Picture Fuzzy Operators with Application in Pattern Recognition
DOI:
https://doi.org/10.26713/cma.v17i1.3541Keywords:
Picture fuzzy set, Difference operator, Possibility operator, Necessary operator, Closure operator, Interior operator, Mean operatorAbstract
In our daily lives, we are to face many uncertain situations where vague or imprecise data are the robust issue for consideration. Conducting these imprecise data is more tough job than precise data. Picture fuzzy set is one of the powerful concept to deal with these kinds of imprecise data effectively because of its diverse operations techniques in several dimensions. In this article, different sorts of operators for picture fuzzy sets are defined and various related properties of these operators are explored. Some mean operators in particular cases are discussed with some of their associated properties. Finally, a real life application is described in make decision.
Downloads
References
[1] K. T. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications, 1st edition, Physica Heidelberg, xviii + 324 pages (1999), DOI: 10.1007/978-3-7908-1870-3.
[2] N. M. Chau, N. T. Lan and N. X. Thao, A new similarity measure of picture fuzzy sets and application in the fault diagnosis of steam turbine, International Journal of Mathematical Sciences and Computing 6(5) (2020), 47 – 55, DOI: 10.5815/ijmsc.2020.05.05.
[3] B. C. Cuong, Picture fuzzy sets, Journal of Computer Science and Cybernetics 30(4) (2014), 409 – 420, DOI: 10.15625/1813-9663/30/4/5032.
[4] B. C. Cuong and V. Kreinovich, Picture fuzzy sets – A new concept for computational intelligence problems, in: Third World Congress on Information and Communication Technologies (WICT2013, Hanoi, Vietnam, 2013), pp. 1 – 6 (2013), DOI: 10.1109/WICT.2013.7113099.
[5] N. V. Dinh and N. X. Thao, Some measures of picture fuzzy sets and their application in multiattribute decision making, International Journal of Mathematical Sciences and Computing 4(3) (2018), 23 – 41, DOI: 10.5815/ijmsc.2018.03.03.
[6] S. Dogra and M. Pal, Picture fuzzy matrix and its application, Soft Computing 24 (2020), 9413 – 9428, DOI: 10.1007/s00500-020-05021-4.
[7] P. Dutta and S. Ganju, Some aspects of picture fuzzy set, Transactions of A. Razmadze Mathematical Institute 172(2) (2018), 164 – 175, DOI: 10.1016/j.trmi.2017.10.006.
[8] A. H. Ganie, S. Singh and P. K. Bhatia, Some new correlation coefficients of picture fuzzy sets with applications, Neural Computing and Applications 32 (2020), 12609 – 12625, DOI: 10.1007/s00521-020-04715-y(0123456789.
[9] H. Garg, Some picture fuzzy aggregation operators and their applications to multicriteria decisionmaking, Arabian Journal for Science and Engineering 42 (2017), 5275 – 5290, DOI: 10.1007/s13369-017-2625-9.
[10] M. K. Hasan, Md. Y. Ali, A. Sultana and N. K. Mitra, Some picture fuzzy mean operators and their applications in decision-making, Journal of Fuzzy Extension and Applications 3(4) (2022), 349 – 361.
[11] C. Jana, T. Senapati, M. Pal and R. R. Yager, Picture fuzzy Dombi aggregation operators: Application to MADM process, Applied Soft Computing 74 (2019), 99 – 109, DOI: 10.1016/j.asoc.2018.10.021.
[12] R. Kadian and S. Kumar, A new picture fuzzy divergence measure based on Jensen-Tsallis information measure and its application to multicriteria decision making, Granular Computing 7 (2022), 113 – 126, DOI: 10.1007/s41066-021-00254-6.
[13] M. J. Khan, P. Kumam, W. Deebani, W. Kumam and Z. Shah, Bi-parametric distance and similarity measures of picture fuzzy sets and their applications in medical diagnosis, Egyptian Informatics Journal 22(2) (2021), 201 – 212, DOI: 10.1016/j.eij.2020.08.002.
[14] S. Khan, S. Abdullah and S. Ashraf, Picture fuzzy aggregation information based on Einstein operations and their application in decision making, Mathematical Sciences 13(3) (2019), 213 – 229, DOI: 10.1007/s40096-019-0291-7.
[15] M. Luo and H. Long, Picture fuzzy geometric aggregation operators based on a trapezoidal fuzzy number and its application, Symmetry 13(1) (2021), 119, DOI: 10.3390/sym13010119.
[16] M. Luo and Y. Zhang, A new similarity measure between picture fuzzy sets and its application, Engineering Applications of Artificial Intelligence 96 (2020), 103956, DOI: 10.1016/j.engappai.2020.103956.
[17] P. Meksavang, H. Shi, S.-M. Lin and H.-C. Liu, An extended picture fuzzy VIKOR approach for sustainable supplier management and its application in the beef industry, Symmetry 11(4) (2019), 468, DOI: 10.3390/sym11040468.
[18] X. T. Nguyen, Evaluating water reuse applications under uncertainty: A novel picture fuzzy multi criteria decision making method, International Journal of Information Engineering and Electronic Business 10(6) (2018), 32 – 39, DOI: 10.5815/ijieeb.2018.06.04.
[19] X. Peng and J. Dai, Algorithm for picture fuzzy multiple attribute decision-making based on new distance measure, International Journal for Uncertainty Quantification 7(2) (2017), 177 – 187, DOI: 10.1615/Int.J.UncertaintyQuantification.2017020096.
[20] M. Qiyas, S. Abdullah, S. Ashraf and M. Aslam, Utilizing linguistic picture fuzzy aggregation operators for multiple-attribute decision-making problems, International Journal of Fuzzy Systems 22 (2020), 310 – 20, DOI: 10.1007/s40815-019-00726-7.
[21] A. Si, S. Das and S. Kar, An approach to rank picture fuzzy numbers for decision making problems, Decision Making: Applications in Management and Engineering 2(2) (2019), 54 – 64, DOI: 10.31181/dmame1902049s.
[22] I. Silambarasan, Some algebraic properties of picture fuzzy sets, Bulletin of the International Mathematical Virtual Institute 11(3) (2021), 429 – 442.
[23] P. Singh, Correlation coefficients for picture fuzzy sets, Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology 28(2) (2015), 591 – 604, DOI: 10.3233/IFS-141338.
[24] S. Singh and A. H. Ganie, Applications of a picture fuzzy correlation coefficient in pattern analysis and decision-making, Granular Computing 7 (2022), 353 – 367, DOI: 10.1007/s41066-021-00269-z.
[25] L. H. Son, Measuring analogousness in picture fuzzy sets: From picture distance measures to picture association measures, Fuzzy Optimization and Decision Making 16 (2016), 359 – 378, DOI: 10.1007/s10700-016-9249-5.
[26] L. H. Son, P. V. Viet and P. V. Hai, Picture inference system: A new fuzzy inference system on picture fuzzy set, Applied Intelligence 46 (2017), 652 – 669, DOI: 10.1007/s10489-016-0856-1.
[27] N. X. Thao, Similarity measures of picture fuzzy sets based on entropy and their application in MCDM, Pattern Analysis and Applications 23(2020), 1203 – 1213, DOI: 10.1007/s10044-019-00861-9.
[28] C. Tian, J.-J. Peng, S. Zhang, W.-Y. Zhang and J.-Q. Wang, Weighted picture fuzzy aggregation operators and their applications to multi-criteria decision-making problems, Computers & Industrial Engineering 137 (2019), 106037, DOI: 10.1016/j.cie.2019.106037.
[29] R. Wang, Methods for MADM with picture fuzzy Muirhead mean operators and their application for evaluating the financial investment risk, Symmetry 11(1) (2019), 6, DOI: 10.3390/sym11010006.
[30] C. Wang, X. Zhou, H. Tu and S. Tao, Some geometric aggregation operators based on picture fuzzy sets and their applications in multiple attribute decision making, Italian Journal of Pure and Applied Mathematics 37 (2017), 477 – 492, URL: https://ijpam.uniud.it/online_issue/201737/44-WangZhouTuTao.pdf.
[31] G. Wei, Picture fuzzy cross-entropy for multiple attribute decision making problems, Journal of Business Economics and Management 17(4) (2016), 491 – 502, DOI: 10.3846/16111699.2016.1197147.
[32] G. Wei, Picture fuzzy hamacher aggregation operators and their application to multiple attribute decision making, Fundamenta Informaticae 157(3) (2018), 271 – 320, DOI: 10.3233/FI-2018-1628.
[33] L. A. Zadeh, Fuzzy sets, Information and Control 8(3) (1965), 338 – 353, DOI: 10.1016/S0019-9958(65)90241-X.
Downloads
Published
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
