Optimizing decision precision with linguistic Pythagorean fuzzy Dombi models

Asima Razzaque; Umme Kalsoom; Dilshad Alghazzawi; Abdul Razaq; Ghaliah Alhamzi; Asima Razzaque; Umme Kalsoom; Dilshad Alghazzawi; Abdul Razaq; Ghaliah Alhamzi

doi:10.3934/math.2025486

AIMS Mathematics

2025, Volume 10, Issue 5: 10675-10708. doi: 10.3934/math.2025486

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Optimizing decision precision with linguistic Pythagorean fuzzy Dombi models

1.
Department of Basic science, Preparatory year, King Faisal University Al Ahsa, Al Hofuf 31982, Saudi Arabia
2.
Department of Mathematics, College of Science, King Faisal University Al Ahsa, Al Hofuf 31982, Saudi Arabia
3.
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
4.
Department of Mathematics, College of Science & Arts, King Abdul Aziz University, Rabigh, Saudi Arabia
5.
Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan
6.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia

Received: 22 January 2025 Revised: 16 April 2025 Accepted: 22 April 2025 Published: 09 May 2025
MSC : 03E72, 94D05

Last-mile distribution is a subject that has drawn significant attention from both academic and industry researchers. There are several reasons for the adoption of drone delivery technology, including the growing number of customers who want more flexible and faster delivery options. Currently, there is a large selection of these models on the market. Therefore, there is a need to develop efficient methods to select the most appropriate drone delivery service. This research employs Dombi aggregation operators (AOs) within the context of linguistic Pythagorean fuzzy sets (LPFS) to tackle issues in drone delivery operations. The incorporation of linguistic concepts within the Pythagorean fuzzy framework improves the precision and dependability of delivery data analysis by providing a more thorough representation of uncertainty, consistent with human intuition and qualitative assessments. The present study presents two novel aggregation operators: the linguistic Pythagorean fuzzy Dombi weighted averaging (LPFDWA) and the linguistic Pythagorean fuzzy Dombi weighted geometric (LPFDWG) operators. Essential structural characteristics of these operators are demonstrated, and important particular cases are described. Furthermore, we developed a systematic approach for handling multi-attribute decision-making issues that incorporate LPF data through the use of the suggested operators. In order to showcase the effectiveness of the developed approaches, we provide a numerical illustration that identifies the top drone delivery service. Finally, we execute an in-depth comparative assessment to evaluate the efficacy of the proposed methods in relation to several established procedures.
- linguistic Pythagorean fuzzy sets,
- Dombi aggregation operators,
- multi-attribute decision-making,
- drone delivery optimization
Citation: Asima Razzaque, Umme Kalsoom, Dilshad Alghazzawi, Abdul Razaq, Ghaliah Alhamzi. Optimizing decision precision with linguistic Pythagorean fuzzy Dombi models[J]. AIMS Mathematics, 2025, 10(5): 10675-10708. doi: 10.3934/math.2025486

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Abstract

Last-mile distribution is a subject that has drawn significant attention from both academic and industry researchers. There are several reasons for the adoption of drone delivery technology, including the growing number of customers who want more flexible and faster delivery options. Currently, there is a large selection of these models on the market. Therefore, there is a need to develop efficient methods to select the most appropriate drone delivery service. This research employs Dombi aggregation operators (AOs) within the context of linguistic Pythagorean fuzzy sets (LPFS) to tackle issues in drone delivery operations. The incorporation of linguistic concepts within the Pythagorean fuzzy framework improves the precision and dependability of delivery data analysis by providing a more thorough representation of uncertainty, consistent with human intuition and qualitative assessments. The present study presents two novel aggregation operators: the linguistic Pythagorean fuzzy Dombi weighted averaging (LPFDWA) and the linguistic Pythagorean fuzzy Dombi weighted geometric (LPFDWG) operators. Essential structural characteristics of these operators are demonstrated, and important particular cases are described. Furthermore, we developed a systematic approach for handling multi-attribute decision-making issues that incorporate LPF data through the use of the suggested operators. In order to showcase the effectiveness of the developed approaches, we provide a numerical illustration that identifies the top drone delivery service. Finally, we execute an in-depth comparative assessment to evaluate the efficacy of the proposed methods in relation to several established procedures.

References

[1]	H. Alolaiyan, U. Kalsoom, U. Shuaib, A. Razaq, A. W. Baidar, Q. Xin, Precision measurement for effective pollution mitigation by evaluating air quality monitoring systems in linguistic Pythagorean fuzzy Dombi environment, Sci. Rep., 14 (2024), 31944. https://doi.org/10.1038/s41598-024-83478-1 doi: 10.1038/s41598-024-83478-1
[2]	D. Alghazzawi, A. Noor, H. Alolaiyan, H. A. E. W. Khalifa, A. Alburaikan, Q. Xin, et al., A novel perspective on the selection of an effective approach to reduce road traffic accidents under Fermatean fuzzy settings, PLoS One, 19 (2024), e0303139. https://doi.org/10.1371/journal.pone.0303139 doi: 10.1371/journal.pone.0303139
[3]	M. R. Seikh, U. Mandal, Multiple attribute group decision making based on quasirung orthopair fuzzy sets: Application to electric vehicle charging station site selection problem, Eng. Appl. Artif. Intell., 115 (2022), 105299. https://doi.org/10.1016/j.engappai.2022.105299 doi: 10.1016/j.engappai.2022.105299
[4]	D. Zhu, Z. Han, X. Du, D. Zuo, L. Cai, C. Xue, Hybrid model integrating fuzzy systems and convolutional factorization machine for delivery time prediction in intelligent logistics, IEEE Trans. Fuzzy Syst., 33 (2025), 406–417. https://doi.org/10.1109/TFUZZ.2024.3472043 doi: 10.1109/TFUZZ.2024.3472043
[5]	U. Mandal, M. R. Seikh, Interval-valued spherical fuzzy MABAC method based on Dombi aggregation operators with unknown attribute weights to select plastic waste management process, Appl. Soft Comput., 145 (2023), 110516. https://doi.org/10.1016/j.asoc.2023.110516 doi: 10.1016/j.asoc.2023.110516
[6]	A. Hussain, K. Ullah, M. Mubasher, T. Senapati, S. Moslem, Interval-valued Pythagorean fuzzy information aggregation based on Aczel-Alsina operations and their application in multiple attribute decision making, IEEE Access, 11 (2023), 34575–34594. https://doi.org/10.1109/ACCESS.2023.3244612 doi: 10.1109/ACCESS.2023.3244612
[7]	M. R. Seikh, U. Mandal, q-Rung orthopair fuzzy Archimedean aggregation operators: Application in the site selection for software operating units, Symmetry, 15 (2023), 1680. https://doi.org/10.3390/sym15091680 doi: 10.3390/sym15091680
[8]	O. Y. Akbulut, Analysis of the corporate financial performance based on Grey PSI and Grey MARCOS model in Turkish insurance sector, Knowl. Decis. Syst. Appl., 1 (2025), 57–69. https://doi.org/10.59543/kadsa.v1i.13623 doi: 10.59543/kadsa.v1i.13623
[9]	H. A. Dağıstanlı, Weapon system selection for capability-based defense planning using Lanchester models integrated with fuzzy MCDM in computer assisted military experiment, Knowl. Decis. Syst. Appl., 1 (2025), 11–23. https://doi.org/10.59543/kadsa.v1i.13601 doi: 10.59543/kadsa.v1i.13601
[10]	L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353. https://doi.org/10.2307/2272014 doi: 10.2307/2272014
[11]	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
[12]	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
[13]	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
[14]	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
[15]	K. T. Atanassov, Intuitionistic fuzzy sets, Physica-Verlag HD, 1999, 1–137. https://doi.org/10.1007/978-3-7908-1870-3_1
[16]	M. Chen, J. M. Tan, Handling multicriteria fuzzy decision-making problems based on vague set theory, Fuzzy Set. Syst., 67 (1994), 163–172. https://doi.org/10.1016/0165-0114(94)90084-1 doi: 10.1016/0165-0114(94)90084-1
[17]	Szmidt, J. Kacprzyk, Intuitionistic fuzzy sets in group decision making, Note. IFS, 2 (1996). Available from: http://ifigenia.org/wiki/issue: nifs/2/1/15-32.
[18]	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
[19]	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
[20]	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
[21]	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
[22]	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
[23]	J. Q. Wang, J. J. Li, The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics, Sci. Tech. Inform., 33 (2009), 8–9.
[24]	H. Zhang, Linguistic intuitionistic fuzzy sets and application in MAGDM, J. Appl. Math., 2014 (2014), 432092. https://doi.org/10.1155/2014/432092 doi: 10.1155/2014/432092
[25]	Y. Ju, X. Liu, D. Ju, Some new intuitionistic linguistic aggregation operators based on Maclaurin symmetric mean and their applications to multiple attribute group decision making, Soft Comput., 20 (2016), 4521–4548. https://doi.org/10.1007/s00500-015-1761-y doi: 10.1007/s00500-015-1761-y
[26]	P. Liu, L. Rong, Y. Chu, Y. Li, Intuitionistic linguistic weighted Bonferroni mean operator and its application to multiple attribute decision making, Sci. World J., 2014 (2014), 545049. https://doi.org/10.1155/2014/545049 doi: 10.1155/2014/545049
[27]	P. Liu, Some geometric aggregation operators based on interval intuitionistic uncertain linguistic variables and their application to group decision making, Appl. Math. Model., 37 (2013), 2430–2444. https://doi.org/10.1016/j.apm.2012.05.032 doi: 10.1016/j.apm.2012.05.032
[28]	P. Liu, P. Wang, Some improved linguistic intuitionistic fuzzy aggregation operators and their applications to multiple-attribute decision making, Int. J. Inf. Technol. Decis. Mak., 16 (2017), 817–850. https://doi.org/10.1142/S0219622017500110 doi: 10.1142/S0219622017500110
[29]	R. R. Yager, Pythagorean fuzzy subsets, In: Proc. Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013, 57–61. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375
[30]	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
[31]	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
[32]	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
[33]	M. Asif, U. Ishtiaq, I. K. Argyros, Hamacher aggregation operators for Pythagorean fuzzy set and its application in multi-attribute decision-making problem, Spectrum Oper. Res., 2 (2025), 27–40. https://doi.org/10.31181/sor2120258 doi: 10.31181/sor2120258
[34]	L. Xiao, G. Huang, W. Pedrycz, D. Pamucar, L. Martínez, G. Zhang, A q-rung orthopair fuzzy decision-making model with new score function and best-worst method for manufacturer selection, Information Sci., 608 (2022), 153–177. https://doi.org/10.1016/j.ins.2022.06.061 doi: 10.1016/j.ins.2022.06.061
[35]	L. Xiao, T. Fang, G. Huang, M. Deveci, An integrated design concept evaluation method based on fuzzy weighted zero inconsistency and combined compromise solution considering inherent uncertainties, Adv. Eng. Inform., 65 (2025), 103097. https://doi.org/10.1016/j.aei.2024.103097 doi: 10.1016/j.aei.2024.103097
[36]	H. Garg, A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making, Int. J. Intell. Syst., 31 (2016), 886–920. https://doi.org/10.1002/int.21809 doi: 10.1002/int.21809
[37]	H. Garg, Generalized Pythagorean fuzzy geometric aggregation operators using Einstein t-norm and t-conorm for multicriteria decision-making process, Int. J. Intell. Syst., 32 (2017), 597–630. https://doi.org/10.1002/int.21860 doi: 10.1002/int.21860
[38]	Z. Ma, Z. Xu, Symmetric Pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems, Int. J. Intell. Syst., 31 (2016), 1198–1219. https://doi.org/10.1002/int.21823 doi: 10.1002/int.21823
[39]	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
[40]	X. D. Peng, Y. Yang, Multiple attribute group decision making methods based on Pythagorean fuzzy linguistic set, Comput. Eng. Appl., 52 (2016), 50–54.
[41]	M. Lin, J. Wei, Z. Xu, R. Chen, Multiattribute group decision-making based on linguistic Pythagorean fuzzy interaction partitioned Bonferroni mean aggregation operators, Complexity, 2018 (2018), 9531064. https://doi.org/10.1155/2018/9531064 doi: 10.1155/2018/9531064
[42]	Y. Du, F. Hou, W. Zafar, Q. Yu, Y. Zhai, A novel method for multiattribute decision making with interval-valued Pythagorean fuzzy linguistic information, Int. J. Intell. Syst., 32 (2017), 1085–1112. https://doi.org/10.1002/int.21881 doi: 10.1002/int.21881
[43]	J. Dombi, A general class of fuzzy operators, the DeMorgan class of fuzzy operators and fuzziness measures induced by fuzzy operators, Fuzzy Set. Syst., 8 (1982), 149–163. https://doi.org/10.1016/0165-0114(82)90005-7 doi: 10.1016/0165-0114(82)90005-7
[44]	P. Liu, J. Liu, S. M. Chen, Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making, J. Oper. Res. Soc., 69 (2018), 1–24. https://doi.org/10.1057/s41274-017-0190-y doi: 10.1057/s41274-017-0190-y
[45]	M. Akram, W. A. Dudek, J. M. Dar, Pythagorean Dombi fuzzy aggregation operators with application in multicriteria decision-making, Int. J. Intell. Syst., 34 (2019), 3000–3019. https://doi.org/10.1002/int.22183 doi: 10.1002/int.22183
[46]	C. Jana, G. Muhiuddin, M. Pal, Some Dombi aggregation of Q-rung orthopair fuzzy numbers in multiple-attribute decision making, Int. J. Intell. Syst., 34 (2019), 3220–3240. https://doi.org/10.1002/int.22191 doi: 10.1002/int.22191
[47]	C. Jana, M. Pal, J. Q. Wang, Bipolar fuzzy Dombi aggregation operators and its application in multiple-attribute decision-making process, J. Amb. Intel. Hum. Comp., 10 (2019), 3533–3549. https://doi.org/10.1007/s12652-018-1076-9 doi: 10.1007/s12652-018-1076-9
[48]	C. Jana, T. Senapati, M. Pal, R. R. Yager, Picture fuzzy Dombi aggregation operators: Application to MADM process, Appl. Soft Comput., 74 (2019), 99–109. https://doi.org/10.1016/j.asoc.2018.10.021 doi: 10.1016/j.asoc.2018.10.021
[49]	S. Ashraf, S. Abdullah, T. Mahmood, Spherical fuzzy Dombi aggregation operators and their application in group decision making problems, J. Amb. Intel. Hum. Comp., 11 (2020), 2731–2749. https://doi.org/10.1007/s12652-019-01333-y doi: 10.1007/s12652-019-01333-y
[50]	H. B. Liu, Y. Liu, L. Xu, Dombi interval-valued hesitant fuzzy aggregation operators for information security risk assessment, Math. Probl. Eng., 2020 (2020), 1–12. https://doi.org/10.1155/2020/3198645 doi: 10.1155/2020/3198645
[51]	I. Masmali, A. Khalid, U. Shuaib, A. Razaq, H. Garg, A. Razzaque, On selection of the efficient water purification strategy at commercial scale using complex intuitionistic fuzzy Dombi environment, Water, 15 (2023), 1907. https://doi.org/10.3390/w15101907 doi: 10.3390/w15101907
[52]	M. R. Seikh, P. Chatterjee, Evaluation and selection of E-learning websites using intuitionistic fuzzy confidence level based Dombi aggregation operators with unknown weight information, Appl. Soft Comput., 163 (2024), 111850. https://doi.org/10.1016/j.asoc.2024.111850 doi: 10.1016/j.asoc.2024.111850
[53]	A. Hussain, K. Ullah, H. Garg, T. Mahmood, A novel multi-attribute decision-making approach based on T-spherical fuzzy Aczel Alsina Heronian mean operators, Granul. Comput., 9 (2024), 21. https://doi.org/10.1007/s41066-023-00442-6 doi: 10.1007/s41066-023-00442-6
[54]	M. Sarfraz, Application of interval-valued T-spherical fuzzy Dombi Hamy mean operators in the antiviral mask selection against COVID-19, J. Decis. Anal. Intell. Comput., 4 (2024), 67–98. https://doi.org/10.31181/jdaic10030042024s doi: 10.31181/jdaic10030042024s
[55]	Y. Liu, J. Liu, Y. Qin, Pythagorean fuzzy linguistic Muirhead mean operators and their applications to multiattribute decision-making, Int. J. Intell. Syst., 35 (2020), 300–332. https://doi.org/10.1002/int.22212 doi: 10.1002/int.22212
[56]	H. Sheng, S. Wang, H. Chen, D. Yang, Y. Huang, J. Shen, et al., Discriminative feature learning with co-occurrence attention network for vehicle ReID, IEEE T. Circ. Syst. Vid., 34 (2024), 3510–3522. https://doi.org/10.1109/TCSVT.2023.3326375 doi: 10.1109/TCSVT.2023.3326375
[57]	G. Sun, Y. Zhang, D. Liao, H. Yu, X. Du, M. Guizani, Bus-trajectory-based street-centric routing for message delivery in urban vehicular ad hoc networks, IEEE T. Veh. Tech., 67 (2018), 7550-7563. https://doi.org/10.1109/TVT.2018.2828651 doi: 10.1109/TVT.2018.2828651
[58]	H. Ni, Q. Zhu, B. Hua, K. Mao, Y. Pan, F. Ali, et al., Path loss and shadowing for UAV-to-ground UWB channels incorporating the effects of built-up areas and airframe, IEEE T. Intell. Transp. Syst., 25 (2024), 17066−17077. https://doi.org/10.1109/TITS.2024.3418952 doi: 10.1109/TITS.2024.3418952
[59]	Z. Zou, S. Yang, L. Zhao, Dual-loop control and state prediction analysis of QUAV trajectory tracking based on biological swarm intelligent optimization algorithm, Sci. Rep., 14 (2024), 19091. https://doi.org/10.1038/s41598-024-69911-5 doi: 10.1038/s41598-024-69911-5
[60]	X. Zhao, T. Wang, Y. Li, B. Zhang, K. Liu, D. Liu, et al., Target-driven visual navigation by using causal intervention, IEEE T. Intell. Vehicl., 9 (2024), 1294−1304. https://doi.org/10.1109/TIV.2023.3288810 doi: 10.1109/TIV.2023.3288810
[61]	S. Zhou, Z. He, X. Chen, W. Chang, An anomaly detection method for UAV based on wavelet decomposition and stacked denoising autoencoder, Aerospace, 11 (2024), 393. https://doi.org/10.3390/aerospace11050393 doi: 10.3390/aerospace11050393
[62]	Y. Yin, Z. Wang, L. Zheng, Q. Su, Y. Guo, Autonomous UAV Navigation with adaptive control based on deep reinforcement learning, Electronics, 13 (2024), 2432. https://doi.org/10.3390/electronics13132432 doi: 10.3390/electronics13132432
[63]	S. Moslem, A novel parsimonious spherical fuzzy analytic hierarchy process for sustainable urban transport solutions, Eng. Appl. Artif. Intell., 128 (2024), 107447. https://doi.org/10.1016/j.engappai.2023.107447 doi: 10.1016/j.engappai.2023.107447
[64]	S. Moslem, Evaluating commuters' travel mode choice using the Z-number extension of Parsimonious Best Worst Method, Appl. Soft Comput., 173 (2025), 112918. https://doi.org/10.1016/j.asoc.2025.112918 doi: 10.1016/j.asoc.2025.112918

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