A Q-RUNG ORTHOPAIR FUZZY MULTI-CRITERIA MODEL INCORPORATING A HESITANCY-DOMINANT UNCERTAINTY MEASURE FOR PRIORITISING PATIENT-SAFETY RISKS IN NURSING CARE
DOI:
https://doi.org/10.5281/zenodo.23101892Keywords:
multi-criteria decision-making, q-rung orthopair fuzzy set, patient safety, nursing care, uncertainty measureAbstract
Background: Ward-level patient-safety scoring tools compress likelihood, harm and detectability into a single crisp number, which limits their capacity to express the vagueness of nursing judgement.
Objective: To propose an uncertainty measure for q-rung orthopair fuzzy (q-ROF) numbers that attains its unique maximum at complete hesitancy, to establish its properties with detailed proofs and to embed it in a transparent weighting and ranking model for prioritising patient-safety risks in nursing care.
Methods: Linguistic ratings of eight patient-safety risks on four criteria (likelihood, harm severity, detection difficulty and care burden) were represented as q-ROF numbers. The proposed measure supplied a matrix-derived criterion weight formed from certainty and contrast; this was blended with author-specified SWARA scenario-priority weights, and risks were ranked with CRADIS. Each matrix cell is an author-assigned, literature-informed scenario rating: the heterogeneous publications provide source facts and context but do not directly determine the fuzzy grade. Ratings are not taken from any experts.
Results: Under the constructed scenario inputs, missed venous thromboembolism (VTE) prophylaxis, unrecognised clinical deterioration and healthcare-associated infection (HAI) formed the leading group, with CRADIS indices of 1.00, 0.973 and 0.925. The q-ROF TOPSIS ranking coincided under identical inputs, which is an internal method-concordance check rather than external validation. Equal criterion weights produced an exact three-way top tie among R4, R6 and R8; average tied ranks gave a Spearman correlation of 0.976 with the blended-weight ranking. Across the q and blend grid, correlations ranged from 0.929 to 1.00; Monte Carlo mean correlations declined from 0.983 to 0.867 as perturbation increased, and the first-place identity became uncertain.
Conclusion: The hesitancy-dominant measure and matrix-derived certainty-contrast weighting provide a transparent workflow. The reported ordering is conditional on an author-constructed scenario, not a validated clinical hierarchy; the inputs and priority weights must be replaced or calibrated with local incident, audit, workload and multidisciplinary judgement data before clinical use.
References
Abraham, P., Augey, L., Duclos, A., Michel, P., & Piriou, V. (2021). Descriptive analysis of patient misidentification from incident report system data in a large academic hospital federation. Journal of Patient Safety, 17(7), e615-e621. https://doi.org/10.1097/PTS.0000000000000478
Al-Hameed, F., Al-Dorzi, H., Qadhi, A., Shaker, A., Al-Gahtani, F., Al-Jassir, F., Zahir, G., Al-Khuwaitir, T., Addar, M., Al-Hajjaj, M., Abdelaal, M., & Aboelnazar, E. (2017). Thromboprophylaxis and mortality among patients who developed venous thromboembolism in seven major hospitals in Saudi Arabia. Annals of Thoracic Medicine, 12(4), 282-289. https://doi.org/10.4103/atm.ATM_101_17
Al-Moteri, M., Plummer, V., Cooper, S., & Symmons, M. (2019). Clinical deterioration of ward patients in the presence of antecedents: A systematic review and narrative synthesis. Australian Critical Care, 32(5), 411-420. https://doi.org/10.1016/j.aucc.2018.06.004
Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
Badida, P., Janakiraman, S., & Jayaprakash, J. (2023). Occupational health and safety risk assessment using a fuzzy multi-criteria approach in a hospital in Chennai, India. International Journal of Occupational Safety and Ergonomics, 29(3), 1047-1056. https://doi.org/10.1080/10803548.2022.2109323
Berdot, S., Gillaizeau, F., Caruba, T., Prognon, P., Durieux, P., & Sabatier, B. (2013). Drug administration errors in hospital inpatients: A systematic review. PLoS ONE, 8(6), Article e68856. https://doi.org/10.1371/journal.pone.0068856
Bouldin, E. L. D., Andresen, E. M., Dunton, N. E., Simon, M., Waters, T. M., Liu, M., Daniels, M. J., Mion, L. C., & Shorr, R. I. (2013). Falls among adult patients hospitalized in the United States: Prevalence and trends. Journal of Patient Safety, 9(1), 13-17. https://doi.org/10.1097/PTS.0b013e3182699b64
Cantero, M., Salamanca, C., Parra, L. M., González-Pérez, M. E., García de la Vega, M., Asensio, Á., & the EPINE Study Group (2026). Attributable mortality to healthcare-associated infections: A comprehensive nationwide assessment in Spain, 2022 and 2023. Eurosurveillance, 31(7), Article 2500139. https://doi.org/10.2807/1560-7917.ES.2026.31.7.2500139
Chanamool, N., & Naenna, T. (2016). Fuzzy FMEA application to improve decision-making process in an emergency department. Applied Soft Computing, 43, 441-453. https://doi.org/10.1016/j.asoc.2016.01.007
Chen, L., Liu, W., & Zhang, J. (2025). An interval type-2 fuzzy multi-criteria decision-making approach for patient bed allocation. Scientific Reports, 15, Article 21019. https://doi.org/10.1038/s41598-025-09199-1
Drnovšek, R., Milavec Kapun, M., Šteblaj, S., & Rajkovič, U. (2025). Multicriteria risk evaluation model: Utilizing fuzzy logic for improved transparency and quality of risk evaluation in healthcare. Risk Management and Healthcare Policy, 18, 637-653. https://doi.org/10.2147/RMHP.S490598
En-Naaoui, A., Kaicer, M., & Aguezzoul, A. (2024). A novel decision support system for proactive risk management in healthcare based on fuzzy inference, neural network and support vector machine. International Journal of Medical Informatics, 186, Article 105442. https://doi.org/10.1016/j.ijmedinf.2024.105442
European Pressure Ulcer Advisory Panel, National Pressure Injury Advisory Panel, & Pan Pacific Pressure Injury Alliance. (2019). Prevention and treatment of pressure ulcers/injuries: Clinical practice guideline. The international guideline (E. Haesler, Ed.). EPUAP/NPIAP/PPPIA.
Gul, M., Ak, M. F., & Guneri, A. F. (2017). Occupational health and safety risk assessment in hospitals: A case study using two-stage fuzzy multi-criteria approach. Human and Ecological Risk Assessment: An International Journal, 23(2), 187-202. https://doi.org/10.1080/10807039.2016.1234363
Haut, E. R., Owodunni, O. P., Shaffer, D. L., McQuigg, D., Samuel, D., Hobson, D. B., Kraus, P. S., Wang, J., Webster, K. L. W., Kantsiper, M., Harris, J. E., Holzmueller, C. G., Varasteh Kia, M., Streiff, M. B., & Lau, B. D. (2025). Implementing a patient-centered education bundle to improve venous thromboembolism prevention. JAMA Surgery, 160(12), 1326-1332. https://doi.org/10.1001/jamasurg.2025.4136
Heikkilä, A., Lehtonen, L., & Junttila, K. (2023). Fall rates by specialties and risk factors for falls in acute hospital: A retrospective study. Journal of Clinical Nursing, 32(15-16), 4868-4877. https://doi.org/10.1111/jocn.16594
Honarmand, K., Wax, R. S., Penoyer, D., Lighthall, G., Danesh, V., Rochwerg, B., Cheatham, M. L., Davis, D. P., DeVita, M., Downar, J., Edelson, D., Fox-Robichaud, A., Fujitani, S., Fuller, R. M., Haskell, H., Inada-Kim, M., Jones, D., Kumar, A., Olsen, K. M., ... Sebat, F. (2024). Society of Critical Care Medicine guidelines on recognizing and responding to clinical deterioration outside the ICU: 2023. Critical Care Medicine, 52(2), 314-330. https://doi.org/10.1097/CCM.0000000000006072
Howanitz, P. J., Renner, S. W., & Walsh, M. K. (2002). Continuous wristband monitoring over 2 years decreases identification errors: A College of American Pathologists Q-Tracks study. Archives of Pathology & Laboratory Medicine, 126(7), 809-815. https://doi.org/10.5858/2002-126-0809-CWMOYD
Jessurun, J. G., Hunfeld, N. G. M., de Roo, M., van Onzenoort, H. A. W., van Rosmalen, J., van Dijk, M., & van den Bemt, P. M. L. A. (2023). Prevalence and determinants of medication administration errors in clinical wards: A two-centre prospective observational study. Journal of Clinical Nursing, 32(1-2), 208-220. https://doi.org/10.1111/jocn.16215
Keers, R. N., Williams, S. D., Cooke, J., & Ashcroft, D. M. (2013). Prevalence and nature of medication administration errors in health care settings: A systematic review of direct observational evidence. Annals of Pharmacotherapy, 47(2), 237-256. https://doi.org/10.1345/aph.1R147
Keršulienė, V., Zavadskas, E. K., & Turskis, Z. (2010). Selection of rational dispute resolution method by applying new step-wise weight assessment ratio analysis (SWARA). Journal of Business Economics and Management, 11(2), 243-258. https://doi.org/10.3846/jbem.2010.12
Khan, M. J., Kumam, P., Shutaywi, M., & Kumam, W. (2021). Improved knowledge measures for q-rung orthopair fuzzy sets. International Journal of Computational Intelligence Systems, 14(1), 1700-1713. https://doi.org/10.2991/ijcis.d.210531.002
LeLaurin, J. H., & Shorr, R. I. (2019). Preventing falls in hospitalized patients: State of the science. Clinics in Geriatric Medicine, 35(2), 273-283. https://doi.org/10.1016/j.cger.2019.01.007
Li, F., Song, M., Xu, L., Deng, B., Zhu, S., & Li, X. (2019). Risk factors for catheter-associated urinary tract infection among hospitalized patients: A systematic review and meta-analysis of observational studies. Journal of Advanced Nursing, 75(3), 517-527. https://doi.org/10.1111/jan.13863
Li, M., Wang, R., Wang, M., Zhao, Y., & Shen, X. (2026). Fuzzy decision support systems for hospital infection management: A circular q-ROF CRADIS method to prevention and control. Scientific Reports, 16, Article 12154. https://doi.org/10.1038/s41598-026-40658-5
Li, Z., Lin, F., Thalib, L., & Chaboyer, W. (2020). Global prevalence and incidence of pressure injuries in hospitalised adult patients: A systematic review and meta-analysis. International Journal of Nursing Studies, 105, Article 103546. https://doi.org/10.1016/j.ijnurstu.2020.103546
Liu, P., & Wang, P. (2018). Some q-rung orthopair fuzzy aggregation operators and their application to multiple-attribute decision making. International Journal of Intelligent Systems, 33(2), 259-280. https://doi.org/10.1002/int.21927
Morris, M. E., Webster, K., Jones, C., Hill, A.-M., Haines, T., McPhail, S., Kiegaldie, D., Slade, S., Jazayeri, D., Heng, H., Shorr, R., Carey, L., Barker, A., & Cameron, I. (2022). Interventions to reduce falls in hospitals: A systematic review and meta-analysis. Age and Ageing, 51(5), Article afac077. https://doi.org/10.1093/ageing/afac077
Peng, X., & Liu, L. (2019). Information measures for q-rung orthopair fuzzy sets. International Journal of Intelligent Systems, 34(8), 1795-1834. https://doi.org/10.1002/int.22115
Peng, X., Dai, J., & Garg, H. (2018). Exponential operation and aggregation operator for q-rung orthopair fuzzy set and their decision-making method with a new score function. International Journal of Intelligent Systems, 33(11), 2255-2282. https://doi.org/10.1002/int.22028
Perez-Aguilar, A., Pancardo, P., Ortiz-Barrios, M., & Ishizaka, A. (2024). Intuitionistic fuzzy multi-criteria hybrid approach for prioritizing seasonal respiratory diseases patients within the public emergency departments. IEEE Access, 12, 178282-178308. https://doi.org/10.1109/ACCESS.2024.3506979
Puška, A., Stević, Ž., & Pamučar, D. (2022). Evaluation and selection of healthcare waste incinerators using extended sustainability criteria and multi-criteria analysis methods. Environment, Development and Sustainability, 24(9), 11195-11225. https://doi.org/10.1007/s10668-021-01902-2
Rana, H., Umer, M., Hassan, U., Asgher, U., Silva-Aravena, F., & Ehsan, N. (2023). Application of fuzzy TOPSIS for prioritization of patients on elective surgeries waiting list - a novel multi-criteria decision-making approach. Decision Making: Applications in Management and Engineering, 6(1), 603-630. https://doi.org/10.31181/dmame060127022023r
Sahle, B. W., Pilcher, D., Peter, K., McFadyen, J. D., Litton, E., & Bucknall, T. (2023). Mortality data from omission of early thromboprophylaxis in critically ill patients highlights the importance of an individualised diagnosis-related approach. Thrombosis Journal, 21, Article 59. https://doi.org/10.1186/s12959-023-00499-y
Saint, S., Greene, M. T., Krein, S. L., Rogers, M. A. M., Ratz, D., Fowler, K. E., Edson, B. S., Watson, S. R., Meyer-Lucas, B., Masuga, M., Faulkner, K., Gould, C. V., Battles, J., & Fakih, M. G. (2016). A program to prevent catheter-associated urinary tract infection in acute care. New England Journal of Medicine, 374(22), 2111-2119. https://doi.org/10.1056/NEJMoa1504906
Shipley, K., Shifrin, M. M., & Roach, K. (2023). Abstract 329: Unrecognized clinical deterioration prior to in-hospital cardiac arrest and associated in-hospital mortality. Circulation, 148(Suppl 1), A329. https://doi.org/10.1161/circ.148.suppl_1.329
Song, Y.-P., Shen, H.-W., Cai, J.-Y., Zha, M.-L., & Chen, H.-L. (2019). The relationship between pressure injury complication and mortality risk of older patients in follow-up: A systematic review and meta-analysis. International Wound Journal, 16(6), 1533-1544. https://doi.org/10.1111/iwj.13243
Storr, J., Twyman, A., Zingg, W., Damani, N., Kilpatrick, C., Reilly, J., Price, L., Egger, M., Grayson, M. L., Kelley, E., Allegranzi, B., & the WHO Guidelines Development Group (2017). Core components for effective infection prevention and control programmes: New WHO evidence-based recommendations. Antimicrobial Resistance & Infection Control, 6, Article 6. https://doi.org/10.1186/s13756-016-0149-9
Suetens, C., Latour, K., Kärki, T., Ricchizzi, E., Kinross, P., Moro, M. L., Jans, B., Hopkins, S., Hansen, S., Lyytikäinen, O., Reilly, J., Deptula, A., Zingg, W., Plachouras, D., & Monnet, D. L. (2018). Prevalence of healthcare-associated infections, estimated incidence and composite antimicrobial resistance index in acute care hospitals and long-term care facilities: Results from two European point prevalence surveys, 2016 to 2017. Eurosurveillance, 23(46), Article 1800516. https://doi.org/10.2807/1560-7917.ES.2018.23.46.1800516
Suh, J., Desai, A., Desai, A., Dela Cruz, J., Mariampillai, A., & Hindenburg, A. (2017). Adherence to thromboprophylaxis guidelines in elderly patients with hospital acquired venous thromboembolism: A case control study. Journal of Thrombosis and Thrombolysis, 43(2), 172-178. https://doi.org/10.1007/s11239-016-1432-6
VanGilder, C. A., Cox, J., Edsberg, L. E., & Koloms, K. (2021). Pressure injury prevalence in acute care hospitals with unit-specific analysis: Results from the International Pressure Ulcer Prevalence (IPUP) Survey Database. Journal of Wound, Ostomy & Continence Nursing, 48(6), 492-503. https://doi.org/10.1097/WON.0000000000000817
Yager, R. R. (2017). Generalized orthopair fuzzy sets. IEEE Transactions on Fuzzy Systems, 25(5), 1222-1230. https://doi.org/10.1109/TFUZZ.2016.2604005
Yokoe, D. S., Advani, S. D., Anderson, D. J., Babcock, H. M., Bell, M., Berenholtz, S. M., Bryant, K. A., Buetti, N., Calderwood, M. S., Calfee, D. P., Deloney, V. M., Dubberke, E. R., Ellingson, K. D., Fishman, N. O., Gerding, D. N., Glowicz, J., Hayden, M. K., Kaye, K. S., Kociolek, L. K., ... Maragakis, L. L. (2023). Introduction to a compendium of strategies to prevent healthcare-associated infections in acute-care hospitals: 2022 updates. Infection Control & Hospital Epidemiology, 44(10), 1533-1539. https://doi.org/10.1017/ice.2023.158
Zhang, X., & Xu, Z. (2014). Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. International Journal of Intelligent Systems, 29(12), 1061-1078. https://doi.org/10.1002/int.21676
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