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A new approach to q-linear Diophantine fuzzy emergency decision support system for COVID19
Open accessAbstract
The emergency situation of COVID-19 is a very important problem for emergency decision support systems. Control of the spread of COVID-19 in emergency situations across the world is a challenge and therefore the aim of this study is to propose a q-linear Diophantine fuzzy decision-making model for the control and diagnose COVID19. Basically, the paper includes three main parts for the achievement of appropriate and accurate measures to address the situation of emergency decision-making. First, we propose a novel generalization of Pythagorean fuzzy set, q-rung orthopair fuzzy set and linear Diophantine fuzzy set, called q-linear Diophantine fuzzy set (q-LDFS) and also discussed their important properties. In addition, aggregation operators play an effective role in aggregating uncertainty in decision-making problems. Therefore, algebraic norms based on certain operating laws for q-LDFSs are established. In the second part of the paper, we propose series of averaging and geometric aggregation operators based on defined operating laws under q-LDFS. The final part of the paper consists of two ranking algorithms based on proposed aggregation operators to address the emergency situation of COVID-19 under q-linear Diophantine fuzzy information. In addition, the numerical case study of the novel carnivorous (COVID-19) situation is provided as an application for emergency decision-making based on the proposed algorithms. Results explore the effectiveness of our proposed methodologies and provide accurate emergency measures to address the global uncertainty of COVID-19.
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LDFNs and q-LDFNs do not have the I-grade, which represents neutrality, and this leads to a lack of some information.
“As mentioned above, LDFNs and q-LDFNs do not have the I-grade, which represents neutrality, which will lead to the lack of some information.”
From T-spherical linear Diophantine fuzzy aggregation operators for multiple attribute decision-making (2023) · cites this paper as [12]
Definition 5 (Basic concepts) describes LDFS using membership and non-membership grades and reference parameters; Definition 6 (Concept of q-rung linear Diophantine fuzzy set) describes the same structure for q-RLDFS and calculates hesitation or indeterminacy rather than specifying a separate neutrality grade. These passages support the absence of an independently specified I-grade, but the paper does not say that this causes information loss. (LLM, conf=0.77)
Experimental — accuracy not yet measuredThe best alternatives obtained by the methods of Riaz and Hashmi [11], Almagrabi et al. [12], and Riaz et al. [45] are the same as those obtained by the proposed operators.
“It is clear from Table 7 that the best alternatives obtained by using the methods of Riaz and Hashmi [11], Almagrabi et al. [12] and Riaz et al. [45] remained our proposed operators.”
From T-spherical linear Diophantine fuzzy aggregation operators for multiple attribute decision-making (2023) · cites this paper as [12]
The q-LDFS is a special case of the T-SLDFS and can be written in the form of a T-SLDFS.
“Thus, the q-LDFS is a special case of the T-SLDFS and can be easily written in the form of a T-SLDFS.”
From T-spherical linear Diophantine fuzzy aggregation operators for multiple attribute decision-making (2023) · cites this paper as [12]
Definition 6 and Corollaries 1–2 describe q-LDFS/q-RLDFS and its relationship to LDFS, but do not address T-SLDFS. Searches for “T-SLDFS special case q-LDFS” and “spherical linear Diophantine fuzzy set” found no passage establishing that q-LDFS is a special case of T-SLDFS or showing how to write it in that form. Page numbers are unavailable in our copy. (LLM, conf=0.76)
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“[3] q-Linear Diophantine fuzzy set (q − LDFS ) $q over a fixed set U depicted in the mathematical type as given:”
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Khan, N., Yaqoob, N., Shams, M., Gaba, Y. U., & Riaz, M. (2021) · Journal of Function Spaces · doi:10.1155/2021/8475863 · Cited by 14
“[31] introduced a new approach to q-linear Diophantine fuzzy emergency decision support system for COVID-19.”
MethodSelf-citationKamacı, H., Marinković, D., Petchimuthu, S., Riaz, M., & Ashraf, S. (2022) · Symmetry · doi:10.3390/sym14102140 · Cited by 14
Self-citationLinear Diophantine Fuzzy Rough Sets on Paired Universes with Multi Stage Decision Analysis
Ayub, S., Shabir, M., Riaz, M., Karaaslan, F., Marinković, D., & Vranješ, Đ. (2022) · Axioms · doi:10.3390/axioms11120686 · Cited by 14
Multi-attribute group decision-making based on bipolar n,m-rung orthopair fuzzy sets
Ibrahim, H. Z. (2023) · Granular Computing · doi:10.1007/s41066-023-00405-x · Cited by 13
“Almagrabi et al. (2021) offered a new method to the linear Diophantine fuzzy emergency decision support system.”
MethodComplex Linear Diophantine Fuzzy Sets over AG-Groupoids with Applications in Civil Engineering
Guan, H., Yousafzai, F., Zia, M. D., Khan, M.-U.-I., Irfan, M., & Hila, K. (2022) · Symmetry · doi:10.3390/sym15010074 · Cited by 13
Asif, M., Ishtiaq, U., Zeb, A., Ahmad, W., & Hou, M. (2024) · International Journal of Fuzzy Systems · doi:10.1007/s40815-024-01842-9 · Cited by 12
Correlation Measures for Cubic m-Polar Fuzzy Sets with Applications
Garg, H., Riaz, M., Khokhar, M. A., & Saba, M. (2021) · Mathematical Problems in Engineering · doi:10.1155/2021/9112586 · Cited by 12
Applications of AG-Groupoids in Decision-Making via Linear Diophantine Fuzzy Sets
Yousafzai, F., Zia, M. D., Khalaf, M. M., Al-Sabri, E. H. A., & Ismail, R. (2023) · Discrete Dynamics in Nature and Society · doi:10.1155/2023/3411475 · Cited by 12
Gul, R., Al-shami, T. M., Ayub, S., Shabir, M., & Hosny, M. M. (2024) · Heliyon · doi:10.1016/j.heliyon.2024.e35942 · Cited by 11
“The devised work can be extended in the framework of CLD-FS [29], IVLD-FSs [53,54], spherical LD-FSs [30], q-LD-FSs [56], and (p, q)-Rung LD-FSs [57].”
BackgroundMethodChaitanya, M. K., Sharma, L. D., Rahul, J., Sharma, D., & Roy, A. (2023) · Biomedical Physics & Engineering Express · doi:10.1088/2057-1976/acbd53 · Cited by 12
Lv, J., Mao, Q., Li, Q., & Yu, R. (2022) · International Journal of Computational Intelligence Systems · doi:10.1007/s44196-022-00088-3 · Cited by 10
“Almagrabi et al. [53] established a decision-making framework to select appropriate prevention alternatives from five aspects.”
BackgroundShams, M., Abdullah, S., Khan, F., Ali, R., & Muhammad, S. (2024) · IEEE Access · doi:10.1109/access.2024.3367117 · Cited by 9
“Almagrabi et al. [76] suggested a novel LDF extension known as the q-rung linear Diophantine fuzzy set (q-RLDFS) and examined its key characteristics.”
BackgroundMethodInfluentialSelf-citationAyub, S., Gul, R., Shabir, M., Hummdi, A. Y., Aljaedi, A., & Bassfar, Z. (2024) · IEEE Access · doi:10.1109/access.2024.3386581 · Cited by 9
“Almagrabi et al. [6] offered a new approach to a q-linear Diophantine fuzzy emergency decision support system for COVID-19.”
BackgroundMethodAhmad, S., Basharat, P., Abdullah, S., Botmart, T., & Jirawattanapanit, A. (2022) · AIMS Mathematics · doi:10.3934/math.2022975 · Cited by 9
“In Tables 5–7, we select three medical authorities to handle the whole crisis / disaster assessment process, and then we have three decision maker for the source data [2].”
BackgroundMethodInfluentialSelf-citationExtended PROMETHEE method with (p,q)-rung linear Diophantine fuzzy sets for robot selection problem
Vimala, J., Surya, A., Kausar, N., Pamucar, D., Šimić, V., & Salman, M. A. (2025) · Scientific Reports · doi:10.1038/s41598-024-81785-1 · Cited by 8
Ranking of linear Diophantine fuzzy numbers using circumcenter of centroids
Iqbal, S., & Yaqoob, N. (2023) · AIMS Mathematics · doi:10.3934/math.2023497 · Cited by 8
Abdullah, S., & Abosuliman, S. S. (2023) · Scientific Reports · doi:10.1038/s41598-023-36095-3 · Cited by 8
“Previous research includes LDFW geometric aggregation (LDFWGA) operator by Raiz and Hashmi 23 , LDF Einstein aggregation operators developed by Lampan et. al, 25 , q-LDF weighted averaging and geometric aggregation al 27 , and several more DM problems 22,24,26 .”
MethodSelf-citationExplainable AI for Improved Financial Decision Support in Trading
Kalra, A., & Mittal, R. (2024) · International Conference on Reliability, Infocom Technologies and Optimization (Trends and Future Directions) (ICRITO) · doi:10.1109/icrito61523.2024.10522366 · Cited by 8
“Innovations in technology have led to the widespread use of Artificial Intelligence (AI), which provides cutting-edge resources for data analysis and decision-making [1-2].”
BackgroundWu, X., Ali, Z., Mahmood, T., & Лю, П. (2023) · International Journal of Fuzzy Systems · doi:10.1007/s40815-023-01502-4 · Cited by 8
“[17] developed the approach of linear Diophantine and QROFSs.”
MethodEmergency shelter materials under a complex non-linear diophantine fuzzy decision support system
Shams, M., Almagrabi, A. O., & Abdullah, S. (2023) · Complex & Intelligent Systems · doi:10.1007/s40747-023-01122-3 · Cited by 8
“The reference parameters have their own constraints in the LDFS. Almagrabi et al. proposed a new extension of LDF, the q-rung linear Diophantine fuzzy set (q-RLDFS), and investigated its important features in [46].”
BackgroundMethodInfluentialSelf-citationEmerging technologies for the management of COVID19: A review
Zafar, N., & Ahamed, J. (2022) · Sustainable Operations and Computers · doi:10.1016/j.susoc.2022.05.002 · Cited by 8
Chander, G. P., & Das, S. R. (2024) · International Journal of Fuzzy Systems · doi:10.1007/s40815-024-01836-7 · Cited by 7
Optimization Algorithms of PERT/CPM Network Diagrams in Linear Diophantine Fuzzy Environment
Parimala, M., Prakash, K., Al-Quran, A., Riaz, M., & Jafari, S. (2023) · Computer Modeling in Engineering & Sciences · doi:10.32604/cmes.2023.031193 · Cited by 6
Abosuliman, S. S., Abdullah, S., & Ali, N. (2025) · Complex & Intelligent Systems · doi:10.1007/s40747-024-01623-9 · Cited by 6
“This extension of Riaz and Hashmi’s concept led to the development of the flexible theory of the q-rung LDFS (q-LDFS) by Almagrabi et al. [26] with the addition of CFs in the q-ROFS structure.”
Self-citationAhmad, S., Wang, J., & Khalid, M. (2023) · Computers & Electrical Engineering · doi:10.1016/j.compeleceng.2023.108898 · Cited by 6
Ayub, S., Shabir, M., & Gul, R. (2023) · Physica Scripta · doi:10.1088/1402-4896/acf811 · Cited by 6
Samy, C. A., Narayanamoorthy, S., Pamucar, D., Geetha, S., Almakayeel, N. M., Sandra, M., & Kang, D. (2026) · Environment Development and Sustainability · doi:10.1007/s10668-026-07341-1 · Cited by 5
Cubic m-polar fuzzy topology with multi-criteria group decision-making
Riaz, M., Akmal, K., Almalki, Y., & Alblowi, S. A. (2022) · AIMS Mathematics · doi:10.3934/math.2022721 · Cited by 5
An Extensive Review of the Literature Using the Diophantine Equations to Study Fuzzy Set Theory
Abirami, K. M., Narayanan, V., Srikanth, R., & Dhanasekaran, P. (2024) · International Journal of Mathematics and Mathematical Sciences · doi:10.1155/2024/5014170 · Cited by 5
Rahman, K., Ali, R., & Lamoudan, T. (2024) · Soft Computing · doi:10.1007/s00500-024-09804-x · Cited by 5
Rambhupal, M., & Voola, P. (2023) · Soft Computing · doi:10.1007/s00500-023-09111-x · Cited by 5
Qiyas, M., Khan, N., Naeem, M., & Okyere, S. (2023) · Journal of Mathematics · doi:10.1155/2023/5839410 · Cited by 5
“Defnition 8 [45].”
MethodLinear Diophantine fuzzy $n$-fold weak subalgebras of a BE-algebra
Tahan, M. A., Rezaei, A., Al-Kaseasbeh, S., Davvaz, B., & Riaz, M. (2023) · Missouri Journal of Mathematical Sciences · doi:10.35834/2023/3502136 · Cited by 4
Surya, A., Vimala, J., & Vizhi, M. T. (2024) · International Journal of Information Technology · doi:10.1007/s41870-024-01837-7 · Cited by 4
“To overcome these RP’s restrictions, Almagrabi [6] introduced and emphasized the key features of the q-rung linear diophan-tine fuzzy set (q-RLDFS), a special generalization of the IFS, q-ROFS, and LDFS but all these theories has some limitation due to lack of parametrization.”
InfluentialGul, R., Ayub, S., Shabir, M., Alballa, T., & Khalifa, H. A. E. (2024) · Computational and Applied Mathematics · doi:10.1007/s40314-024-02805-4 · Cited by 4
“In addition, the hybridization of LD-FRS with complex LD-FSs (Kamacı 2022), q -LD- FSs (Almagrabi et al. 2021), and ( p , q ) -RLD-FSs (Panpho and Yiarayong 2023) will be a hot research topic in the near future.”
InfluentialSurya, A., & Vimala, J. (2024) · Information Sciences · doi:10.1016/j.ins.2024.121591 · Cited by 4
Linear Diophantine Fuzzy Subspaces of a Vector Space
Tahan, M. A., Hošková-Mayerová, Š., Al-Kaseasbeh, S., & Tahan, S. A. (2023) · Mathematics · doi:10.3390/math11030503 · Cited by 4
Ashraf, S., Garg, H., Kousar, M., Askar, S., & Abbas, S. (2023) · AIMS Mathematics · doi:10.3934/math.2023907 · Cited by 4
Self-citationPetchimuthu, S., & Kamacı, H. (2023) · GAZI UNIVERSITY JOURNAL OF SCIENCE · doi:10.35378/gujs.1013358 · Cited by 4
“In 2021, Almagrabi et al. [23] put forward that the sum of the reference parameters, where an alternative satisfies the attribute acquired by expert is wider than one, so LDFS fails to achieve his/her goal regarding reference parameters.”
Yiarayong, P. (2024) · International Journal of Systems Assurance Engineering and Management · doi:10.1007/s13198-024-02540-3 · Cited by 3
Chander, G. P., & Das, S. R. (2025) · Applied mathematics/Applied Mathematics. A Journal of Chinese Universities/Gao-xiao yingyong shuxue xuebao · doi:10.1007/s11766-025-4550-0 · Cited by 3
“…C 4 , C 5 g for precise and efficient decision-making by three decision makers Opinions of the decision makers regarding the alternatives and attributes are represented using q-RLDFS which are shown using the decision matrices D l ( l = 1, 2, 3) as shown below in Tables 6, 7, and 8 [10] respectively.”
InfluentialKhan, A., Khan, S., Rahimzai, A. A., & Abdullah, S. (2025) · Scientific Reports · doi:10.1038/s41598-025-89665-y · Cited by 3
“Almagrabi et al. 29 introduced the idea of a q-rung linear Diophantine fuzzy set (q-RLDFS).”
Self-citationBrainy, J. R. V. J., Narayanamoorthy, S., Sandra, M., Pamucar, D., Nguyen, P.-H., Pragathi, S., & Kang, D. (2025) · Renewable Energy · doi:10.1016/j.renene.2025.124217 · Cited by 3
Khan, M., Khan, A., Ismail, M., & Ziar, R. A. (2026) · International Journal of Computational Intelligence Systems · doi:10.1007/s44196-025-01079-w · Cited by 3
“…G 5 > G 3 WASPAS [ 68] G 4 > G 5 > G 3 > G 2 > G 1 MARCOS [ 69] G 4 > G 5 > G 2 > G 3 > G 1 SAW [70 ] G 4 > G 5 > G 2 > G 3 > G 1 Existing operator Non-LDFWA [ 14] operator International Journal of Computational Intelligence Systems https://doi.org/10.1007/s44196-025-01079-w Step 6 : Utilizing Eqs.”
InfluentialKhan, S. Z., Alballa, T., Rahim, M., Alodhaibi, S. S., & Khalifa, H. A. E.-W. (2026) · Cognitive Computation · doi:10.1007/s12559-025-10539-6 · Cited by 3
“Definition 7 [33 ] Consider a finite set U .”
Alohali, H., Khan, M. B., Macías‐Díaz, J. E., & Sikander, F. (2024) · AIMS Mathematics · doi:10.3934/math.20241685 · Cited by 3
Ahmed, W., & Mustafa, G. (2025) · Expert Systems with Applications · doi:10.1016/j.eswa.2025.126777 · Cited by 3
Rahman, K. U., & Iqbal, Q. (2022) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-221538 · Cited by 3
“Lampan et al. [37], Almagrabi et al. [38] Introduced linear Diophantine fuzzy Einstein operators and q-linear Diophantine fuzzy operators respectively and also applied them on group decision making problem.”
RetractedAnnamalai, S., & Vimala, J. (2024) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-219414 · Cited by 3
RetractedNi, Y.-Z., Wang, F., Zhang, H., & Kim, S.-M. (2025) · Scientific Reports · doi:10.1038/s41598-025-17833-1 · Cited by 2
“To compare the effectiveness and practical superiority of the proposed q-RLDF WASPAS model, a comparative study is conducted with two well-established DM models: q-RLDF MADM 22 and the q-RLDF weighted Jaccard similarity measure (WJSM) model 49 .”
InfluentialBilal, M., Nawaz, M. S., Abdullah, S., & Ali, N. (2025) · Journal Of Big Data · doi:10.1186/s40537-025-01286-4 · Cited by 2
“Alaa O. Almagrabi et al. [48] use a q-LDFS for emergency decision-making for COVID-19.”
Self-citationZindani, D., & Singh, S. (2025) · Journal of Engineering and Applied Science · doi:10.1186/s44147-025-00789-4 · Cited by 2
“To further enhance the accurate representation of the uncertain and vague information, Almagrabi [2] introduced the concept of q-RLDFS that combines the novel aspects of q-ROFS and LDFS and thereby leading to more generalized form of representation over the PFS.”
Mirza, M. U., Anjum, R., Alkahtani, B. S. T., Min, H., & Anjum, M. (2024) · IEEE Access · doi:10.1109/access.2024.3457613 · Cited by 2
“Reference [14] proposes a q-linear Diophantine fuzzy decision-making model to address the unique issues presented by the COVID-19 pandemic and help manage the crisis.”
BackgroundKhan, M. B., Pamucar, D., Abdelwahed, M., Zamri, N., & Ciurdariu, L. (2025) · AIMS Mathematics · doi:10.3934/math.2025552 · Cited by 2
“This concept was further refined, leading to a novel decision-making approach demonstrated through the use of linear Diophantine fuzzy graphs [17].”
Qadir, A., Abdullah, S., Rahimzai, A. A., & Khan, S. (2025) · Scientific Reports · doi:10.1038/s41598-025-02121-9 · Cited by 2
Self-citationQiyas, M., Naeem, M., Khan, N., & Khan, F. (2023) · IEEE Access · doi:10.1109/access.2023.3295112 · Cited by 2
Razzaque, H., Ashraf, S., Sohail, M., & Abdeljawad, T. (2024) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-235397 · Cited by 2
“Almagrabi [3] introduced the q-linear Diophantine fuzzy set (q-LDFS) in the COVID-19 emergency situation for emergency decision support systems.”
Self-citationRetractedKannan, J., & Rajareega, S. (2025) · Engineering Research Express · doi:10.1088/2631-8695/ae16ff · Cited by 1
Wan, B., Zhou, S., Han, M., Qu, T., & Cheng, Y. (2026) · Journal of Mathematics in Industry · doi:10.1186/s13362-025-00180-1 · Cited by 1
“While the score functions are widely used for ranking alternatives under interval-valued intuitionistic fuzzy sets [60–63], they exhibit certain deficiencies.”
Li, X., Du, Y., Hao, Y., Zhao, S., & Ren, W. (2026) · Textile Research Journal · doi:10.1177/00405175251389168 · Cited by 1
Shehzadi, M., Fahmi, A., Abdeljawad, T., & Khan, A. U. (2024) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-238716 · Cited by 1
“Almagrabi [1] introduced it and emphasised some of its most important features.”
A Hybrid Fuzzy Extension and Its Application in Multi-Attribute Decision Making
Surya, A., Vimala, J., & Banu, K. A. (2024) · Contemporary Mathematics · doi:10.37256/cm.5220244390 · Cited by 1
“Definition 2.3 [6] An q-RLDFS Q on U is described as are MS degree, NMS degree and their corresponding RPs respectively, with the restrictions that 0 [12] An Cq-RLDFS Q on U is described as ) are CMS degree, CNMS degree and their corresponding complex valued RPs (CRPs) respectively, with the…”
BackgroundMethodInfluentialAhmad, S., Bibi, B., & Wang, J. (2023) · Research Square · doi:10.21203/rs.3.rs-2505472/v1
A disaster rescue support system with 3D GIS and robot captured data
Lin, S.-Y., Li, C.-C., Wei, Z.-Y., Chi, C., Rau, J.-Y., Teng, W., & Hou, T. (2023) · IEEE International Conference on Consumer Electronics - Taiwan (ICCE-Taiwan) · doi:10.1109/icce-taiwan58799.2023.10226711
Metadata
- Authors
- Almagrabi, A. O., Abdullah, S., Shams, M., Al-Otaibi, Y. D., & Ashraf, S.
- Affiliations
- King Abdulaziz University (SA)
- Abdul Wali Khan University Mardan (PK)
- Corresponding author
- Shams, Maria
- Venue
- Journal of Ambient Intelligence and Humanized Computing
- Published
- 2021-04-05
- Volume
- 13
- Issue
- 4
- Pages
- 1687-1713
- ISSN
- 1868-5137 (ISSN-L)
- 1868-5145
- PMC
- PMC8019990
- OpenAlex
- W3139668460
- Cited by
- 114
- References
- 74
- Citations by year
- 2026: 16 · 2025: 15 · 2024: 23 · 2023: 33 · 2022: 21 · 2021: 6
- FWCI
- 12.62
- Type
- journal article
- Language
- en
- Update notices
- correction (2021-05-06)
- Open access
- bronze
- doi.org
- Locations
- Journal of Ambient Intelligence and Humanized Computing (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Funders
- King Abdulaziz University ((GCV19-10- 1441)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Multi-Criteria Decision Making
- Social Sciences › Decision Sciences › Management Science and Operations Research › Fuzzy and Soft Set Theory
- Physical Sciences › Mathematics › Statistics and Probability › Fuzzy Systems and Optimization
- Keywords
- emergency decision support, COVID-19 pandemic, linear Diophantine fuzzy sets, aggregation operators, ranking algorithms, uncertainty aggregation, COVID-19 diagnosis
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