung, K.C., Julian, P.A. (2014). Complete pattern recognition approach under Atanassov’s intuitionistic fuzzy sets. Knowledge-Based Systems, 66, 36–45.
 
Cuong, B. (2013). Picture fuzzy sets-sets – a new concept for computational intelligence problems. In: Proceedings of the Third World Congress on Information and Communication Technologies (WICT 2013), Hanoi. IEEE, pp. 1–6.
 
Cuong, B., Kreinovitch, V., Ngan, R.T. (2016). A classification of representable t-norm operators for picture fuzzy sets. In: Eighth International Conference on Knowledge and Systems Engineering (KSE 2016), Hanoi. IEEE, pp. 19–24.
 
Dhivya, J., Sridevi, B. (2019). A novel similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers with applications to pattern recognition and medical diagnosis. A Journal of Chinese Universities, 34, 229–252.
 
Dinh, N.V., Thao, N.X. (2018). Some measures of picture fuzzy sets and their application in multi-attribute decision making. Mathematical Sciences and Computing, 3, 23–41.
 
Dutta, P. (2017). Medical diagnosis via distance measures on picture fuzzy sets. Advances in Modelling and Analysis A, 54, 137–152.
 
Garg, H. (2017). Some picture fuzzy aggregation operators and their applications to multicriteria decision making. Research Article – Systems Engineering, 42, 5275–5290.
 
Hwang, C.M., Yang, M.S., Hung, W.L. (2018). New similarity measure of intuitionistic fuzzy sets based on the jaccard index with its application to clustering. International Journal of Intelligent Systems, 38(8), 1672–1688.
 
Jiang, Q., Jin, X. (2019). A new similarity/distance measure between intuitionistic fuzzy sets based on the transformed isosceles triangles and its applications to pattern recognition. Expert Systems with Applications, 116, 439–453.
 
Joshi, D., Kumar, S. (2018). An approach to multi-criteria decision making problems using dice similarity measure for picture fuzzy sets. In: Communications in Computer and Information Science, 1–6.
 
Khan, M.S., Lohani, Q.M.D. (2016). A similarity measure for atanassov intuitionistic fuzzy sets and its application to clustering. In: 2016 International Workshop on Computational Intelligence (IWCI), pp. 232–239. https://doi.org/10.1109/IWCI.2016.7860372.
 
Li, J.H., Zeng, W.Y. (2015). A new dissimilarity measure between intuitionistic fuzzy sets and its application in multipile attribute decision making. International Journal of Fuzzy Systems, 29, 1311–1320.
 
Liu, M., Zeng, S.Z. (2019). Picture fuzzy weighted distance measures and their applications to investment selection. Amfiteatru Economic, 21, 682–695.
 
Luo, M.X., Zhang, Y. (2020). A new similarity measure between picture fuzzy sets and its application. Engineering Applications of Artificial Intelligence, 96, 103956.
 
Luo, M.X., Long, H.F. (2021). Picture fuzzy geometric aggregation operators based on a trapezoidal fuzzy number and its application. Symmetry, 13(1), 119.
 
Luo, X., Li, W., Zhao, W. (2018). Picture fuzzy weighted distance measures and their applications to investment selection. Applied Intelligence, 48, 2792–2808.
 
Ngan, R.T., Song, L.H., Cuong, B.C. (2018). H-max distance measure of intuitionistic fuzzy sets in decision making. Applied Soft Computing, 69, 393–425.
 
Singh, P., Mishra, N.K., Kumar, M., Saxena, S., Singh, V. (2018). Risk analysis of flood disaster based on similarity measures in picture fuzzy environment. Afrika Matematika, 29, 1019–1038.
 
Son, L.H. (2016). Generalized picture distance measure and applications to picture fuzzy clustering. Applied Soft Computing, 46, 284–295.
 
Song, Y.F., Wang, X.D., Lei, L., Quan, W., Huang, W.L. (2016). An evidential view of similarity measure for Atanassov’s intuitionistic fuzzy sets. Journal of Intelligent and Fuzzy Systems, 31, 1653–1668.
 
Wang, F., Mao, J. (2018). Aggregation similarity measure based on intuitionistic fuzzy closeness degree and its application to clustering analysis. Journal of Intelligent and Fuzzy Systems, 35, 609–625.
 
Wei, G.W. (2016). Picture fuzzy cross-entropy for multiple attribute decision making problems. Journal of Business Economics and Management, 17, 491–502.
 
Wei, G.W. (2017a). Picture fuzzy aggregation operators and their application to multiple attribute decision making. Journal of Intelligent and Fuzzy Systems, 33, 713–724.
 
Wei, G.W. (2017b). Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision making. Informatica, 144, 547–564.
 
Wei, G.W. (2018). Picture fuzzy hamacher aggregation operators and their application to multiple attribute decision making. Fundamenta Informaticae, 157, 271–320.
 
Wei, G.W., Gao, H. (2018). The generalized dice similarity measures for picture fuzzy sets and their applications. Informatica, 160, 107–124.
 
Wei, G.W., Alsaadi, F.T., Hayat, T., Alsaedi, A. (2018). Projection models for multiple attribute decision making with picture fuzzy information. International Journal of Machine Learning and Cybernetics, 9, 491–502.
 
Wei, G.W., Zhang, S.Q., Lu, J.P., Wu, J., Wei, C. (2019). An extended bidirectional projection method for picture fuzzy MAGDM and its application to safety assessment of construction project. IEEE Access, 7, 166138–166147.
 
Wei, G.W., Wang, J., Gao, H., Wei, C. (2021). Approaches to multiple attribute decision making based on picture 2-tuple linguistic power Hamy mean aggregation operators. RAIRO-Operations Research, 55, 435–460.
 
Xu, S.P., Zhang, H., Jiang, S.L. (2009). Image similarity measure based on intuitionistic fuzzy set. Pattern Recognition and Artificial Intelligence, 22, 157–161.
 
Zadeh, L.A. (1965). Fuzzy sets. Information Control, 8, 338–353.
 
Zhang, S.Q., Wei, G.W., Alsaadi, F.E., Hayat, T., Wei, C., Zhang, Z.Z.P. (2020). MABAC method for multiple attribute group decision making under picture 2-tuple linguistic environment. Soft Computing, 24, 5819–5829.

Biographies

Luo Minxia
mxluo@cjlu.edu.cn

M. Luo obtained her PhD degree in computer science from Northwestern Polytechnical University, China. She is now a professor at Department of Information and Computing Science of the China Jiliang University, China. Her research fields are fuzzy logic theory, medical diagnosis, pattern recognition and fuzzy decision theory. She has published over 130 papers in international and domestic peer reviewed journals.

Zhang Yue
S1808070113@cjlu.edu.cn

Y. Zhang obtained her MSc degree in applied mathematics from China Jiliang University, Hangzhou, China. Her research interests include fuzzy logic, and fuzzy decision theory.

Fu Li
fl0971@163.com

L. Fu obtained her PhD degree from ShaanXi Normal University, China. She is now a professor at School of Mathematics and Statistics of Qinghai Nationalities University, China. Her research fields are fuzzy logic theory, soft set theory.


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Copyright
© 2021 Vilnius University
Open access article under the CC BY license.

Keywords
picture fuzzy sets similarity measure multi-attribute decision making

Funding
This work is supported by the National Natural Science Foundation of China (Nos. 61773019, 11871210) and Scientific Research and Innovation Team of Qinghai Nationalities University.

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