A parametric similarity measure for extended picture fuzzy sets and its application in pattern recognition

Document Type : Research Paper

Authors

1 Department of Mathematics, Quchan University of Technology, Iran, Department of Computing and Information Systems, University of Melbourne, Australia

2 Department of Computing and Information Systems, University of Melbourne, Australia

Abstract

This article advances the idea of extended picture fuzzy set (E-PFS), which is especially an augmentation of generalised spherical fuzzy set (GSFS) by releasing the restricted selection of $p$ in the description of GSFSs.
Moreover, by the use of triangular conorm term in the description of E-PFS, it indeed widens the scope of E-PFS not only compared to picture fuzzy set (PFS) and spherical fuzzy set (SFS), but also to GSFS. In the sequel, a given fundamental theorem concerning E-PFS depicts its more ability in comparison with the special types to deal with the ambiguity and uncertainty.
Further, we propose a parametric E-PFS similarity measure which plays a critical role in information theory.
In order for revealing the advantages and authenticity of E-PFS similarity measure, we exhibit its applicability in multiple criteria decision making entitling the recognition of building material, the recognition of patterns, and the selection process of mega project(s) in developing countries.
Furthermore, through the experimental studies, we demonstrate that E-PFS is able to handle uncertain information in real-life decision procedures with no extra parameter, and it has a prominent role in decision making whenever the concepts of  PFS, SFS and GSFS do not make sense.

Keywords

References

[1] M. Akram, A. Bashir, S. Edalatpanah, A hybrid decision-making analysis under complex q-rung picture fuzzy Einstein averaging operators, Computational and Applied Mathematics, 40 (2021), 305.
[2] M. Akram, A. Habib, J. Alcantud, An optimization study based on Dijkstra algorithm for a network with trapezoidal picture fuzzy numbers, Neural Computing and Applications, 33 (2021), 1329-1342.
[3] M. Akram, C. Kahraman, K. Zahid, Extension of TOPSIS model to the decision-making under complex spherical fuzzy information, Soft Computing, 25 (2021), 10771-10795.
[4] S. Ashraf, S. Abdullah, T. Mahmood, Spherical fuzzy Dombi aggregation operators and their application in group decision making problems, Journal of Ambient Intelligence and Humanized Computing, 11 (2020), 2731-2749.
[5] S. Ashraf, S. Abdullah, T. Mahmood, F. Ghani, T. Mahmood, Spherical fuzzy sets and their applications in multiattribute decision making problems, Journal of Intelligent and Fuzzy Systems, 36 (2019), 2829-2844.
[6] K. Atanassov, Intuitionistic fuzzy sets, Theory and Applications, Physica-Verlag: Heidelberg, Germany, 1999.
[7] B. Cuong, Picture fuzzy sets, Journal of Computer Science and Cybernetics, 30 (2014), 409-420.
[8] B. Farhadinia, Study on division and subtraction operations for hesitant fuzzy sets, interval-valued hesitant fuzzy sets and typical dual hesitant fuzzy sets, Journal of Intelligent and Fuzzy Systems, 28 (2015), 1393-1402.
[9] B. Farhadinia, E. Herrera-Viedma, Multiple criteria group decision making method based on extended hesitant fuzzy sets with unknown weight information, Applied Soft Computing, 78 (2019), 310-323.
[10] B. Farhadinia, H. Liao, Score-based multiple criteria decision making process by using p-rung orthopair fuzzy sets, Informatica, (2020), 1-31, DOI:10.15388/20-INFOR412.
[11] B. Farhadinia, Z. Xu, Novel hesitant fuzzy linguistic entropy and cross-entropy measures in multiple criteria decision making, Applied Intelligence, 48 (2018), 3915-3927.
[12] B. Farhadinia, Z. Xu, Information measures for hesitant fuzzy sets and their extensions, Springer, Berlin, 2019.
[13] A. Ganie, S. Singh, A picture fuzzy similarity measure based on direct operations and novel multi-attribute decisionmaking method, Neural Computing and Applications, (2021), DOI:10.1007/s00521-020-05682-0.
[14] A. Ganie, S. Singh, P. Bhatia, Some new correlation coefficients of picture fuzzy sets with applications, Neural Computing and Applications, 32 (2020), 12609-12625.
[15] H. Garg, M. Munir, K. Ullah, T. Mahmood, N. Jan, Algorithm for T-spherical fuzzy multi-attribute decision making based on improved interactive aggregation operators, Symmetry, 10 (2018), 670.
[16] Y. Jin, S. Ashraf, S. Abdullah, Spherical fuzzy logarithmic aggregation operators based on entropy and their application in decision support systems, Entropy, 21 (2019), 628.
[17] M. Khan, P. Kumam, W. Deebani, W. Kumam, Z. Shah, Distance and similarity measures for spherical fuzzy sets and their applications in selecting mega projects, Mathematics, 8 (2020), 519. DOI:10.3390/
math8040519.
[18] 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, (2018), 1-13.
[19] M. Munir, H. Kalsoom, K. Ullah, T. Mahmood, Y. Chu, T-spherical fuzzy Einstein hybrid aggregation operators and their applications in multi-attribute decision making problems, Symmetry, 12 (2020), 365.
[20] S. Quek, M. Munir, T. Mahmood, K. Ullah, L. Son, Multi-attribute multi-perception decision-making based on generalized T-spherical fuzzy weighted aggregation operators on neutrosophic sets, Mathematics, 7 (2019), 780.
[21] M. Rafiq, S. Ashraf, S. Abdullah, T. Mahmood, S. Muhammad, The cosine similarity measures of spherical fuzzy sets and their applications in decision making, Journal of Intelligent and Fuzzy Systems, 36 (2019), 6059-6073.
[22] F. Smarandache, Neutrosophic set is a generalization of intuitionistic fuzzy set, inconsistent intuitionistic fuzzy set (Picture fuzzy set, ternary fuzzy Set), Pythagorean fuzzy set, q-Rung orthopair fuzzy set, spherical fuzzy set, etc, (2019), arXiv:1911.07333, http://arxiv.org/abs/1911.07333.
[23] N. Thong, L. Son, HIFCF: An effective hybrid model between picture fuzzy clustering and intuitionistic fuzzy recommender systems for medical diagnosis, Expert Systems with Application, 42 (2015), 3682-3701.
[24] K. Ullah, H. Garg, T. Mahmood, N. Jan, Z. Ali, Correlation coefficients for T-spherical fuzzy sets and their applications in clustering and multi-attribute decision making, Soft Computing, 24 (2020), 1647-1659.
[25] K. Ullah, T. Mahmood, N. Jan, Similarity measures for t-spherical fuzzy sets with applications in pattern recognition, Symmetry, 10 (2018), 193.
[26] K. Ullah, T. Mahmood, N. Jan, Z. Ali, A note on geometric aggregation operators in spherical fuzzy environment and its application in multi-attribute decision making, Journal of Engineering and Applied Science, 37 (2018), DOI: 10.25211/jeas.v37i2.2871.
[27] L. Wang, H. Zhang, J. Wang, L. Li, Picture fuzzy normalized projection-based VIKOR method for the risk evaluation of construction project, Applied Soft Computing, 64 (2018), 216-226.
[28] 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.
[29] G. Wei, Picture fuzzy cross-entropy for multiple attribute decision making problems, Journal of Business Economics and Management, 17 (2016), 491-502.
[30] G. Wei, Some cosine similarity measures for picture fuzzy sets and their applications to strategic decision making, Informatica, 28 (2017), 547-564.
[31] G. Wei, Picture 2-tuple linguistic bonferroni mean operators and their application to multiple attribute decision making, International Journal of Fuzzy Systems, 19 (2017), 997-1010.
[32] G. Wei, Some similarity measures for picture fuzzy sets and their applications, Iranian Journal of Fuzzy Systems, 15 (2018), 77-89.
[33] G. Wei, H. Gao, The generalized dice similarity measures for picture fuzzy sets and their applications, Informatica, 29 (2018), 107-124.
[34] M. Wu, T. Chen, J. Fan, Similarity measures of T-spherical fuzzy sets based on the cosine function and their applications in pattern recognition, IEEE Access, 8 (2020), 98181-98192.
[35] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
[36] S. Zeng, A. Hussain, T. Mahmood, M. Irfan-Ali, S. Ashraf, M. Munir, Covering-based spherical fuzzy rough set model hybrid with TOPSIS for multi-attribute decision-making, Symmetry, 11 (2019), 547.
Iranian Journal of Fuzzy Systems
Volume 19, Issue 6
November and December 2022
Pages 141-160

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