AN AUTOMATED CONSISTENCY ADJUSTMENT ALGORITHM FOR DELPHI–ANALYTICAL HIERARCHY PROCESS MODELS: DESIGN, IMPLEMENTATION, AND VALIDATION
DOI:
https://doi.org/10.33003/fjs-2026-1006-4702Keywords:
Delphi-AHP hybridization, Consistency Ratio, Judgment Matrix Adjustment, Deterministic Algorithm, Decision Support SystemsAbstract
Despite the widespread use of the Delphi and Analytic Hierarchy Process (AHP) methods for prioritizing complex problems, a persistent limitation is the persistence of inconsistencies in expert judgment matrices during the AHP data elicitation stage. Existing solutions, particularly genetic algorithm–based approaches, often entail high computational complexity due to population-based search, crossover, and mutation operations, making them less efficient and more difficult to implement in practical settings. There is therefore a need for a simpler, deterministic, and practically implementable consistency ratio (CR) adjustment mechanism within Delphi–AHP frameworks. To address this problem, this study develops a deterministic, automated consistency adjustment algorithm that efficiently corrects inconsistencies in AHP pairwise comparison matrices without relying on genetic algorithm mechanisms. The proposed algorithm was evaluated through controlled experiments on synthetic matrices with varying levels of inconsistency. A design science research methodology guided the development and implementation of the algorithm in a C# web-based decision support system. The framework was validated empirically using data collected from a Delphi–AHP study involving e-learning experts from public and private Nigerian
References
Amenta, P., Lucadamo, A., & Marcarelli, G. (2021). On the choice of weights for aggregating judgments in non-negotiable AHP group decision making.
European Journal of Operational Research, 288(1), 294–301. https://doi.org/10.1016/j.ejor.2020.05.048
Ashour, M., & Mahdiyar, A. (2024). A comprehensive state-of-the-art survey on the recent modified and hybrid analytic hierarchy process approaches. Applied Soft Computing, 150, 111014. https://doi.org/10.1016/j.asoc.2023.111014
Farid, S., Ahmad, R., & Alam, M. (2015). A Hierarchical Model for E-learning Implementation Challenges using AHP. Malaysian Journal of Computer Science, 28(3), Article 3. https://jupidi.um.edu.my/index.php/MJCS/article/view/6861
Han, E. (2021). The Application of Delphi-AHP Method in the Priority of Policies for Expanding the Use of Artificial Intelligence. Journal of Internet Computing and Services, 22(4), 99–110. https://doi.org/10.7472/jksii.2021.22.4.99
Humphrey-Murto, S., & Wit, M. de. (2019). The Delphi method—More research please. Journal of Clinical Epidemiology, 106, 136–139. https://doi.org/10.1016/j.jclinepi.2018.10.011
Khan, A. W., Khan, M. U., Khan, J. A., Ahmad, A., Khan, K., Zamir, M., Kim, W., & Ijaz, M. F. (2021). Analyzing and Evaluating Critical Challenges and Practices for Software Vendor Organizations to Secure Big Data on Cloud Computing: An AHP-Based Systematic Approach. IEEE Access, 9, 107309–107332. IEEE Access. https://doi.org/10.1109/ACCESS.2021.3100287
Koczkodaj, W. W., Herman, M. W., & Orlowski, M. (1999). Managing Null Entries in Pairwise Comparisons. Knowledge and Information Systems, 1(1), 119–125. https://doi.org/10.1007/BF03325094
Krebs, S., Ferrari, J., Schürer, A., Chiari, A., Neumann, C., Lang, W., & Sykora, M. (2022). Pre-hospital and intrahospital workflow optimization for patients with suspected ischemic stroke due to large vessel occlusion—Findings from a tertiary care facility. BMC Neurology, 22(1), 497. https://doi.org/10.1186/s12883-022-03033-1
Li, Q., Yin, X., Meng, S., Liu, Y., & Ying, Z. (2020). A security event description of intelligent applications in edge-cloud environment. Journal of Cloud Computing, 9(1), Article 1. https://doi.org/10.1186/s13677-020-00171-0
Lin, C., Kou, G., Peng, Y., & Alsaadi, F. E. (2022). Aggregation of the nearest consistency matrices with the acceptable consensus in AHP-GDM. Annals of Operations Research, 316(1), 179–195. https://doi.org/10.1007/s10479-020-03572-1
Liu, Z.-L., Liu, F., Zhang, J.-W., & Pedrycz, W. (2023). Optimizing consistency and consensus in group decision making based on relative projection between multiplicative reciprocal matrices. Expert Systems with Applications, 224, 119948. https://doi.org/10.1016/j.eswa.2023.119948
Madzík, P., & Falát, L. (2022). State-of-the-art on analytic hierarchy process in the last 40 years: Literature review based on Latent Dirichlet Allocation topic modelling. PLOS ONE, 17(5), e0268777. https://doi.org/10.1371/journal.pone.0268777
Muhammad, A., Shaikh, A., Naveed, Q. N., & Qureshi, M. R. N. (2020). Factors Affecting Academic Integrity in E-Learning of Saudi Arabian Universities. An Investigation Using Delphi and AHP. IEEE Access, 8, 16259–16268. IEEE Access. https://doi.org/10.1109/ACCESS.2020.2967499
Pressman, R. S., & Maxim, B. R. (2020). Software engineering: A practitioner’s approach (Ninth edition). McGraw-Hill Education.
Saaty, T. L. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3), 234–281. https://doi.org/10.1016/0022-2496(77)90033-5
Saaty, T. L., & Vargas, L. G. (2012). Why is the Principal Eigenvector Necessary? In T. L. Saaty & L. G. Vargas (Eds.), Models, Methods, Concepts & Applications of the Analytic Hierarchy Process (pp. 63–70). Springer US. https://doi.org/10.1007/978-1-4614-3597-6_4
Salomon, V. A. P., & Gomes, L. F. A. M. (2024). Consistency Improvement in the Analytic Hierarchy Process. Mathematics, 12(6). https://doi.org/10.3390/math12060828
Sommerville, I. (2002). Software engineering (6. ed., [Nachdr.]). Addison-Wesley.
Tajani, Z., Tajani, C., Khattabi, I., & Sabbane, M. (2023). A metaheuristic approach to improve consistency of the pairwise matrix in AHP. Mathematical Modeling and Computing, 10, 1164. https://science.lpnu.ua/mmc/all-volumes-and-issues/volume-10-number-4-2023/metaheuristic-approach-improve-consistency
The Analytic Hierarchy Process – What It Is and How It Is Used. (n.d.). ResearchGate. Retrieved September 7, 2025, from https://www.researchgate.net/publication/247759937_The_Analytic_Hierarchy_Process_-_What_It_Is_and_How_It_Is_Used
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Copyright (c) 2026 Muyideen Adeyemi Bello, Juliana Ndunagu, Isma'eel Ahmad Barroon, Adekunle Musa Ajibabe, Ameerat Olorunkemi Bello, Nuraddeen Ibrahim Isa
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