The analytic hierarchy process—what it is and how it is used
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The number of Level 1 criteria (n = 6) remained within Saaty's recommended range (7 ± 2) for cognitively tractable pairwise comparison.
“The number of Level 1 criteria (n = 6) remained within Saaty's [23] recommended range (7 ± 2) for cognitively tractable pairwise comparison.”
From Toward Sustainable AI Literacy in Higher Education: A Delphi–AHP Approach to Identifying Key Components of AI/Data Extracurricular Programs (2026) · cites this paper as [23]
Section 4 (page unavailable) says the number of elements compared should be small and specifically fewer than 10, which includes six criteria. It does not recommend a 7 ± 2 range or give cognitive tractability as the reason; its stated concern is that errors can distort priorities when many elements are compared. (LLM, conf=0.87)
Experimental — accuracy not yet measuredThe resulting six-criterion structure remained within Saaty's recommended range (7 ± 2), allowing cognitively tractable pairwise comparison while preserving full domain coverage.
“The resulting six-criterion structure remained within Saaty's [23] recommended range (7 ± 2), allowing cognitively tractable pairwise comparison while preserving full domain coverage.”
From Toward Sustainable AI Literacy in Higher Education: A Delphi–AHP Approach to Identifying Key Components of AI/Data Extracurricular Programs (2026) · cites this paper as Saaty's [23]
Section 4 (page unavailable) says the number of elements compared should be small, specifically fewer than 10, so six criteria are consistent with its guidance for pairwise comparison. The paper does not give a recommended range of 7 ± 2 or establish that the citing study’s six criteria preserve full domain coverage. Section 2 (page unavailable) instead advises making a hierarchy complex enough to capture the situation while keeping it small and nimble. (LLM, conf=0.86)
Experimental — accuracy not yet measuredAHP decomposes complex problems into hierarchical structures of goal, criteria, and alternatives, and quantifies relative importance through pairwise comparisons.
“The Analytic Hierarchy Process (AHP), developed by Saaty [23], is a multi-criteria decision-making technique that decomposes complex problems into hierarchical structures of goal, criteria, and alternatives, and then quantifies relative importance through pairwise comparisons.”
From Toward Sustainable AI Literacy in Higher Education: A Delphi–AHP Approach to Identifying Key Components of AI/Data Extracurricular Programs (2026) · cites this paper as [23]
AHP enables the conversion of qualitative expert judgments into numerical weights, with built-in consistency verification through the Consistency Ratio (CR).
“AHP enables the conversion of qualitative expert judgments into numerical weights, with built-in consistency verification through the Consistency Ratio (CR).”
From Toward Sustainable AI Literacy in Higher Education: A Delphi–AHP Approach to Identifying Key Components of AI/Data Extracurricular Programs (2026) · cites this paper as [23]
The consistency ratio of the AHP aggregated comparison matrix was 0.015.
“The consistency ratio of 0.015 confirms acceptable logical consistency well within Saaty's [23] threshold of 0.10.”
From Toward Sustainable AI Literacy in Higher Education: A Delphi–AHP Approach to Identifying Key Components of AI/Data Extracurricular Programs (2026) · cites this paper as [23]
AHP is used to determine criteria weights and rank alternatives based on expert judgment.
“One of the most commonly used multi-criteria decision-making methods is the Analytic Hierarchy Process (AHP), which is used to determine criteria weights and rank alternatives based on expert judgment [41].”
From An Integrated AHP–Fuzzy AHP Evaluation Framework for Large Language Models in Software Engineering Education (2026) · cites this paper as [41]
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Research works printed but not linked: 7
- Mervis Hall, Univ. Pittsburgh, Pittsburgh, PA 15260.) (Available in French under the title Deader face a la complexite. Entreprise Moderne D'Edition, Paris, 1984).
- T. L. Saaty and K. P. Kearns, Analytical Planning. Pergamon Press, Oxford (1985).
- T. L. Saaty, Absolute and relative measurement with the AHP. The most livable cities in the United States. Socio-econ. Plum Sci. 20(6), 3277331 (1986).
- R. P. Hamalainen and T. 0. Seppalainen. The analytic network process in energy policy planning. Socio-econ. Plum. Sci. 20(6), 3999405 (1986).
- T. L. Saaty, Inconsistency and rank preservation. J. math. Psychol. 28(2), 2055214 (1984).
- T. L. Saaty, Axiomatic foundation of the Analytic Hierarchy Process. Mgmt Sci. 32(7), 841-855 (1986).
- F. Zahedi, The Analytic Hierarchy Process-a survey of the method and its applications. Interfaces 16(4), 96-108 (1986).
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“(Saaty 1987).”
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“Respondents are required to fill out the upper triangular component of the questionnaire’s matrix.”
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“…criterion for the objectives and perform a consistency test 5 A two-by-two comparison of the program hierarchy was made to obtain the relative importance of the programs to each other 6 Calculate the score for each option and the option with the highest score will become the final decision [25].”
MethodWang, S.-K., Tang, J., Liu, C., Li, Q.-B., Sun, Z., & Huo, E.-G. (2024) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2024.140690 · Cited by 28
Alencar, M. V., Gimenez, B. G., Sasahara, C., Elliff, C. I., Velis, C. A., Rodrigues, L. S., Conti, L. A., DIAS, S. L. F. G., Cetrulo, T. B., Scrich, V. M., et al. (2023) · Marine Pollution Bulletin · doi:10.1016/j.marpolbul.2023.115382 · Cited by 37 · see citing works
Khan, Z., & Jhamnani, B. (2023) · Journal of Spatial Science · doi:10.1080/14498596.2023.2236051 · Cited by 28
Pimenta, L., Duarte, L. B., Teodoro, A., Beltrão, N., Gomes, D., & Oliveira, R. (2025) · Land · doi:10.3390/land14081543 · Cited by 27 · see citing works
Mukhlis, M., Zaman, K., Zahari, Andu, Y., Shafie, N. A., Sanusi, Z., Ghazali, A., & Mahyideen, J. M. (2025) · International Journal of Economic Sciences · doi:10.31181/ijes1412025182 · Cited by 27
Malla, S., & Ohgushi, K. (2024) · Smart Construction and Sustainable Cities · doi:10.1007/s44268-024-00041-7 · Cited by 27 · see citing works
“The AHP by Saaty [57] is an extensively utilized and efficient approach in MCDM for assessing the importance of individual criteria or factors considered within a study.”
InfluentialDey, B., Ador, M. A., Haque, M. M., Ferdous, J., Halim, M. A., Uddin, M. B., & Ahmed, R. (2024) · Heliyon · doi:10.1016/j.heliyon.2024.e36956 · Cited by 27
“The Saaty (1987) scale, ranging from 1 to 9 were used to compare variables, indicating the relative importance of each factor.”
Liu, X., & Liu, Y. (2024) · Omega · doi:10.1016/j.omega.2024.103116 · Cited by 28 · see citing works
Abdul, D., Jiang, W.-Q., Tanveer, A., & Sameeroddin, M. (2023) · The Arabian journal for science and engineering · doi:10.1007/s13369-023-08334-2 · Cited by 27 · see citing works
“Saaty [99] developed the AHP, one of the most used MCDM methods for determining complex and multifaceted decision problems [100].”
Li, Q.-M., Zheng, J.-P., Yuan, S., Zhang, L., Dong, R.-M., & Fu, H.-H. (2023) · Building and Environment · doi:10.1016/j.buildenv.2023.111080 · Cited by 27
“Then, the factors are assigned values according to the hierarchical assignment method ( A nalytic H ierarchy P rocess, AHP) [51,52].”
Villanueva Zacarias, A. G., Reimann, P., & Mitschang, B. (2018) · Procedia CIRP · doi:10.1016/j.procir.2018.03.215 · Cited by 26 · see citing works
Tuesta-Trauco, K. M., Salas-López, R., Barboza, E., Zabaleta-Santisteban, J., Medina-Medina, A. J., Rivera-Fernandez, A., Sánchez-Vega, J. A., Noriega-Salazar, N. M., Oliva-Cruz, M., Tariq, A., et al. (2025) · Remote Sensing · doi:10.3390/rs17040637 · Cited by 26
Beyond FVD: Enhanced Evaluation Metrics for Video Generation Quality
Luo, G., Favero, G., Luo, Z.-H., Jolicoeur-Martineau, A., & Pal, C. (2024) · arXiv.org · doi:10.48550/arxiv.2410.05203 · Cited by 26
“The Analytic Hierarchy Process (AHP) Saaty (1987) aggregates responses using a pairwise comparison matrix to derive a priority vector for noise distortion types.”
Evaluation of gold mineralisation potential using AHP systems and weighted overlay analysis
Abubakar, F., Alao, J., Ogah, A. J., Ayuba, R., Lekdukun, M., Baba, Y., Sadiq, F. K., Samson, E., & Aliyu, A. (2024) · Scientific Reports · doi:10.1038/s41598-024-70957-8 · Cited by 26
“In this study, weight values were assigned, criteria were compared using expert judgements, and the AHP model was then utilised to process the weight values 74–76 .”
MethodBiswakarma, P., Joshi, V., Abdo, H., Almohamad, H., Dughairi, A. A. A., & Al-Mutiry, M. (2023) · Geomatics, Natural Hazards & Risk · doi:10.1080/19475705.2023.2273781 · Cited by 26
“The rankings are calculated using the eigen vector method, and the consistency of the solution is checked using the consistency ratio (Saaty1987).”
MethodClass Label Representativeness in Machine Learning-Based Mineral Prospectivity Mapping
Parsa, M., & Cumani, R. (2025) · Natural Resources Research · doi:10.1007/s11053-025-10468-z · Cited by 25 · see citing works
“Toselectthe best set of models, we adopted a simplified multi-criteria decision-making approach, namely the analytic hierarchical process (AHP: Saaty, 1987).”
Service Function Chain Deployment With VNF-Dependent Software Migration in Multi-Domain Networks
Zhang, Y., Wang, R., Hao, J., Wu, Q., Teng, Y., Wang, P., & Niyato, D. (2025) · IEEE Transactions on Mobile Computing · doi:10.1109/tmc.2024.3514173 · Cited by 25
“The AHP [43] decomposes the problem into a hierarchical problem.”
Mondal, S., Parveen, M. T., Alam, A., Rukhsana, Islam, N., Całka, B., Bashir, B., & Zhran, M. (2024) · ISPRS Int. J. Geo Inf. · doi:10.3390/ijgi13110388 · Cited by 25
- Authors
- Saaty, R. W.
- Corresponding author
- Saaty, R.W.
- Venue
- Mathematical Modelling
- Publisher
- Elsevier BV
- Published
- 1987
- Volume
- 9
- Issue
- 3-5
- Pages
- 161-176
- ISSN
- 0270-0255 (ISSN-L)
- OpenAlex
- W2046078150
- Cited by
- 5,380
- References
- 15
- Citations by year
- 2026: 623 · 2025: 735 · 2024: 697 · 2023: 662 · 2022: 518 · 2021: 481 · 2020: 382 · 2019: 284 · 2018: 226 · 2017: 173 · 2016: 124 · 2015: 107 · 2014: 62 · 2013: 52 · 2012: 39
- FWCI
- 4.84
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Mathematical Modelling (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Multi-Criteria Decision Making
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Game Theory and Voting Systems
- Social Sciences › Business, Management and Accounting › Strategy and Management › Strategic Planning and Analysis
- Keywords
- analytic hierarchy process, ratio scale, measurement theory, axioms, inconsistency, rank preservation, reversal, absolute measurement, relative measurement, multi-criteria decision making
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