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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 [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]
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“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]
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“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]
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“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]
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“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]
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“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: 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
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“The AHP [43] decomposes the problem into a hierarchical problem.”
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“The research employed a relative importance scale ranging from 1 to 9 (Likert scale) as proposed by Saaty [64,65].”
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“In 1980, Saaty developed the AHP method (Saaty, 1987).”
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“’ is 0.58 for the 3 × 3 matrix [20].”
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“Saaty developed the AHP method in the 1970s as a means of assigning weights to alternatives in decision-making [61].”
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“Saaty [42] divides the pairwise comparison scale in the Analytic Hierarchy Process into 1 to 9 levels, representing equally important, slightly important, fairly important, very important, absolutely important, and the adjacent values between each scale, as shown in Table 1.”
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“The AHP is multicriteria decision analysis framework developed by 5,21 , works based on pairwise comparison matrix (Table 2) used to derive the priority scale of the criterion relying on preferences using Saaty’s scale (Table 3).”
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“The AHP was first familiarized by Saaty as the purpose of decision-making framework (Saaty 1987 ).”
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“During the comparison, values were assigned to the factors based on Saaty ’ s [98] scale (Table 4).”
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“The AHP, introduced by Saaty, is a structured technique widely applied for determining subjective weights in complex multicriteria decision-making scenarios by decomposing the decision problem into a hierarchical framework 61 .”
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“(7) are given in Table 7. where, RI in the Eq.”
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“Thematic layers were assigned weights using the Saaty (1987) preference scale, where values ranged from 1 to 9, with higher values indicating greater vulnerability.”
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“The process involves building a preference matrix, ensuring consistency, and calculating criteria weights that sum to 100% 59,60 .”
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“%) is acceptable for the analysis (Saaty 1987).”
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“Furthermore, Insights from Saaty [43], the creator of the Analytic Hierarchy Process, shed light on the number of experts required for effective MCDM methods.”
BackgroundGhimire, M., Pandey, S., & Woo, J. (2024) · Energy for Sustainable Development · doi:10.1016/j.esd.2024.101414 · Cited by 20
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“The changes in measurement, relationships within and between groups of structural pieces, and deviations from consistency are of paramount importance to AHP [54].”
BackgroundBoonmee, C., & Thoenburin, P. (2023) · Expert systems with applications · doi:10.1016/j.eswa.2023.123002 · Cited by 20
Fedai, Y. (2023) · Processes · doi:10.3390/pr11102872 · Cited by 20
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“For such tools, the AHP analysis (Saaty 1987 ) provides a pairwise comparison of the components at each level of the decision-making process.”
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“Saaty (1987) recommended allowing some level of inconsistency (CR not more than 0.10), in order to reflect new knowledge along the answers, although this is still considered a strict interpretation, and some studies have relaxed this threshold (Mahmoud and Hine, 2013; Kulisic et al., 2021; Kuli ˇ…”
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“For weight calculation, the AHP is a widely accepted subjective evaluation method [50–53].”
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“• The weights are determined using the Analytic Hierarchy Process (AHP), a widely recognized MADM method [39].”
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“Then, the calculated consistency ratio (CR) which demonstrates the validity of Saaty [92] comparison was computed using Equation (6).”
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“In order to evaluate the relative importance of various thematic layers and their specific categories, the consistency ratio (CR) was calculated based on the method proposed by Saaty (1987, 1980) and Li and Hong (2023).”
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“The AHP approach, introduced by Saaty [50], establishes a hierarchical model where pairwise comparisons determine the relative importance of criteria and alternatives, leading to overall performance scores.”
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“Normalized plant density index maps are crucial as they illustrate variations in temperature fluctuations of the natural surface based on plant densities [89,90].”
BackgroundPeng, Y., Li, Y., Cheng, W.-Y., & Wang, K. (2024) · Sustainability · doi:10.3390/su16031256 · Cited by 17
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“The hierarchy structure begins with the overall objective, descends to criteria, and finally to alternatives (Saaty, 1987).”
InfluentialSahl, A. B., Orosz, Á., How, B. S., Friedler, F., & Teng, S.-Y. (2023) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2023.140179 · Cited by 17
“Note that the weight can be determined using various approaches such as the analytical hierarchy approach (Saaty, 1987), Shannon entropy approach (Nascimento and Prudente, 2018), and principal component analysis (PCA) (How and Lam, 2017).”
MethodLin, H., Deng, X., Yu, J., Jiang, X., & Zhang, D. (2023) · Sustainability · doi:10.3390/su151914538 · Cited by 21
“The analytic hierarchy process (AHP) is a decision-making tool developed by Saaty [30].”
Asare, P., Atún, F., & Pfeffer, K. (2023) · Applied spatial analysis and policy · doi:10.1007/s12061-023-09541-y · Cited by 17
“According to Saaty (1987), the CR value derived means the values for the PWCM are consistent.”
Batool, K., Zhao, Z., Nureen, N., & Irfan, M. F. (2023) · Environmental Science and Pollution Research · doi:10.1007/s11356-023-28767-4 · Cited by 22
Flood Vulnerability and Risk Mapping in Arba Minch City Using Remote Sensing, GIS, and AHP
Kasahun, M., Diriba, D., Lemma, T., Karuppannan, S., & Kanko, N. (2025) · Scientific African · doi:10.1016/j.sciaf.2025.e02976 · Cited by 16
Iqbal, A., Soni, L., Qazi, A. W., & Nazir, H. (2025) · Remote Sensing · doi:10.3390/rs17111818 · Cited by 16
“To ensure the accuracy and validity of the weight assignments, the Consistency Index (CI) and Consistency Ratio (CR) were computed using Saaty’s equations [71].”
InfluentialEnhancing Analytic Hierarchy Process Modelling Under Uncertainty With Fine‐Tuning LLM
Park, H., Oh, H., Gao, F., & Kwon, O. (2025) · Expert Systems · doi:10.1111/exsy.70051 · Cited by 18
“Moreover, while previous studies have demonstrated the general applicability of LLMs in various stages of decision-making (Saaty 1987a; Brynjolfsson and McAfee 2017), there is a significant lack of research specifically exploring how LLMs can assist in the development and evaluation of AHP models.”
InfluentialOh, Y., Pasman, H. J., Khan, S. A., & Park, S. (2025) · International Journal of Hydrogen Energy · doi:10.1016/j.ijhydene.2025.01.333 · Cited by 18
EV adoption in India: barriers and policy solutions from manufacturers' and consumers' perspectives
Patel, M., Singh, R., Arora, P., & Mahapatra, D. (2024) · Energy for Sustainable Development · doi:10.1016/j.esd.2024.101583 · Cited by 16
Asefa, W., & Degefu, M. A. (2024) · Environmental Systems Research · doi:10.1186/s40068-024-00387-y · Cited by 16
Huang, Y.-Q., Liu, L., Zhen, Y., Wang, C., Ning, X., Li, K., Wang, T.-P., & Lu, Q. (2024) · Energy · doi:10.1016/j.energy.2024.133051 · Cited by 16
Ullah, S., Iqbal, M., Waseem, M., Abbas, A., Masood, M., Nabi, G., Tariq, M. A. U. R., & Sadam, M. (2024) · Sustainability · doi:10.3390/su16219266 · Cited by 16
Martins, T., Leitão, T. E., Oliveira, M. M., Panagiotou, C., Stefan, C., Chkirbene, A., & Portela, M. M. (2024) · Groundwater for Sustainable Development · doi:10.1016/j.gsd.2024.101280 · Cited by 16
Salih, A., Hassaballa, A., & Eltawil, M. (2024) · Energy · doi:10.1016/j.energy.2024.131623 · Cited by 16
Geospatial Analysis of Flood Risk Hazard in Zambezi Region, Namibia
Mshelia, Z., Nyam, Y., Moisès, D. J., & Belle, J. (2024) · Environmental Challenges · doi:10.1016/j.envc.2024.100915 · Cited by 16
Life cycle assessment-based decision making under methodological uncertainty: A framework proposal
Marson, A., Zuliani, F., Fedele, A., & Manzardo, A. (2024) · Journal of Cleaner Production · doi:10.1016/j.jclepro.2024.141288 · Cited by 16
López-Bravo, C., Mora-López, L., Sidrach‐de‐Cardona, M., & Márquez-Ballesteros, M. (2024) · Renewable Energy · doi:10.1016/j.renene.2024.120387 · Cited by 16
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
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