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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“We also conducted consistency tests, where a consistency index CR ≤ 0.1 indicates a reasonable construction of the hierarchical structure model [33].”
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“An eigenvalue represents a scaling factor that stretches or shrinks the eigenvector when multiplied by the matrix [82].”
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“The AHP is a multi-criteria decision-making method that integrates qualitative and quantitative analysis (Saaty 1987).”
Terrestrial environmental sensitivity index mapping (TESIM) of the coastal areas of the Niger Delta region of Nigeria
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“…knowledge, and practical experience using the 1–9 scale Table 3 shows the demographic characteristics of the experts interviewed in the second round. approach suggested by Saaty [37], as shown in Table 4, i.e., assigning a scale value from 1 to 9 to each Through an online survey, dimension based on”
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Site selection within the maritime spatial planning: Insights from use-cases on aquaculture, offshore wind energy and aggregates extraction
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Double stochastic preference analysis on group decision making with interval additive preference relations
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“This method aims to measure qualitative aspects and produced uniform weight coefficients that amount to 100% (Saaty 1991) by comparing two characteristics simultaneously (Saaty 1987).”
A comparative study of original equipment manufacturer brake pads using tribological testing and hybrid ranking for enhanced decision making and cost effectiveness
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“The AHP techniques developed by Saaty (1987) were used for determining the priorities of multiple criteria decision problems in flood analysis.”
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Evaluating Expressway Safety Based on Fuzzy Comprehensive Evaluation with AHP-Entropy Method: A Case Study of Jinliwen Expressway in Zhejiang Province, China
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“The value of RI is determined by the order of judgement matrix [45,46], which is shown in Table 2.”
Method
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Land suitability analysis of new urban areas using MIF-AHP and bivariate analysis methods in Latakia, Syria
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“The index Consistency Ratio (RC) was checked and confirmed to be less than 10% (R. W. Saaty, 1987, 2007).”
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“We entered our selected criteria and pairwise comparison of criteria on a 1-9 scale (Table 2), given by Saaty (1987), as input.”
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“According to the reciprocal property, inverse scaling is applied for the less important parameters, thus ranging from 1/9 to 1 Saaty (1987).”
Influential
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“The CR was calculated using the following formula: Land 2025 , 14 , 658 where CI stands for the Consistency Index, and RI is the Random Index—a predefined value that is dependent on the order of the matrix (n) [56]; in this study with n = 5, the selected RI value is 1.12.”
Influential
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“…in ensuring that our AHP-derived weights accurately reﬂect the relative importance of water quality parameters in the context of our urban-rural study area ( Ishizaka and Labib 2009 ; Saaty 1987 , 1977 ). where n = number of factors (i.e., 10) and λ = average value of the consistency vector.”
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“The score values (1) are 1 and 9 by equal importance and extreme importance, respectively (Saaty 1987).”
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“AHP is a strong tool for prioritizing and assigning weights among many conflicting criteria utilizing their pairwise comparison (Saaty, 1987).”
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“Saaty (1987, 2004) developed the AHP method as a valuable tool for analyzing decision problems.”
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“The AHP model was developed by Saaty 50 , is a multi-objective decision making approach that employs a pairwise comparison procedure to arrive at a scale of preferences among a set of alternatives 51 .”
Method
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“Among others, the combination of the Analytic Hierarchy Process (AHP; [61]) and the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS; [62]) is widely applied in decision-making problems.”
A two-stage stochastic preference analysis on group decision making with interval additive preference relations
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“The optimal choice is the one with the highest value (priority) for each criterion and the overall objective [28,29].”
Background
Evaluating flood potential in the Mahanadi River Basin, India, using Gravity Recovery and Climate Experiment (GRACE) data and topographic flood susceptibility index under non-stationary framework
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“The random index corresponds to the number of parameters given by Saaty (1987).”
Influential
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“The Analytic Hierarchy Process (AHP), introduced by Saaty, provides a suitable approach for addressing complex MCDM problems, assisting decision-makers in identifying priorities and making well-informed decisions (Saaty 1987).”
Method
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“Each group then assigned a relative weight to each factor, using a simplified version of the Analytic Hierarchy Process (AHP) (Saaty 1987).”
Method
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“The expert ratings were then compiled and analyzed to obtain the assigned values for each indicator [47].”
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“Similarly, Krysiak and Kluczek [31] assessed the sustainable development of photovoltaic modules using a multi-criteria decision-making method based on the analytic hierarchy process [32].”
Method
DTI-BR model applied in Foz do Iguaçu, Brazil, for its transformation into a smart tourism destination
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Multi-criteria analysis for rapid vulnerability assessment of marine species to climate change
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“Step IV Consistency check of the model The random index and recommended consistency ratio are one of the most efficiently used decision-making practices proposed (Saaty, 1987).”
Influential
Assessing sustainable energy systems using interval-valued Fermatean fuzzy sets-based decision-making model
Liu, Z., Weng, Z., Letchmunan, S., Deveci, M., Huang, Y., Pamucar, D., & Siarry, P. (2026) · Applied Soft Computing · doi:10.1016/j.asoc.2025.114261 · Cited by 9
Climate change and flood susceptibility in Bocas del Toro, Panama: A multi-criteria spatial analysis approach
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“Experts weighed the importance of criteria and sub-criteria using paired comparison matrices based on a Saaty [63] scale (see Table 4).”
Critical Success Factors in Agile-Based Digital Transformation Projects
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“Developed by [80], AHP facilitates decision-making in complex environments by decomposing a problem into a structured hierarchy and applying pairwise comparisons to evaluate the priority of each element.”
Influential
Delta-scale mapping of coastal erosion vulnerability at the modern Yellow River Delta and implications for geomorphic sustainability
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Mapping Flood Hazard in Driouch Region (north-eastern of Morocco) using AHP and Numerical Approaches
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A combined AHP-DEMATEL model approach to build tech-enabled resilient supply chain
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Aladaileh, M., & Lahuerta-Otero, E. (2025) · Sustainable Technology and Entrepreneurship · doi:10.1016/j.stae.2025.100101 · Cited by 9
Towards a wildfire vulnerability index using expert judgement
Papathoma-Köhle, M., Hausharter, D., Schlögl, M., & Fuchs, S. (2025) · International Journal of Wildland Fire · doi:10.1071/wf24114 · Cited by 9
The potential for urban agriculture (UA) in Cape Town, South Africa: a suitability analysis
Kanosvamhira, T., Musasa, T., & Mupepi, O. (2025) · Ann. GIS · doi:10.1080/19475683.2025.2455430 · Cited by 9
“The number of comparisons for the decision elements (that is, criteria or alternatives) in a particular level was derived using (Number of comparisons = n (n − 1)/2) (Saaty 1987).”
A novel approach of the application of drainage morphometry and analytical hierarchy process to the flood susceptibility assessment of the ungauged Kakum River basin, using remote sensing data
Quaicoe, J., & Sapah, M. (2024) · Modeling Earth Systems and Environment · doi:10.1007/s40808-024-02199-6 · Cited by 9
“AHP, suggested by Saaty (1987), is the most commonly used and effective method in the MCDM process to assign the relative importance of each criterion or factor considered in a study.”
Influential
Comparative Efficacy and Safety of Cardio-Renoprotective Pharmacological Interventions in Chronic Kidney Disease: An Umbrella Review of Network Meta-Analyses and a Multicriteria Decision Analysis
Bellos, I., Marinaki, S., Λάγιου, Π., & Benetou, V. (2024) · Biomolecules · doi:10.3390/biom15010039 · Cited by 10
Development of Delay and Disruption Cause Monitoring Framework for Megaprojects: A Claim Management Approach from the Contractor’s Perspective to Enhance Sustainability in the Built Environment
Okudan, O., Çevikbaş, M., & Işık, Z. (2024) · Sustainability · doi:10.3390/su162410856 · Cited by 9
Spatial Analysis of Landslide Hazard Vulnerability Using Decision Support System in the Sile-Sago Watershed, Lake Chamo Rift Valley Basin, Ethiopia.
Ayele, A. B., Tura, A. L., Utallo, A. U., & Mekonnen, A. G. (2024) · Environmental Challenges · doi:10.1016/j.envc.2024.101057 · Cited by 9
A Geographic Information System-Based Model and Analytic Hierarchy Process for Wind Farm Site Selection in the Red Sea
Al-Braheem, L., & Almutlaq, F. (2024) · ISPRS Int. J. Geo Inf. · doi:10.3390/ijgi13110416 · Cited by 9
A Comprehensive Evaluation of Agricultural Drought Vulnerability Using Fuzzy‐AHP‐Based Composite Index Integrating Sensitivity and Adaptive Capacity
Bera, D., & Dutta, D. (2024) · Hydrological Processes · doi:10.1002/hyp.15331 · Cited by 9
Increased socio-vulnerability to floods around flood protection structures: case study of Ganga and Brahmaputra basins (India)
Singh, A., Gautam, S., & Dhanya, C. T. (2024) · Hydrological Sciences Journal · doi:10.1080/02626667.2024.2413014 · Cited by 9
“The pairwise matrix is tested using the consistency ratio (CR; Saaty 1987, Lin and Xiaohong 2010), which compares the consistency of the pair-wise matrix (consistency index, CI) to the consistency of a random matrix (random index, RI) of the same number of criteria.”
Influential
The Sustainable Management of Ecohotels for the Support of Ecotourism—A Case Study
Pavolová, H., Bakalár, T., Tokarčík, A., & Cimboláková, I. (2024) · Sustainability · doi:10.3390/su16208863 · Cited by 9
Evaluation Research on Resilience of Coal-to-Liquids Industrial Chain and Supply Chain
Wu, A., Li, P., Sun, L., Su, C., & Wang, X. (2024) · Systems · doi:10.3390/systems12100395 · Cited by 11
Tackling local environmental challenges with livelihoods strategies: insights from small-scale farmers in the vulnerable region of Ghana
Boateng, B. O., Mensah, H., Simpeh, E., Opoku, P., & Boateng, L. A. (2024) · International Journal of Agricultural Sustainability · doi:10.1080/14735903.2024.2399407 · Cited by 9
“Its theoretical foundation is bolstered by the Analytic Hierarchy Process (AHP), introduced by Saaty (1987), which has demonstrated efficacy in addressing complex decision-making problems.”
A New Approach to Detect Driver Distraction to Ensure Traffic Safety and Prevent Traffic Accidents: Image Processing and MCDM
Alemdar, K. D., & Çodur, M. (2024) · Sustainability · doi:10.3390/su16177642 · Cited by 9
Applying the analytic hierarchy process for investigating key indicators of responsible innovation in the Taiwan software service industry
Chang, T., & Hsieh, Y.-C. (2024) · Technology in Society · doi:10.1016/j.techsoc.2024.102690 · Cited by 13
Investigating Engine Performance and Emission Characteristics of a CI Engine Fueled with Waste Fried Oil Blend Containing Butanol, Alumina, and Silver Nanoparticles
Mishra, S., Sanghamitra, S., Majji, D., Abrar, I., Deshmukh, S. S., & Dutta, A. (2024) · The Arabian journal for science and engineering · doi:10.1007/s13369-024-09512-6 · Cited by 9
“The random index (RI) value is contingent on the criterion number involved in problem analysis [26].”
Multi-Agent Dynamic Fog Service Placement Approach
Šatkauskas, N., & Venčkauskas, A. (2024) · Future Internet · doi:10.3390/fi16070248 · Cited by 9
“AHP was first introduced R. W. Saaty in [57].”
Background
A review of macroeconomic modelling tools for analysing industrial transformation
Elberry, A. M., Garaffa, R., Faaij, A. P. C., & van der Zwaan, B. (2024) · Renewable and Sustainable Energy Reviews · doi:10.1016/j.rser.2024.114462 · Cited by 8
Research on a Multi-Objective Optimization Method for Transient Flow Oscillation in Multi-Stage Pressurized Pump Stations
Ding, Y., Shen, G., & Wan, W. (2024) · Water · doi:10.3390/w16121728 · Cited by 9
“This eigenvector is normalized to determine the weights of each sub-objective [31].”
Method
A novel Multiple-Expert Protocol to manage uncertainty and subjective choices in probabilistic single and multi-hazard risk analyses
Selva, J., Argyroudis, S., Cotton, F., Esposito, S., Iqbal, S. M., Lorito, S., Stojadinović, B., Basili, R., Hoechner, A., Mignan, A., et al. (2024) · International Journal of Disaster Risk Reduction · doi:10.1016/j.ijdrr.2024.104641 · Cited by 9
How to choose a suitable network tariff? - Evaluating network tariffs under increasing integration of distributed energy resources
Heider, A., Huber, J., Farhat, Y., Hertig, Y., & Hug, G. (2024) · Energy Policy · doi:10.1016/j.enpol.2024.114050 · Cited by 9
GIS-based floating offshore wind turbine installation site selection using fuzzy analytic hierarchy process in northeast Aegean Sea
Erkurtulmuş, S. A., & Peşman, E. (2024) · Brodogradnja · doi:10.21278/brod75204 · Cited by 9
“One of the MCDM methods is an Analytic Hierarchy Process (AHP), proposed by Thomas L. Saaty in 1977 [26].”
Method
Forecasting groundwater fluctuations caused by earthquakes using fuzzy logic and AHP Method: A case study from Iran
Gooya, H. R., Katibeh, H., & Maleki, A. (2024) · Earth Science Informatics · doi:10.1007/s12145-024-01264-z · Cited by 9
“(4): (1) where CR is consistency ratio, RI is a random index and its values are shown in Table 1 (Saaty 1987).”
Assessment of suitable hydrogen carriers for maritime transport based on energy, environmental, geopolitical and cost implications
Cava, C., Palone, O., Cedola, L., & Borello, D. (2024) · International journal of hydrogen energy · doi:10.1016/j.ijhydene.2025.02.118 · Cited by 9
Managed aquifer recharge site suitability analysis in the Nabogo Basin of Ghana using GIS and Monte Carlo simulation-aided analytic hierarchy process
Adam, A. B., Appiah-Adjei, E., Adjei, K., Gyampo, M. A., & Owusu-Ansah, E. (2024) · Arabian Journal of Geosciences · doi:10.1007/s12517-024-11865-z · Cited by 9
“7) which indicates the consistency and quality of the comparison (Saaty 1987).”
Identification of soil erosion-susceptible areas using revised universal soil loss equation, analytical hierarchy process and the fuzzy logic approach in sub-watersheds Boussellam and K’sob Algeria
Benaiche, M., Mokhtari, E., Berghout, A., Abdelkebir, B., & Engel, B. (2023) · Environmental Earth Sciences · doi:10.1007/s12665-023-11339-7 · Cited by 9
“The integration of an analytical hierarchy process (AHP) technique (Saaty 1987) and a geographic information system (GIS) platform is one of the most significant instruments (Mokhtari et al. 2023).”
A Geospatial Approach to Identify and Evaluate Ecological Restoration Sites in Post-Fire Landscapes
Dosis, S., Petropoulos, G. P., & Kalogeropoulos, K. (2023) · Land · doi:10.3390/land12122183 · Cited by 10
Safety–Security Analysis of Maritime Surveillance Systems in Critical Marine Areas
Şengül, B., Yılmaz, F., & Uğurlu, Ö. (2023) · Sustainability · doi:10.20944/preprints202311.0412.v1 · Cited by 9
Ranking Technologies of Additive Manufacturing of Removable Complete Dentures by the Results of Their Mechanical Testing
Grachev, D. I., Zolotnitsky, I., Stepanov, D., Kozulin, A., Mustafaev, M., Deshev, A., Arutyunov, D. S., Tlupov, I. V., Panin, S., & Arutyunov, S. (2023) · Dental journal · doi:10.3390/dj11110265 · Cited by 9
“According to the analytic hierarchy process (AHP) method, the weights of the criteria were calculated using a pairwise comparison table [33].”
Method

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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