A picture fuzzy distance measure and its application to pattern recognition problems

Document Type : Research Paper

Author

Post Graduate Department of Mathematics, Government Degree College, Baramulla-193101, J \& K, India

10.22111/ijfs.2023.7347

Abstract

The picture fuzzy sets are very useful in those uncertain problems which could not be solved by fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets, fermatean fuzzy sets, and q-rung orthopair fuzzy sets. For example, medical diagnosis, personnel selection, human voting, etc. All of these problems require answers of the type no, yes, abstain, and refusal. To compare two picture fuzzy sets, the distance measures play an important role. There are a lot of studies about the distance measures of picture fuzzy sets available in the literature. However, all of these distance measures lead to unreasonable results in most of the problems. So, we in this paper suggest a new distance measure for picture fuzzy sets that is more effective than all of the available distance measures. We also demonstrate its utility in classification and diagnostic problems and contrast its performance with the available ones.

Keywords

References

[1] M. Akram, I. Ullah, T. Allahviranloo, A new method to solve linear programming problems in the environment of picture fuzzy sets, Iranian Journal of Fuzzy Systems, (2022). DOI: 10.22111/IJFS.2022.7117.
[2] V. Arya, S. Kumar, A new picture fuzzy information measure based on shannon entropy with applications in opinion polls using extended VIKORTODIM approach, Computational and Applied Mathematics, 39 (2020), 197.
[3] S. Ashraf, S. Abdullah, T. Mahmood, M. Aslam, Cleaner production evaluation in gold mines using novel distance measure method with cubic picture fuzzy numbers, International Journal of Fuzzy Systems, 21 (2019), 2448-2461.
[4] S. Ashraf, T. Mahmood, S. Abdullah, Q. Khan, Different approaches to multi-criteria group decision making problems for picture fuzzy environment, Bulletin of Brazilian Mathematical Society, 50 (2019), 373-397.
[5] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
[6] B. C. Cuong, Picture fuzzy sets, Journal of Computer Science and Cybernetics, 30 (2015), 409-420.
[7] B. C. Cuong, V. Kreinovich, Picture fuzzy sets - A new concept for computational intelligence problems, In: 2013 Third World Congress on Information and Communication Technologies (WICT 2013), IEEE (2013), 1-6.
[8] N. V. Dinh, N. X. Thao, Some measures of picture fuzzy sets and their application in multi-attribute decision making, International Journal of Mathematical Science and Computing, 4 (2018), 23-41.
[9] P. Dutta, Medical diagnosis based on distance measures between picture fuzzy sets, International Journal of Fuzzy Systems, 7 (2018), 15-36.
[10] A. H. Ganie, Some novel correlation coefficients of spherical fuzzy sets with their application in pattern recognition, Songklanakarin Journal of Science and Technology, 44 (2022), 636-645.
[11] A. H. Ganie, S. Singh, An innovative picture fuzzy distance measure and novel multi-attribute decision-making method, Complex and Intelligent Systems, 7 (2021), 781-805.
[12] A. H. Ganie, S. Singh, P. K. Bhatia, Some new correlation coefficients of picture fuzzy sets with applications, Neural Computing and Applications, 32 (2020), 12609-12625.
[13] A. Guleria, R. K. Bajaj, A novel probabilistic distance measure for picture fuzzy sets with its application in classification problems, Hacettepe Journal of Mathematics and Statistics, 49 (2020), 2134-2153.
[14] F. K. Gundogdu, S. Duleba, S. Moslem, S. Aydin, Evaluating public transport service quality using picture fuzzy analytic hierarchy process and linear assignment model, Applied Soft Computing, 100 (2021), 106920.
[15] R. Gupta, S. Kumar, A new similarity measure between picture fuzzy sets and applications to pattern recognition and clustering problems, Granular Computing, 7 (2022), 561-576.
[16] C. Jana, T. Senapati, M. Pal, R. R. Yager, Picture fuzzy Dombi aggregation operators: Application to MADM process, Applied Soft Computing, 74 (2019), 99-109.
[17] R. Joshi, A new picture fuzzy information measure based on Tsallis-Havrda-Charvat concept with applications in presaging poll outcome, Computational and Applied Mathematics, 39 (2020), 71.
[18] R. Joshi, A novel decision-making method using R-norm concept and VIKOR approach under picture fuzzy environment, Expert System with Applications, 147 (2020), 113228.
[19] M. J. Khan, P. Kumam, W. Kumam, A. N. Al-kenani, Picture fuzzy soft robust VIKOR method and its applications in decision-making, Fuzzy Information and Engineering, 13 (2021), 296-322.
[20] M. J. Khan, P. Kumam, P. Liu, W. Kumam, An adjustable weighted soft discernibility matrix based on generalized picture fuzzy soft set and its applications in decision making, Journal of Intelligent and Fuzzy Systems, 38 (2020), 2103-2118.
[21] M. J. Khan, P. Kumar, W. Deebani, W. Kumam, Z. Shah, Bi-parametric distance and similarity measures of picture fuzzy sets and their applications in medical diagnosis, Egyptian Informatics Journal, 22 (2021), 201-212.
[22] M. J. Khan, S. Phiangsungneon, W. Kumam, Applications of generalized picture fuzzy soft set in concept selection, Thai Journal of Mathematics, 18 (2020), 296-314.
[23] L. Li, Y. Xie, X. Chen, A method for root cause diagnosis with picture fuzzy sets based dynamic uncertain causality graph, Journal of Intelligent and Fuzzy Systems, 41 (2021), 387-397.
[24] M. Lin, C. Huang, Z. Xu, MULTIMOORA based MCDM model for site selection of car sharing station under picture fuzzy environment, Sustainable Cities and Societies, 53 (2020), 101873.
[25] M. Liu, S. Zeng, T. Balezentis, D. Streimikiene, Picture fuzzy weighted distance measures and their application to investment selection, Amfiteatru Economic, 21 (2019), 682-695.
[26] J. Lu, S. Zhang, J. Wu, Y. Wei, CORPAS method for multiple attribute group decision making under picture fuzzy environment and their application to green supplier selection, Technological and Economic Development of Economy, 27 (2021), 369-385.
[27] M. Luo, Y. Zhang, L. Fu, A new similarity measure for picture fuzzy sets and its application to multi-attribute decision making, Informatica, 32 (2021), 543-564.
[28] T. Mahmood, K. Ullah, Q. Khan, N. Jan, An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets, Neural Computing and Applications, 31 (2019), 7041-7053.
[29] X. Peng, J. Dai, Algorithm for picture fuzzy multiple attribute decision-making based on new distance measure, International Journal for Uncertainty Quantification, 7 (2017), 177-187.
[30] A. Pinar, F. E. Boran, A novel distance measure on q-rung picture fuzzy sets and its application to decision making and classification problems, Artificial Intelligence Review, 55 (2022), 1317-1350.
[31] D. Ramot, R. Milo, M. Friedman, A. Kandel, Complex fuzzy sets, IEEE Transactions on Fuzzy Systems, 10 (2022), 171-186.
[32] M. Riyahi, A. B. Saeid, M. K. Rafsanjani, Improved q-rung orthopair and T-spherical fuzzy sets, Iranian Journal of Fuzzy Systems, 19 (2022), 155-170.
[33] N. T. Roan, S. C. Arnau, M. A. Diaz, J. M. M. Rubio, P. Lopez, F. Andujar, S. H. Le, M. Van Vu, F.
Smarandache, The picture fuzzy distance measure in controlling network power consumption, Infinite Study, (2020).
[34] R. Sahu, S. R. Dash, S. Das, Career selection of students using hybridized distance measure based on picture fuzzy set and rough set theory, Decision Making: Applications in Management and Engineering, 4 (2021), 104-126.
[35] V. Simic, S. Karagoz, M. Deveci, N. Aydin, Picture fuzzy extension of the CODAS method for multi-criteria vehicle shredding facility location, Expert System with Applications, 175 (2021), 114644.
[36] P. Singh, Correlation coefficients for picture fuzzy sets, Journal of Intelligent and Fuzzy Systems, 28 (2015), 591-604.
[37] S. Singh, A. H. Ganie, S. Lalotra, On generalized correlation coefficients of picture fuzzy sets with their applications, International Journal of Fuzzy System Applications, 10 (2021), 59-81.
[38] P. Singh, N. K. Mishra, M. Kumar, S. Saxena, V. Singh, Risk analysis of flood disaster based on similarity measures in picture fuzzy environment, Afrika Mathematica, 29 (2018), 1019-1038.
[39] L. H. Son, Generalized picture distance measure and applications to picture fuzzy clustering, Applied Soft Computing, 46 (2016), 284-295.
[40] L. H. Song, Measuring analogousness in picture fuzzy sets: From picture distance measures to picture association measures, Fuzzy Optimization and Decision Making, 16 (2017), 359-378.
[41] N. X. Thao, M. Ali, L. T. Nhung, H. K. Gianey, F. Smarandache, A new multi-criteria decision making algorithm for medical diagnosis and classification problems using divergence measure of picture fuzzy sets, Journal of Intelligent and Fuzzy Systems, 37 (2019), 7785-7796.
[42] R. Verma, B. Rohtagi, Novel similarity measures between picture fuzzy sets and their application to pattern recognition and medical diagnosis, Granular Computing, (2022). DOI: 10.1007/s41066-021-00294-y.
[43] C. Wang, X. Zhou, H. Tu, S. Tao, 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 (2017), 477-492.
[44] G. Wei, Picture fuzzy cross-entropy for multiple attribute decision making problems, Journal of Business Economics and Management, 17 (2016), 491-502.
[45] G. Wei, Some similarity measures for picture fuzzy sets and their applications, Iranian Journal of Fuzzy Systems, 15 (2018), 77-89.
[46] G. Wei, Picture fuzzy Hamacher aggregation operators and their application to multiple attribute decision making, Fundamenta Informaticae, 157 (2018), 271-320.
[47] G. Wei, S. Zhang, J. Lu, J. Wu, C. Wei, An extended bidirectional projection method for picture fuzzy MAGDM and its application to safety assessment of construction project, IEEE Access, 7 (2019), 166138-166147.
[48] R. R. Yager, Pythagorean fuzzy subsets, In: 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), IEEE (2013), 57-61.
[49] R. R. Yager, Generalized orthopair fuzzy sets, IEEE Transactions on Fuzzy Sets and Systems, 25 (2017), 1222-1230.
[50] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
[51] S. Zhang, G. Wei, H. Gao, C. Wei, Y. Wei, EDAS method for multiple criteria group decision making with picture fuzzy information and its application to green suppliers selections, Technological and Economic Development of Economy, 25 (2019), 1123-1138.
[52] R. Zhao, M. Luo, S. Li, A dynamic distance measure of picture fuzzy sets and its application, Symmetry, 13 (2021), 436.
Iranian Journal of Fuzzy Systems
Volume 20, Issue 1
January and February 2023
Pages 71-85

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