Canned routine for AHP

Description

ahp is a canned routine that returns a data.frame of individuals' priorities (based on ahp.indpref), number of missing values, consistency ratios, and top three pairs of inconsistent pairwise comparisons. An optional argument agg allows the user to generate a data.frame of aggregated priorities alongside individual priorities.

Usage

ahp(
  df,
  atts,
  negconvert = FALSE,
  reciprocal = TRUE,
  method = "eigen",
  aggmethod = "geometric",
  qt = 0,
  censorcr = Inf,
  agg = FALSE,
  ID = NULL,
  col = NULL,
  suppress = "none"
)

Arguments

Value

If agg = TRUE, returns a list of the results with two elements, indpref and aggpref. ⁠$indpref⁠ contains individual preference weight (same as ahp.indpref), consistency ratios, and the top three most inconsistent pairwise comparisons (same as ahp.pwerror). ⁠$aggpref⁠ contains the Aggregated Priorities and Standard Deviations. Otherwise (i.e. default setting), outputs a data.frame with only ⁠$indpref⁠.

Author(s)

Frankie Cho

References

Saaty TL (2004). “Decision making — the Analytic Hierarchy and Network Processes (AHP/ANP).” Journal of Systems Science and Systems Engineering, 13(1), 1–35. ISSN 1861-9576, doi: 10.1007/s11518-006-0151-5, https://doi.org/10.1007/s11518-006-0151-5.

Examples

data(city200)
ahp(df = city200, atts = c('cult', 'fam', 'house', 'jobs', 'trans'), negconvert = TRUE)

Aggregate individual judgments

Description

Aggregate individual judgments from pairwise comparison matrices

Usage

ahp.aggjudge(ahpmat, atts, aggmethod = "geometric", qt = 0)

Arguments

Value

A data.frame of the aggregated pairwise judgments of all the decision-makers.

Author(s)

Frankie Cho

Examples

## Computes individual judgments with geometric mean and aggregates them
## with a trimmed arithmetic mean

data(city200)
atts <- c('cult', 'fam', 'house', 'jobs', 'trans')

cityahp <- ahp.mat(df = city200, atts = atts, negconvert = TRUE)
ahp.aggjudge(cityahp, atts, aggmethod = 'tmean', qt = 0.1)

Aggregate priority weights

Description

Compute and aggregate individual priority weights from pairwise comparison matrices

Usage

ahp.aggpref(ahpmat, atts, method = "geometric", aggmethod = method, qt = 0)

Arguments

Value

A data.frame of the aggregated priorities of all the decision-makers.

Author(s)

Frankie Cho

References

Saaty TL (2003). “Decision-making with the AHP: Why is the principal eigenvector necessary.” European Journal of Operational Research, 145(1), 85 - 91. ISSN 0377-2217, http://www.sciencedirect.com/science/article/pii/S0377221702002278.

Examples

## Computes individual priorities with geometric mean and aggregates them
## with a trimmed arithmetic mean

library(magrittr)

data(city200)
atts <- c('cult', 'fam', 'house', 'jobs', 'trans')

cityahp <- ahp.mat(df = city200, atts = atts, negconvert = TRUE)
ahp.aggpref(cityahp, atts, method = 'geometric', aggmethod = 'tmean', qt = 0.1)

Calculates the consistency ratio of each decision-maker

Description

The ahp.cr function calculates the consistency ratio of each decision-maker, defined by the following equation:

CR = (\lambda-n)/((n-1)(RI))

Where \lambda is the maximum eigenvalue of the pairwise comparison matrix, n is the number of attributes, and RI is the random index. Following Saaty and Tran (2007), the RI is a function of n and is the consistency ratio of randomly generated pairwise comparison matrices.

Usage

ahp.cr(ahpmat, atts, ri = NULL)

Arguments

Value

A list of consistency ratios of each decision-maker.

Author(s)

Frankie Cho

References

Saaty TL, Tran LT (2007). “On the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process.” Mathematical and Computer Modelling, 46(7), 962 - 975. ISSN 0895-7177, Decision Making with the Analytic Hierarchy Process and the Analytic Network Process, http://www.sciencedirect.com/science/article/pii/S0895717707000787.

Examples

data(city200)
atts <- c('cult', 'fam', 'house', 'jobs', 'trans')

cityahp <- ahp.mat(df = city200, atts = atts, negconvert = TRUE) 
ahp.cr(cityahp, atts)

Matrix of the product between the pairwise comparison value and pj/pi

Description

Consider the comparison matrix where element a_{ij} contains the pairwise comparison between the attributes i and j. The weights of the matrix was constructed as in agg.indpref using the Perron eigenvector where p_{i} and p_{j} are the weights of the i^{th} and the j^{th} element respectively. ahp.error constructs a matrix \epsilon_{ij} = a_{ij}p_{j}/p_{i}.

Usage

ahp.error(ahpmat, atts, reciprocal = FALSE)

Arguments

Value

A list of matrices containing \epsilon_{ij} = a_{ij}p_{j}/p_{i} for each decision-maker, with elements from the lower triangle set as NA automatically (since it is essentially equal to the element in the upper triangle).

Author(s)

Frankie Cho

References

Saaty TL (2004). “Decision making — the Analytic Hierarchy and Network Processes (AHP/ANP).” Journal of Systems Science and Systems Engineering, 13(1), 1–35. ISSN 1861-9576, doi: 10.1007/s11518-006-0151-5, https://doi.org/10.1007/s11518-006-0151-5.

Examples

atts <- c('cult', 'fam', 'house', 'jobs', 'trans')

data(city200)

cityahp <-  ahp.mat(city200, atts, negconvert = TRUE)
ahp.error(cityahp, atts)

Replace inconsistent pairwise comparisons

Description

Based on the matrix derived from ahp.error, replaces the top n number of inconsistent pairwise comparisons with a value calculated by from the method in Harker (1987). While there are strong arguments against replacing inconsistent values without the decision-maker's consent for the sake of satisfying the consistency ratio criterion of consistency ratio < 0.1 (see Saaty and Tran (2007)), it is often not possible for enumerators to ask respondents to change their answers based on consistency, whereas truncating inconsistent decisions may make the dataset unrepresentative of the population. Researchers should think carefully and explain fully the methods used to process AHP data, and whenever possible, use a lower number of iterations.

Usage

ahp.harker(
  ahpmat,
  atts,
  round = FALSE,
  limit = FALSE,
  iterations = 1,
  stopcr = 0,
  printiter = TRUE
)

Arguments

Value

A list of matrices with values replaced with consistent values.

Author(s)

Frankie Cho

References

Harker P (1987). “Incomplete pairwise comparisons in the analytic hierarchy process.” Mathematical Modelling, 9(11), 837 - 848. ISSN 0270-0255, http://www.sciencedirect.com/science/article/pii/0270025587905033.

Saaty TL, Tran LT (2007). “On the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process.” Mathematical and Computer Modelling, 46(7), 962 - 975. ISSN 0895-7177, Decision Making with the Analytic Hierarchy Process and the Analytic Network Process, http://www.sciencedirect.com/science/article/pii/S0895717707000787.

See Also

ahp.error ahp.cr

Examples

atts <- c('cult', 'fam', 'house', 'jobs', 'trans')

data(city200)

cityahp <- ahp.mat(city200, atts, negconvert = TRUE)
ahp.harker(cityahp, atts)

Computes priority weights of individual decision-makers

Description

ahp.indpref computes the individual priorities of the decision-makers, and returns a data.frame containing the priority weights of the decision-makers.

Usage

ahp.indpref(ahpmat, atts, method = "geometric")

Arguments

Value

A data.frame of the individual priorities of all the decision-makers.

Author(s)

Frankie Cho

References

Saaty TL (2003). “Decision-making with the AHP: Why is the principal eigenvector necessary.” European Journal of Operational Research, 145(1), 85 - 91. ISSN 0377-2217, http://www.sciencedirect.com/science/article/pii/S0377221702002278.

Examples

data(city200)
atts <- c('cult', 'fam', 'house', 'jobs', 'trans')

cityahp <- ahp.mat(df = city200, atts = atts, negconvert = TRUE) 
ahp.indpref(cityahp, atts, method = "eigen")

Generate AHP pairwise matrices from survey data

Description

ahp.mat takes in paired comparisons from survey data with questions using the analytic hierarchy process and converts it into pairwise comparison matrices for each individual decision-maker. Examples based on Saaty (2004).

Usage

ahp.mat(df, atts, negconvert = FALSE, reciprocal = TRUE)

Arguments

Value

A list of pairwise comparison matrices of each decision-maker.

Author(s)

Frankie Cho

References

Saaty TL (2004). “Decision making — the Analytic Hierarchy and Network Processes (AHP/ANP).” Journal of Systems Science and Systems Engineering, 13(1), 1–35. ISSN 1861-9576, doi: 10.1007/s11518-006-0151-5, https://doi.org/10.1007/s11518-006-0151-5.

Examples

data(city200)
atts <- c('cult', 'fam', 'house', 'jobs', 'trans')
ahp.mat(df = city200, atts = atts, negconvert = TRUE)

Impute missing observations using the method in Harker (1987)

Description

Imputes the missing values of a list of matrices produced by ahp.mat using the methods and assumptions made in Harker (1987). Missing values must be coded as NA. As suggested in Harker (1987), a minimum of n-1 comparisons must be made, where n is the number of attributes (assuming that the decision-maker is perfectly consistent). Note that the algorithm assumes that the NA values will be imputed under perfect consistency with the other pairwise comparisons made.

Usage

ahp.missing(ahpmat, atts, round = FALSE, limit = FALSE)

Arguments

Value

A list of matrices with all NA values imputed.

Author(s)

Frankie Cho

References

Harker P (1987). “Incomplete pairwise comparisons in the analytic hierarchy process.” Mathematical Modelling, 9(11), 837 - 848. ISSN 0270-0255, http://www.sciencedirect.com/science/article/pii/0270025587905033.

Examples

library(magrittr)

atts <- c('cult', 'fam', 'house', 'jobs', 'trans')

data(city200)

set.seed(42)
## Make a dataframe that is missing at random
missing.df <- city200[1:10,]
for (i in 1:10){
  missing.df[i, round(stats::runif(1,1,10))] <- NA
}
missingahp <- ahp.mat(missing.df, atts, negconvert = TRUE)
ahp.missing(missingahp, atts)

Finds the pairwise comparisons with the maximum amount of inconsistency

Description

After constructing a list of matrices with \epsilon_{ij} = a_{ij}w_{j}/w_{i} (following ahp.error), this algorithm extracts the top n numbers of pairwise comparison matrices with the highest \epsilon_{ij} for each decision-maker.

Usage

ahp.pwerror(ahpmat, atts, npw = 3)

Arguments

Value

A list of matrices containing \epsilon_{ij} = a_{ij}w_{j}/w_{i} for each decision-maker, with elements from the lower triangle set as NA automatically (since it is essentially equal to the element in the upper triangle).

Author(s)

Frankie Cho

References

Saaty TL (2004). “Decision making — the Analytic Hierarchy and Network Processes (AHP/ANP).” Journal of Systems Science and Systems Engineering, 13(1), 1–35. ISSN 1861-9576, doi: 10.1007/s11518-006-0151-5, https://doi.org/10.1007/s11518-006-0151-5.

Examples

library(magrittr)

atts <- c('cult', 'fam', 'house', 'jobs', 'trans')

data(city200)

cityahp <- ahp.mat(city200, atts, negconvert = TRUE)
ahp.error(cityahp, atts)

Generate random indices

Description

The ahp.ri function calculates the mean consistency indices of a specific numbers of random number pairwise comparison matrices.

The random index of one pairwise comparison matrix is given as below, where lambda is the maximum eigenvalue and n is the number of attributes.

RI = (\lambda-n)/((n-1)

ahp.ri creates nsims number of pairwise comparison matrices with number of dimensions=dim, and returns its average.

Usage

ahp.ri(nsims, dim, seed = 42)

Arguments

Value

The generated random index, which is numeric.

Author(s)

Frankie Cho

Examples

ahp.ri(nsims = 10000, dim = 5, seed = 42)

AHP Survey package

Description

The ahpsurvey package provides a workflow for researchers to reformat data and run analytic hierarchy process on data that are originally formatted using the survey data entry mode. A diversified toolbox is available for researchers to explore ways to impute missing pairwise comparisons or to adjust comparisons based on consistency, and to conveniently customize the methods which weights derived from surveys are extracted and aggregated.

Author(s)

Frankie Cho htcho@connnect.hku.hk

Dataframe of one decision-maker based on Saaty (2004)

Description

A data.frame of one decision-maker with weights the same as Saaty (2004), with the pairwise comparisons of atts: c('cult', 'fam', 'house', 'jobs', 'trans'), about a choosing the best city to live in based on five attributes: Culture, Family, House, Jobs, and Transportation. Negative values in the data denote that the attribute on the left is more important than the right, thus if used with ahp.mat, negconvert must be set to TRUE.

Usage

data(city1)

Format

A data frame with 1 row and 10 variables, which are pairwise comparisons of atts.

Source

Saaty (2004)

A dataframe of 200 simulated decision-makers based on Saaty (2004)

Description

A data.frame of one decision-maker with weights the same as Saaty (2004), with the pairwise comparisons of atts: c('cult', 'fam', 'house', 'jobs', 'trans'), about a choosing the best city to live in based on five attributes: Culture, Family, House, Jobs, and Transportation. The choices of 200 decision-makers are simulated based on the underlying weights and randomness generated by a normal random distribution. The true weights are stored in data(city1). The normal random distribution was set with a mean at the true weight value and a standard deviation of ⁠2,1,2,1.5,2,1.5,2.5,0.5,0.5,1⁠ in chronological order of the columns in city200.

Usage

data(city200)

Format

A data.frame with 200 row and 10 variables, which are pairwise comparisons of atts.

Source

Saaty TL (2004). “Decision making — the Analytic Hierarchy and Network Processes (AHP/ANP).” Journal of Systems Science and Systems Engineering, 13(1), 1–35. ISSN 1861-9576, doi: 10.1007/s11518-006-0151-5, https://doi.org/10.1007/s11518-006-0151-5.