The DOI matches its Crossref record.
The analytic hierarchy process—what it is and how it is used
Open accessOverview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“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]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“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]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“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]
The cited source says what the claim attributes to it.
In the citing paper
“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 cited source says what the claim attributes to it.
In the citing paper
“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]
The cited source says what the claim attributes to it.
In the citing paper
“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]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
No references could be resolved yet.
Research works printed but not linked: 12
- Saaty, 1982, Decision Making for Leaders
- Saaty, 1986, Absolute and relative measurement with the AHP. The most livable cities in the United States, Socio-econ. Plann. Sci., 20, 327, 10.1016/0038-0121(86)90043-1 · DOI
- Saaty, 1987, Stimulus—response with reciprocal kernels: the rise and fall of sensation, J. math. Sci.
- Aczél, 1983, Procedures for synthesizing ratio judgements, J. math. Psychol., 27, 93, 10.1016/0022-2496(83)90028-7 · DOI
- Hämäläinen, 1986, The analytic network process in energy policy planning, Socio-econ. Plann. Sci., 20, 399, 10.1016/0038-0121(86)90054-6 · DOI
- Harker, 1987, Alternative modes of questioning in the Analytic Hierarchy Process, Mathl Modelling, 9, 353, 10.1016/0270-0255(87)90492-1 · DOI
- Saaty, 1984, Inconsistency and rank preservation, J. math. Psychol., 28, 205, 10.1016/0022-2496(84)90027-0 · DOI
- Saaty, 1986, Axiomatic foundation of the Analytic Hierarchy Process, Mgmt Sci., 32, 841, 10.1287/mnsc.32.7.841 · DOI
- Saaty, 1987, Rank generation, preservation and reversal in the Analytic Hierarchy Process, Decis. Sci., 10.1111/j.1540-5915.1987.tb01514.x · DOI
- Aczél, 1987, Synthesizing judgements: a functional equations approach, Mathl Modelling, 9, 311, 10.1016/0270-0255(87)90487-8 · DOI
- Vargas, 1982, Reciprocal matrices with random coefficients, J. math. Modelling, 3, 69, 10.1016/0270-0255(82)90013-6 · DOI
- Zahedi, 1986, The Analytic Hierarchy Process—a survey of the method and its applications, Interfaces, 16, 96, 10.1287/inte.16.4.96 · DOI
Cited by
Sorted by citations
Items 1,001–1,013 of 1,013
Dubickis, M., Putans, R., & Hovlanne, Z. (2025) · Journal of Open Innovation: Technology, Market and Complexity · doi:10.1016/j.joitmc.2025.100665 · Cited by 2
Liu, X., Lv, Y., Li, W., Peng, L.-H., & Wu, Z. (2025) · Buildings · doi:10.3390/buildings15193518 · Cited by 2
Frichi, Y., Aboueljinane, L., & Jawab, F. (2025) · International Conference on Advances in System Simulation · doi:10.1177/00375497251375466 · Cited by 2
“Introduced by Saaty in the 1970s, AHP is a widely used and effective MCDM method, 53 particularly valued for its reliability, flexibility, and ease of use.”
A Participatory Decision-making Strategy for Geoconservation Implemented in Portland, Jamaica
Salgado-Jauregui, E., Ellins, K., Henry, D., Gordon-Smith, D., & Martindale, R. (2025) · Geoheritage · doi:10.1007/s12371-025-01136-y · Cited by 2
“The responses recorded in the form include a quantitative component that corresponds with the fundamental scale of Saaty (1987) and a qualitative component that describes each participant’s rationale justifying their choices.”
InfluentialEvaluating Key Spatial Indicators for Shared Autonomous Vehicle Integration in Old Town Spaces
Yao, S., Budthimedhee, K., Teeravarunyou, S., Chen, X., & Zhang, Z. (2025) · World Electric Vehicle Journal · doi:10.3390/wevj16090501 · Cited by 2
Determination of sustainable areas for ecotourism using GIS-based AHP
Kaya, S., Genç, L., & Kozak, M. (2025) · International Journal of Tourism Cities · doi:10.1080/20565607.2025.2550460 · Cited by 2
Eloranta, V., Grönman, A., Sihvonen, V., & Luoranen, M. (2025) · Cleaner Environmental Systems · doi:10.1016/j.cesys.2025.100326 · Cited by 2
A Framework for Data Lifecycle Model Selection
Iacono, M., Mastroianni, M., Riccio, C., & Viscardi, B. (2025) · Future Internet · doi:10.3390/fi17090390 · Cited by 2
Zhong, R., Wang, Z., Wang, H., Jin, Y., Bai, S., & Gao, X. (2025) · Entropy · doi:10.3390/e27090897 · Cited by 1
“The values of γ are given in Table 2 Saaty [43].”
A model proposal for disaster resilient neighborhoods: Düzce City case
Yüksel, K. U., & Karaçor, E. L. K. (2025) · City, Territory and Architecture · doi:10.1186/s40410-025-00280-w · Cited by 2
“Thomas Saaty introduced the Analytic Hierarchy Process (AHP) in the 1970s as a multi-criteria decision-making process, which he later improved (1987).”
Feng, L., Xie, J., & Ke, Y. (2025) · Sustainability · doi:10.3390/su18010164 · Cited by 1
Jović, J. L., Domazet, D. S., Vesić, N. O., Ranđelović, B. M., & Simjanović, D. J. (2026) · Mathematics · doi:10.3390/math14101637 · Cited by 1
He, Y., Smirnov, I., Fedrushkov, D., Kovalchuk, S., & Revin, I. (2026) · arXiv · doi:10.48550/arxiv.2604.03742
“The AHP, originally proposed by Saaty [15,14], is a classical MCDM framework designed to decompose complex decision problems into hierarchical structures.”
Metadata
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
