Cited by 5,380Multi-Criteria Decision MakingGame Theory and Voting SystemsStrategic Planning and Analysis

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The analytic hierarchy process—what it is and how it is used

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Saaty, R.W.·1987·Mathematical Modelling

DOI 10.1016/0270-0255(87)90473-8

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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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Method
Identifying Key Barriers to joining an Energy Community using AHP
Dioba, A., Giannakopoulou, A., Struthers, D., Stamos, A., Dewitte, S., & Fróes, I. (2024) · Energy · doi:10.1016/j.energy.2024.131478 · Cited by 30
Exploration of urban neighborhood blue-green space quality patterns and influencing factors in waterfront cities based on MGWR and OPGD models
Cen, Q.-Y., Zhou, X., & Qiu, H. (2024) · Urban Climate · doi:10.1016/j.uclim.2024.101942 · Cited by 30
Optimal Allocation of Water Reservoirs for Sustainable Wildfire Prevention Planning via AHP-TOPSIS and Forest Road Network Analysis
Arabatzis, G., Kolkos, G., Stergiadou, A., Kantartzis, A., & Tampekis, S. (2024) · Sustainability · doi:10.3390/su16020936 · Cited by 29
“The estimation of the weighting coefﬁcients of the criteria for potential water reservoir installation sites was conducted using the analytic hierarchy process (AHP) method [47].”
Method
RETRACTED: Exploring Groundwater Quality Assessment: A Geostatistical and Integrated Water Quality Indices Perspective
Masood, M. U., Rashid, M., Haider, S., Naz, I., Pande, C. B., Heddam, S., Alshehri, F., Elkhrachy, I., Ahsan, A., & Sammen, S. S. (2023) · Water · doi:10.3390/w16010138 · Cited by 32
“Respondents are required to fill out the upper triangular component of the questionnaire’s matrix.”
Background
Retracted
Selection and thermophysical assessment of phase change materials (PCMs) for space cooling applications in buildings
Abass, P. J., & Muthulingam, S. (2023) · Numerical Heat Transfer, Part A Applications · doi:10.1080/10407782.2023.2292183 · Cited by 29
“The AHP, initially introduced by Saaty [38] within the context of an arms control and disarma-ment agency project, constitutes a measurement-based theory catering to both continuous and discrete pair-wise comparisons.”
“Sustainable cycle-tourism for society: Integrating multi-criteria decision making and land use approaches for route selection”
Carra, M., Pavesi, F., & Barabino, B. (2023) · Sustainable cities and society · doi:10.1016/j.scs.2023.104905 · Cited by 29
How does pedestrian accessibility vary for different people? Development of a Perceived user-specific Accessibility measure for Walking (PAW)
Jehle, U., Larriva, M. T. B., BaghaiePoor, M., & Büttner, B. (2024) · Transportation Research Part A: Policy and Practice · doi:10.1016/j.tra.2024.104203 · Cited by 28
Urban natural gas pipeline operational vulnerability under the influence of a social spatial distribution structure: A case study of the safety risk patterns in Kunming, China
Xu, J.-R., Ji, C., Yang, L.-H., Liu, Y., Xie, Z., Fu, X., Jiang, F., Liao, M., & Zhao, L. (2024) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2024.110593 · Cited by 28
Comparing the effectiveness of landslide susceptibility mapping by using the Frequency ratio and hybrid MCDM models
Barman, J., Ali, S. S., Nongrem, T., Biswas, B., Rao, K. S., Pramanik, M., Hasher, F. B. B., & Zhran, M. (2024) · Results in Engineering · doi:10.1016/j.rineng.2024.103205 · Cited by 28
Evaluating alternative fuels for a bus fleet: An Italian case
Borghetti, F., Carra, M., Besson, C., Matarrese, E., Maja, R., & Barabino, B. (2024) · Transport Policy · doi:10.1016/j.tranpol.2024.05.025 · Cited by 28
Evaluation of electric car styling based on analytic hierarchy process and Kansei engineering: A study on mainstream Chinese electric car brands
Qi, Y., & Kim, K. (2024) · Heliyon · doi:10.1016/j.heliyon.2024.e26999 · Cited by 29
“…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].”
Method
Techno-economic-environmental analysis and fluid selection of transcritical organic Rankine cycle with zeotropic mixtures
Wang, 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
Advancing plastic pollution hotspotting at the subnational level: Brazil as a case study in the Global South
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
Development of flood susceptibility map using a GIS-based AHP approach: a novel case study on Idukki district, India
Khan, Z., & Jhamnani, B. (2023) · Journal of Spatial Science · doi:10.1080/14498596.2023.2236051 · Cited by 28
GIS-Based Flood Susceptibility Mapping Using AHP in the Urban Amazon: A Case Study of Ananindeua, Brazil
Pimenta, L., Duarte, L. B., Teodoro, A., Beltrão, N., Gomes, D., & Oliveira, R. (2025) · Land · doi:10.3390/land14081543 · Cited by 27
Adaptive Utility Ranking Algorithm for Evaluating Blockchain-Enabled Microfinance in Emerging - A New MCDM Perspective
Zaman, M. M. K., Rodzi, Z. M., Andu, Y., Shafie, N. A., Sanusi, Z. M., Ghazali, A. W., & Mahyideen, J. M. (2025) · International Journal of Economic Sciences · doi:10.31181/ijes1412025182 · Cited by 32
Flood vulnerability map of the Bagmati River basin, Nepal: a comparative approach of the analytical hierarchy process and frequency ratio model
Malla, S., & Ohgushi, K. (2024) · Smart Construction and Sustainable Cities · doi:10.1007/s44268-024-00041-7 · Cited by 27
“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.”
Influential
Strategic insights for sustainable growth of mushroom farming industry in Bangladesh: A comprehensive evaluation using SWOT-AHP and TOPSIS frameworks
Dey, 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.”
Sensitivity analysis of the parameters for preference functions and rank reversal analysis in the PROMETHEE II method
Liu, X., & Liu, Y. (2024) · Omega · doi:10.1016/j.omega.2024.103116 · Cited by 28
Comprehensive Analysis of Renewable Energy Technologies Adoption in Remote Areas Using the Integrated Delphi-Fuzzy AHP-VIKOR Approach
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
“Saaty [99] developed the AHP, one of the most used MCDM methods for determining complex and multifaceted decision problems [100].”
RAV model: Study on urban refined climate environment assessment and ventilation corridors construction
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].”
A framework to guide the selection and configuration of machine-learning-based data analytics solutions in manufacturing
Villanueva Zacarias, A. G., Reimann, P., & Mitschang, B. (2018) · Procedia CIRP · doi:10.1016/j.procir.2018.03.215 · Cited by 26
Land Suitability for Pitahaya (Hylocereus megalanthus) Cultivation in Amazonas, Perú: Integrated Use of GIS, RS, F-AHP, and PROMETHEE
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 .”
Method
An integrated quantitative and qualitative approach for landslide susceptibility mapping in West Sikkim district, Indian Himalaya
Biswakarma, 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).”
Method
Class 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
“Toselectthe best set of models, we adopted a simpliﬁed multi-criteria decision-making approach, namely the analytic hierarchical process (AHP: Saaty, 1987).”

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)
DOI: 10.1016/0270-0255(87)90473-8
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: www.elsevier.com/tdm/userlicense/1.0/ (tdm)
www.elsevier.com/open-access/userlicense/1.0/ (vor, 9696 d)
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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