A New Similarity Measure of Picture Fuzzy Sets and Application in the Fault Diagnosis of Steam Turbine

Full Text (PDF, 262KB), PP.47-55

Views: 0 Downloads: 0


Ngoc Minh Chau 1 Nguyen Thi Lan 1 Nguyen Xuan Thao 1,*

1. Faculty of Information Technology, Vietnam National University of Agriculture, Trau Quy, Gia Lam, Ha Noi, Viet Nam.

* Corresponding author.

DOI: https://doi.org/10.5815/ijmsc.2020.05.05

Received: 8 May 2020 / Revised: 17 Jun. 2020 / Accepted: 15 Jul. 2020 / Published: 8 Oct. 2020

Index Terms

Picture fuzzy set, similarity measure, fault turbine.


Picture fuzzy set is an extension of fuzzy sets and intuitionistic sets. It is demonstrated have a wide application in the fact and theoretical. In this paper, we propose some novel similarity measures between picture fuzzy sets. The novel similarity measure is constructed by combining negative functions of each degree membership of picture fuzzy set. This similarity is shown that is better other similarity measures of picture fuzzy sets in some cases. Next, we apply them in several pattern recognition problems. Finally, we apply them to find the fault diagnosis of the steam turbine.

Cite This Paper

Ngoc Minh Chau, Nguyen Thi Lan, Nguyen Xuan Thao. " A New Simialrity Measure Of Picture Fuzzy Sets And Application In The Fault Diagnosis Of Steam Turbine ", International Journal of Mathematical Sciences and Computing (IJMSC), Vol.6, No.5, pp.47-55, 2020. DOI: 10.5815/IJMSC.2020.05.05


[1]K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and Systems, 20(1) (1986), 87-96.

[2]K. Atanassov, On Intuitionistic Fuzzy Sets Theory, Springer, Berlin, 2012.

[3]K. Atanassov, and G.  Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy sets and systems, 31(3) (1989), 343-349.

[4]B.C. Cường, Picture fuzzy sets, Journal of Computer Science and Cybernetics 30.4 (2014): 409-420.

[5]Dinh NV, NX Thao, NM Chau, On the picture fuzzy database: theories and application, Journal of Scientist and Development (2015), 13(6), 1028-1035.

[6]Dinh, N. V., Thao, N. X., & Chau, N. M. (2017). Some dissimilarity measures of picture fuzzy set. the 10th Fundamental and Applied IT Research (FAIR’2017), 104-109.

[7]Dinh, NV, & Thao, N. X. (2018). Some measures of picture fuzzy sets and their application in multi-attribute decision making. Int. J. Math. Sci. Comput.(IJMSC), 4(3), 23-41.

[8]Dinh, NV, Thao, N. X., & Chau, N. M. (2019). Distance and dissimilarity measure of picture fuzzy sets. Proceeding of Publishing House for Science and Technology.

[9]Dutta, P., & Ganju, S. (2017). Some aspects of picture fuzzy set. Transactions of A. Razmadze Mathematical Institute 172(2), 164-175.

[10]Hoa, N. D., & Thong, P. H. (2017). Some Improvements of Fuzzy Clustering Algorithms Using Picture Fuzzy Sets and Applications for Geographic Data Clustering. VNU Journal of Science: Computer Science and Communication Engineering, 32(3).

[11]Le, N. T., Van Nguyen, D., Ngoc, C. M., & Nguyen, T. X. (2018). NEW DISSIMILARITY MEASURES ON PICTURE FUZZY SETS AND APPLICATIONS. Journal of Computer Science and Cybernetics, 34(3), 219-231.

[12]Nguyen, X. T. (2018). Evaluating Water Reuse Applications under Uncertainty: A Novel Picture Fuzzy Multi Criteria Decision Making Medthod. International Journal of Information Engineering and Electronic Business, 10(6), 32-39.

[13]Nhung, L.T., & Nguyen, X. T. (2018). A novel multi-criteria decision making method for evaluating water reuse applications under uncertainty. Vietnam Journal of Agricultural Sciences, 1(3), 230-239.

[14]Singh, P. (2015). Correlation coefficients for picture fuzzy sets. Journal of Intelligent & Fuzzy Systems, 28(2), 591-604.

[15]Son LH. (2015). DPFCM: A novel distributed picture fuzzy clustering method on picture fuzzy sets 42(1), 51-66.

[16]Son, L. H. (2016). Generalized picture distance measure and applications to picture fuzzy clustering. Applied Soft Computing, 46(C), 284-295.

[17]Thao, N.X., & Dinh, N. V. (2015). Rough picture fuzzy set and picture fuzzy topologies. Journal of Computer Science and Cybernetics, 31(3), 245.

[18]Thao, N. X., & Smarandache, F. (2016). (I, T)-Standard neutrosophic rough set and its topologies properties. V14, pp 65-70.

[19]Thao, N. X., Cuong, B. C., & Smarandache, F. (2016). Rough standard neutrosophic sets: an application on standard neutrosophic information systems. Infinite Study.

[20]Thao, N. X., Cuong, B. C., Ali, M., & Lan, L. H. (2018). Fuzzy equivalence on standard and rough neutrosophic sets and applications to clustering analysis. In Information Systems Design and Intelligent Applications (pp. 834-842). Springer, Singapore.

[21]Thao, N.X (2020a). A new correlation coefficient of the Pythagorean fuzzy sets and its applications. Soft Computing 24, 9467–9478. https://doi.org/10.1007/s00500-019-04457-7.

[22]Thao, N.X (2020b). Similarity measures of picture fuzzy sets based on entropy and their application in MCDM. Pattern Anal Applic 23, 1203–1213 (2020). https://doi.org/10.1007/s10044-019-00861-9

[23]Thong, N. T. (2015). HIFCF: An effective hybrid model between picture fuzzy clustering and intuitionistic fuzzy recommender systems for medical diagnosis. Expert Systems with Applications, 42(7), 3682-3701.

[24]Thong, P. H. (2016). Picture fuzzy clustering: a new computational intelligence method. Soft computing, 20(9), 3549-3562.

[25]Ye, J. (2017). Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine. Soft Computing, 21(3), 817-825.

[26]Wang, C., Zhou, X., Tu, H., & Tao, S. (2017). Some geometric aggregation operators based on picture fuzzy sets and their application in multiple attribute decision making. Italian Journal of Pure and Applied Mathematics, 37, 477-492.

[27]Wei, G. (2016). Picture fuzzy cross-entropy for multiple attribute decision making problems. Journal of Business Economics and Management, 17(4), 491-502.

[28]Wei, G. (2017). Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision making. Informatica, 28(3), 547-564.

[29]Wei, G. (2018). Some similarity measures for picture fuzzy sets and their applications. Iranian Journal of Fuzzy Systems, 15(1), 77-89.

[30]L. A. Zadeh, Fuzzy sets, Information and control 8(3) (1965), 338-353.