Crafting optimal cardiovascular treatment strategy in Pythagorean fuzzy dynamic settings

Mehwish Shehzadi; Hanan Alolaiyan; Umer Shuaib; Abdul Razaq; Qin Xin; Mehwish Shehzadi; Hanan Alolaiyan; Umer Shuaib; Abdul Razaq; Qin Xin

doi:10.3934/math.20241516

AIMS Mathematics

2024, Volume 9, Issue 11: 31495-31531. doi: 10.3934/math.20241516

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Crafting optimal cardiovascular treatment strategy in Pythagorean fuzzy dynamic settings

1.
Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
2.
Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia
3.
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
4.
Faculty of Science and Technology, University of the Faroe Islands, Vestarabryggja 15, FO 100, Torshavn, Denmark

Received: 14 August 2024 Revised: 13 October 2024 Accepted: 22 October 2024 Published: 05 November 2024
MSC : 90B50, 94D05

The prevalence of cardiovascular disease (CVD) is a major issue in world health. There is a compelling desire for precise and effective methods for making decisions to determine the most effective technique for treating CVD. Here, we focused on the urgent matter at hand. Pythagorean fuzzy dynamic settings are exceptionally proficient at capturing ambiguity because they can handle complex problem specifications that involve both Pythagorean uncertainty and periodicity. In this article, we introduced a pair of novel aggregation operators: The Pythagorean fuzzy dynamic ordered weighted averaging (PFDOWA) operator and the Pythagorean fuzzy dynamic ordered weighted geometric (PFDOWG) operator, and we proved various structural properties of these concepts. Using these operators, we devised a systematic methodology to handle multiple attribute decision-making (MADM) scenarios incorporating Pythagorean fuzzy data. Moreover, we endeavored to address a MADM problem, where we discerned the most efficacious strategy for the management of CVD through the application of the proposed operators. Finally, we undertook an exhaustive comparative analysis to evaluate the ability of the suggested methods in connection with several developed procedures, therefore demonstrating the reliability of the generated methodologies.
- Pythagorean fuzzy set,
- dynamic aggregation operators,
- cardiovascular disease
Citation: Mehwish Shehzadi, Hanan Alolaiyan, Umer Shuaib, Abdul Razaq, Qin Xin. Crafting optimal cardiovascular treatment strategy in Pythagorean fuzzy dynamic settings[J]. AIMS Mathematics, 2024, 9(11): 31495-31531. doi: 10.3934/math.20241516

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Abstract

The prevalence of cardiovascular disease (CVD) is a major issue in world health. There is a compelling desire for precise and effective methods for making decisions to determine the most effective technique for treating CVD. Here, we focused on the urgent matter at hand. Pythagorean fuzzy dynamic settings are exceptionally proficient at capturing ambiguity because they can handle complex problem specifications that involve both Pythagorean uncertainty and periodicity. In this article, we introduced a pair of novel aggregation operators: The Pythagorean fuzzy dynamic ordered weighted averaging (PFDOWA) operator and the Pythagorean fuzzy dynamic ordered weighted geometric (PFDOWG) operator, and we proved various structural properties of these concepts. Using these operators, we devised a systematic methodology to handle multiple attribute decision-making (MADM) scenarios incorporating Pythagorean fuzzy data. Moreover, we endeavored to address a MADM problem, where we discerned the most efficacious strategy for the management of CVD through the application of the proposed operators. Finally, we undertook an exhaustive comparative analysis to evaluate the ability of the suggested methods in connection with several developed procedures, therefore demonstrating the reliability of the generated methodologies.

References

[1]	D. Alghazzawi, A. Noor, H. Alolaiyan, H. A. El-Wahed Khalifa, A. Alburaikan, S. Dai, et al., A comprehensive study for selecting optimal treatment modalities for blood cancer in a Fermatean fuzzy dynamic environment, Sci. Rep., 14 (2024), 1896. https://doi.org/10.1038/s41598-024-51942-7 doi: 10.1038/s41598-024-51942-7
[2]	X. Gao, X. Cai, Y. Yang, Y. Zhou, W. Zhu, Diagnostic accuracy of the HAS-BLED bleeding score in VKA- or DOAC-treated patients with atrial fibrillation: a systematic review and meta-analysis, Front. Cardiovasc. Med., 8 (2021), 757087. https://doi:10.3389/fcvm.2021.757087 doi: 10.3389/fcvm.2021.757087
[3]	M. I. Faraz, G. Alhamzi, A. Imtiaz, I. Masmali, U. Shuaib, A. Razaq, et al., A decision-making approach to optimize COVID-19 treatment strategy under a conjunctive complex fuzzy environment, Symmetry, 15 (2023), 1370. https://doi.org/10.3390/sym15071370 doi: 10.3390/sym15071370
[4]	L. A. Zadeh, Fuzzy sets, Information and control, 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
[5]	S. Kahne, A contribution to the decision making in environmental design, Proc. IEEE, 63 (1975), 518–528. https://doi.org/10.1109/PROC.1975.9779 doi: 10.1109/PROC.1975.9779
[6]	R. Jain, A procedure for multiple-aspect decision making using fuzzy sets, Int. J. Syst. Sci., 8 (1977), 1–7. https://doi.org/10.1080/00207727708942017 doi: 10.1080/00207727708942017
[7]	D. Dubois, H. Prade, Operations on fuzzy numbers, Int. J. Syst. Sci., 9 (1978), 613–626. https://doi.org/10.1080/00207727808941724 doi: 10.1080/00207727808941724
[8]	R. R. Yager, Aggregation operators and fuzzy systems modeling, Fuzzy Set. Syst., 67 (1994), 129–145. https://doi.org/10.1016/0165-0114(94)90082-5 doi: 10.1016/0165-0114(94)90082-5
[9]	K. T. Atanassov, Intuitionistic fuzzy sets, In: Intuitionistic fuzzy sets, Heidelberg: Physica, 1999, 1–137. https://doi.org/10.1007/978-3-7908-1870-3_1
[10]	E. Szmidt, J. Kacprzyk, Intuitionistic fuzzy sets in group decision making, Notes on Intuitionistic Fuzzy Sets, 2 (1996), 15–32.
[11]	D.-F. Li, Multiattribute decision making models and methods using intuitionistic fuzzy sets, J. Comput. Syst. Sci., 70 (2005), 73–85. https://doi.org/10.1016/j.jcss.2004.06.002 doi: 10.1016/j.jcss.2004.06.002
[12]	Z. Xu, R. R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets, Int. J. Gen. Syst., 35 (2006), 417–433. https://doi.org/10.1080/03081070600574353 doi: 10.1080/03081070600574353
[13]	Z. Xu, Intuitionistic fuzzy aggregation operators, IEEE Trans. Fuzzy Syst., 15 (2007), 1179–1187. https://doi.org/10.1109/TFUZZ.2006.890678 doi: 10.1109/TFUZZ.2006.890678
[14]	H. Zhao, Z. Xu, M. Ni, S. Liu, Generalized aggregation operators for intuitionistic fuzzy sets, Int. J. Intell. Syst., 25 (2010), 1–30. https://doi.org/10.1002/int.20386 doi: 10.1002/int.20386
[15]	Y. Xu, H. Wang, The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making, Appl. Soft Comput., 12 (2012), 1168–1179. https://doi.org/10.1016/j.asoc.2011.11.003 doi: 10.1016/j.asoc.2011.11.003
[16]	J.-Y. Huang, Intuitionistic fuzzy Hamacher aggregation operators and their application to multiple attribute decision making, J. Intell. Fuzzy Syst., 27 (2014), 505–513. https://doi.org/10.3233/IFS-131019 doi: 10.3233/IFS-131019
[17]	R. Verma, Generalized Bonferroni mean operator for fuzzy number intuitionistic fuzzy sets and its application to multiattribute decision making, Int. J. Intell. Syst., 30 (2015), 499–519. https://doi.org/10.1002/int.21705 doi: 10.1002/int.21705
[18]	T. Senapati, G. Chen, R. R. Yager, Aczel–Alsina aggregation operators and their application to intuitionistic fuzzy multiple attribute decision making, Int. J. Intell. Syst., 37 (2022), 1529–1551. https://doi.org/10.1002/int.22684 doi: 10.1002/int.22684
[19]	R. R. Yager, Pythagorean fuzzy subsets, In: 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), Edmonton, AB, Canada, 2013, 57–61. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375
[20]	R. R. Yager, A. M. Abbasov, Pythagorean membership grades, complex numbers, and decision making, Int. J. Intell. Syst., 28 (2013), 436–452. https://doi.org/10.1002/int.21584 doi: 10.1002/int.21584
[21]	X. Zhang, Z. Xu, Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets, Int. J. Intell. Syst., 29 (2014), 1061–1078. https://doi.org/10.1002/int.21676 doi: 10.1002/int.21676
[22]	R. R. Yager, Pythagorean membership grades in multicriteria decision making, IEEE Trans. Fuzzy Syst., 22 (2013), 958–965. https://doi.org/10.1109/TFUZZ.2013.2278989 doi: 10.1109/TFUZZ.2013.2278989
[23]	X. Zhang, A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making, Int. J. Intell. Syst., 31 (2016), 593–611. https://doi.org/10.1002/int.21796 doi: 10.1002/int.21796
[24]	X. Peng, H. Yuan, Fundamental properties of Pythagorean fuzzy aggregation operators, Fund. Inform., 147 (2016), 415–446. https://doi.org/10.3233/FI-2016-1415 doi: 10.3233/FI-2016-1415
[25]	G. Wei, Pythagorean fuzzy interaction aggregation operators and their application to multiple attribute decision making, J. Intell. Fuzzy Syst., 33 (2017), 2119–2132. https://doi.org/10.3233/JIFS-162030 doi: 10.3233/JIFS-162030
[26]	S. Zeng, J. Chen, X. Li, A hybrid method for Pythagorean fuzzy multiple-criteria decision making, Int. J. Inf. Tech. Decis., 15 (2016), 403–422. https://doi.org/10.1142/S0219622016500012 doi: 10.1142/S0219622016500012
[27]	X. Peng, Y. Yang, Some results for Pythagorean fuzzy sets, Int. J. Intell. Syst., 30 (2015), 1133–1160. https://doi.org/10.1002/int.21738 doi: 10.1002/int.21738
[28]	X. Peng, Y Yang, Pythagorean fuzzy Choquet integral based MABAC method for multiple attribute group decision making, Int. J. Intell. Syst., 31 (2016), 989–1020. https://doi.org/10.1002/int.21814 doi: 10.1002/int.21814
[29]	S. Zeng, Pythagorean fuzzy multiattribute group decision making with probabilistic information and OWA approach, Int. J. Intell. Syst., 32 (2017), 1136–1150. https://doi.org/10.1002/int.21886 doi: 10.1002/int.21886
[30]	H. Garg, Generalised Pythagorean fuzzy geometric interactive aggregation operators using Einstein operations and their application to decision making, J. Exp. Theor. Artif. Intell., 30 (2018), 763–794. https://doi.org/10.1080/0952813X.2018.1467497 doi: 10.1080/0952813X.2018.1467497
[31]	H. Garg, Some methods for strategic decision‐making problems with immediate probabilities in Pythagorean fuzzy environment, Int. J. Intell. Syst., 33 (2018), 687–712. https://doi.org/10.1002/int.21949 doi: 10.1002/int.21949
[32]	H. Garg, Linguistic Pythagorean fuzzy sets and its applications in multiattribute decision‐making process, Int. J. Intell. Syst., 33 (2018), 1234–1263. https://doi.org/10.1002/int.21979 doi: 10.1002/int.21979
[33]	D. Liang, Y. Zhang, Z. Xu, A. P. Darko, Pythagorean fuzzy Bonferroni mean aggregation operator and its accelerative calculating algorithm with the multithreading, Int. J. Int. Syst., 33 (2018), 615–633. https://doi.org/10.1002/int.21960 doi: 10.1002/int.21960
[34]	S. Naz, S. Ashraf, M. Akram, A novel approach to decision-making with Pythagorean fuzzy information, Mathematics, 6 (2018), 95. https://doi.org/10.3390/math6060095 doi: 10.3390/math6060095
[35]	M. Akram, A. Habib, F. Ilyas, J. M. Dar, Specific types of Pythagorean fuzzy graphs and application to decision-making, Math. Comput. Appl., 23 (2018), 42. https://doi.org/10.3390/mca23030042 doi: 10.3390/mca23030042
[36]	M. Akram, J. M. Dar, A. Farooq, Planar graphs under Pythagorean fuzzy environment, Mathematics, 6 (2018), 278. https://doi.org/10.3390/math6120278 doi: 10.3390/math6120278
[37]	M. Akram, J. M. Dar, S. Naz, Certain graphs under Pythagorean fuzzy environment, Complex Intell. Syst., 5 (2019), 127–144. https://doi.org/10.1007/s40747-018-0089-5 doi: 10.1007/s40747-018-0089-5
[38]	Z. Xu, R. R. Yager, Dynamic intuitionistic fuzzy multi-attribute decision making, Int. J. Approx. Reason., 48 (2008), 246–262. https://doi.org/10.1016/j.ijar.2007.08.008 doi: 10.1016/j.ijar.2007.08.008
[39]	G. W. Wei, Some geometric aggregation functions and their application to dynamic multiple attribute decision making in the intuitionistic fuzzy setting, Int. J. Uncertain. Fuzz., 17 (2009), 179–196. https://doi.org/10.1142/S0218488509005802 doi: 10.1142/S0218488509005802
[40]	J. Zhou, W. Su, T. Baležentis, D. Streimikiene, Multiple criteria group decision-making considering symmetry with regards to the positive and negative ideal solutions via the Pythagorean normal cloud model for application to economic decisions, Symmetry, 10 (2018), 140. https://doi.org/10.3390/sym10050140 doi: 10.3390/sym10050140
[41]	C. Huang, M. Lin, Z. Xu, Pythagorean fuzzy MULTIMOORA method based on distance measure and score function: its application in multicriteria decision making process, Knowl. Inf. Syst., 62 (2020), 4373–4406. https://doi.org/10.1007/s10115-020-01491-y doi: 10.1007/s10115-020-01491-y
[42]	M. Lin, C. Huang, R. Chen, H. Fujita, X. Wang, Directional correlation coefficient measures for Pythagorean fuzzy sets: their applications to medical diagnosis and cluster analysis, Complex Intell. Syst., 7 (2021), 1025–1043. https://doi.org/10.1007/s40747-020-00261-1 doi: 10.1007/s40747-020-00261-1
[43]	Z. Zhang, Y. Li, X. Wang, Y. Liu, W. Tang, W. Ding, et al., Investigating river health across mountain to urban transitions using Pythagorean fuzzy cloud technique under uncertain environment, J. Hydrol., 620 (2023), 129426. https://doi.org/10.1016/j.jhydrol.2023.129426 doi: 10.1016/j.jhydrol.2023.129426
[44]	G. Alhamzi, S. Javaid, U. Shuaib, A. Razaq, H. Garg, A. Razzaque, Enhancing interval-valued Pythagorean fuzzy decision-making through Dombi-based aggregation operators, Symmetry, 15 (2023), 765. https://doi.org/10.3390/sym15030765 doi: 10.3390/sym15030765
[45]	K. Rahman, S. Abdullah, A. Ali, F. Amin, Pythagorean fuzzy ordered weighted averaging aggregation operator and their application to multiple attribute group decision-making, EURO J. Decis. Process., 8 (2020), 61–77. https://doi.org/10.1007/s40070-020-00110-z doi: 10.1007/s40070-020-00110-z
[46]	T. Sun, J. Lv, X. Zhao, W. Li, Z. Zhang, L. Nie, In vivo liver function reserve assessments in alcoholic liver disease by scalable photoacoustic imaging, Photoacoustics, 34 (2023), 100569. https://doi.org/10.1016/j.pacs.2023.100569 doi: 10.1016/j.pacs.2023.100569
[47]	Y. Huang, C. Wang, T. Zhou, F. Xie, Z. Liu, H. Xu, et al., Lumican promotes calcific aortic valve disease through H3 histone lactylation, Eur. Heart J., 45 (2024), 3871–3885. https://doi.org/10.1093/eurheartj/ehae407 doi: 10.1093/eurheartj/ehae407
[48]	P.-C. Fu, J.-Y. Wang, Y. Su, Y.-Q. Liao, S.-L. Li, G.-L. Xu, et al., Intravascular ultrasonography assisted carotid artery stenting for treatment of carotid stenosis: two case reports, World J. Clin. Cases, 11 (2023), 7127–7135. https://doi.org/10.12998/wjcc.v11.i29.7127 doi: 10.12998/wjcc.v11.i29.7127
[49]	Y. Zhao, W. Xiong, C. Li, R. Zhao, H. Lu, S. Song, et al., Hypoxia-induced signaling in the cardiovascular system: pathogenesis and therapeutic targets, Sig. Transduct. Target. Ther., 8 (2023), 431. https://doi.org/10.1038/s41392-023-01652-9 doi: 10.1038/s41392-023-01652-9
[50]	P. Bing, Y. Liu, W. Liu, J. Zhou, L. Zhu, Electrocardiogram classification using TSST-based spectrogram and ConViT, Front. Cardiovasc. Med., 9 (2022), 983543. https://doi.org/10.3389/fcvm.2022.983543 doi: 10.3389/fcvm.2022.983543
[51]	K. Rahman, S. Abdullah, F. Husain, M. A. Khan, M. Shakeel, Pythagorean fuzzy ordered weighted geometric aggregation operator and their application to multiple attribute group decision making, J. Appl. Environ. Biol. Sci., 7 (2017), 67–83.

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