Analytic Hierarchy Process for Survey Data

The Analytic Hierarchy Process is a versatile multi-criteria decision-making tool introduced by Saaty (1987) that allows decision-makers to weigh attributes and evaluate alternatives presented to them. This package provides a consistent methodology for researchers to reformat data and run analytic hierarchy process in R on data that are formatted using the survey data entry mode. It is optimized for performing the analytic hierarchy process with many decision-makers, and provides tools and options for researchers to aggregate individual preferences and test multiple options. It also allows researchers to quantify, visualize and correct for inconsistency in the decision-maker's comparisons.

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The ahpsurvey package provides a consistent methodology for researchers to reformat data and run the analytic hierarchy process (AHP), introduced by Thomas Saaty, on data that are formatted with the survey data entry mode. It is optimised for performing the AHP with many decision-makers, and provides tools and options for researchers to aggregate individual preferences and concurrently test multiple aggregation options. It also allows researchers to quantify, visualise and correct for inconsistent pairwise comparisons.


Install ahpsurvey directly from CRAN:

install.packages("ahpsurvey",repos = "")

Or, install the development version of ahpsurvey from Github with:

# install.packages("devtools")


The ahpsurvey allows one to input a data.frame consisting of pairwise comparisons data collected through questionnaires and output an informative output of the aggregated priorities of all observations, the individual priorities, consistency ratios, and the most inconsistent pairwise comparisons.

city200 %>% head()
#>   cult_fam cult_house cult_jobs cult_trans fam_house fam_jobs fam_trans
#> 1        2         -2         2         -6        -4       -4        -8
#> 2        2         -4         1         -4        -4       -2        -8
#> 3        4         -2         1         -3        -7       -3        -5
#> 4        8         -4         3         -4        -8        1        -7
#> 5        3         -3         5         -6        -8        1        -4
#> 6        6         -4         2         -4        -7       -2        -4
#>   house_jobs house_trans jobs_trans
#> 1          4          -3         -8
#> 2          4          -3         -7
#> 3          4          -3         -6
#> 4          4          -3         -9
#> 5          4          -3         -6
#> 6          4          -3         -6

Take a data.frame like that above and calculate the aggregated priorities of the 200 decision-makers.

## Define the attributes used
output <- ahp(city200, atts <- c("cult", "fam", "house", "jobs", "trans"), negconvert = TRUE, agg = TRUE)
#> [1] "Number of observations censored = 0"
#>          AggPref  SD.AggPref
#> cult  0.15261018 0.033564038
#> fam   0.44827276 0.057695635
#> house 0.07052519 0.008844754
#> jobs  0.27579123 0.053734270
#> trans 0.03965027 0.006700507

And can show the detailed individual priorities of the 200 decision-makers and the consistency ratio of each decision-maker using that list:

#>        cult       fam      house      jobs      trans         CR
#> 1 0.1709466 0.4587181 0.08547330 0.2507636 0.03409845 0.06125366
#> 2 0.2291009 0.3935620 0.08292558 0.2531962 0.04121537 0.02962755
#> 3 0.1540045 0.4921905 0.08239372 0.2213908 0.05002052 0.06327989
#> 4 0.1242495 0.4634863 0.06162027 0.3159930 0.03465092 0.09308731
#> 5 0.1521676 0.3556904 0.07239889 0.3748108 0.04493236 0.10604443
#> 6 0.1536560 0.4738939 0.07106456 0.2516808 0.04970479 0.10740624

Further arguments allow you to specify the aggregation method, impute missing values and identify and correct inconsistent responses.


An overview of the functions in this package are as follows:

  • ahp: A canned AHP routine
  • ahp.mat: Generate AHP pairwise matrices from survey data
  • ahp.indpref: Priority weights of individual decision-makers
  • ahp.aggpref: Aggregate individual priorities (AIP)
  • ahp.aggjudge: Aggregate individual judgements (AIJ)
  • Saaty’s Consistency Ratio
  • ahp.error: The product between the pairwise comparison value and pj/pi
  • ahp.pwerror: Finds the pairwise comparisons with the maximum amount of inconsistency
  • ahp.missing: Impute missing pairwise comparsions
  • ahp.harker: Replace inconsistent pairwise comparisons


For a detailed example of how the above function works, look no further than the vignettes, which are stored in /my-vignette.pdf. There, you can find a detailed step-by-step instruction of how to use the function using a simulated survey dataset and visualise the output using ggplot2.

Future development

I have plans to add the following features in the future, perhaps after I finish writing up my masters thesis :-(

  • Multiple level of attributes: right now, you can always multiply the weights manually, but I’m looking to develop this feature in a convenient function
  • Comparing alternatives: or a way to export the matrices to be used in other packages which does this
  • Sensitivity analysis
  • More ways to impute missing data
  • Fuzzy AHP (or integration with existing packages)

Please let me know if there are any features which could be useful to you in a feature request or contribution.



This project is licensed under the MIT License.


ahpsurvey 0.4.0

  • Allows for an ID column/ columns for the ahp routine so that the output can preserve some column with an individual identifier(s).

  • Adds an col argument for ahp to specify the columns and its order of the pairwise comparison variables directly to ahp.

ahpsurvey 0.3.1

  • Added ahp.ri, which allows users to self-generate random indices used to calculate the consistency ratio.

  • Replaced default values of RI in with values generated in ahp.ri with 500000 simulations.

ahpsurvey 0.3.0

  • Added a new canned routine, ahp, which provides a detailed output using some of the best functions in ahpsurvey.

  • Edited wording in the documentation to make it a bit more consistent.

ahpsurvey 0.2.2

  • Fixed a bug where ahp.missing throws an error when a mix of complete and incomplete pairwise matrices is passed through it.

  • Fixed the html vignette file

ahpsurvey 0.2.1

Responded to CRAN maintainer Uwe Ligges's comments:

  • Added reference about the method in the Description field in the form Authors (year) doi:.....

  • Corrected the MIT license based on the CRAN template

ahpsurvey 0.2.0

Removed the eigen option in the ahp.indpref and ahp.aggpref functions -- now users have to specify eigen with method = "eigen".

ahpsurvey 0.1.0

  • Fresh release

  • PDF vignette to be added for accurate output of the vignette

  • Checked with no errors on build_win() and on local machine running OSX High Sierra

Reference manual

It appears you don't have a PDF plugin for this browser. You can click here to download the reference manual.


0.4.1 by Frankie Cho, a year ago

Browse source code at

Authors: Frankie Cho [aut, cre]

Documentation:   PDF Manual  

MIT + file LICENSE license

Imports Rdpack, stats, magrittr, knitr, tidyr, dplyr, randomNames

Suggests ggplot2, scales

See at CRAN