The goal of PrometheeTools is to provide PROMETHEE (Preference Ranking Organisation METHod for Enrichment of Evaluations), a multicriteria decision-making method, to handle a large number of alternatives to obtain partial and complete rankings. Moreover, the package provides the GLNF (Global Local Net Flow) sorting algorithm to classify alternatives into ordered categories and the SILS function to measure the classification quality based on sorting methods.
You can install the released version of PrometheeTools from CRAN with:
install.packages("PrometheeTools")You can install the development version of PrometheeTools from GitHub with:
# install.packages("devtools")
devtools::install_github("ifelipebj/PrometheeTools")PROMETHEE is a multicriteria method that quantifies preference relationships and obtains the positive, negative and net flows of the alternatives, generating rankings that reflect the decision-maker’s preferences. This function applies PROMETHEE I (partial ranking) and PROMETHEE II (complete ranking). This function can handle large number of alternatives.
Usage:
PROMETHEEII(matrix_evaluation, data_criteria)This function applies the GLNF Sorting (Global Local Net Flow Sorting) algorithm to classify the alternatives into ordered groups according to the decision-maker’s preferences in multiple criteria context. GLNF sorting is based on PROMETHEE net flows and a set of limiting profiles. This algorithm starts from a global classification (global search) that is enhanced by two local searches, intra-categorical and inter-categorical.
Usage:
GLNF(matrix_evaluation, data_criteria)This function computes a quality index for SILS
(Silhouette for Sorting), which relies on PROMETHEE II net flows to
assess the classifications produced by PROMETHEE-based ordered sorting
methods.
Usage:
SILS(matrix_evaluation, data_criteria, k, SILS_plot = TRUE)The evaluation matrix for the evaluation_matrix is
formed by a set of alternatives A = (a1,a2,…,a_i,…,a_n) and a set of
criteria G = (g1,g2,…,g_j,…,g_m), it must be structured as follows:
| Alternative | Criterion 1 | Criterion 2 | … | Criterion j | … | Criterion m |
|---|---|---|---|---|---|---|
| Alternative 1 | ||||||
| Alternative 2 | ||||||
| … | ||||||
| Alternative i | ||||||
| … | ||||||
| Alternative n |
Where: - Alternative are the names or identifiers of the
alternatives being evaluated. - Criterion 1,
Criterion 2, etc. are placeholders for the specific names
of your criteria. - Each cell in the matrix represents the value of the
corresponding criterion for a specific alternative.
The incorporation of limiting profiles that define the category in
the matrix_evaluation is a crucial step to apply the
GLNF and SILS functions. These profiles are
denoted using the syntax “r” followed by the profile number. For sorting
into k groups, there should defined k+1
limiting profiles with R=(r1,r2,…,rk+1) being the set of
limiting profiles. “r1” and “r2” represent the limiting profiles for the
first group (most preferred), and “rk” and
“rk+1” denote the profiles for the k-th group
(least preferred). Finally, the set A and R are added into a new set of
alternatives Z = (a1,a2,…,a_n,r1,r2,…,rk+1).
To implement SILS,is necessary to add a new column
Category at the end of the evaluation_matrix
with the classification in (the alternatives assignment to categories)
to be evaluated. Write the classification in number format (e.g.:
1,2,3,…,k).
Replace the placeholders with the actual names of your criteria and provide appropriate values for each alternative-criterion combination.
The criteria parameters table for the data_criteria
should be structured as follows:
| Parameter | Criterion 1 | Criterion 2 | … | Criterion j | … | Criterion m |
|---|---|---|---|---|---|---|
| Function Type | ||||||
| Indifference Threshold | ||||||
| Preference Threshold | ||||||
| Objective | ||||||
| Weight |
Where: - Criterion 1, Criterion 2, etc. are
placeholders for the specific names of your criteria. -
Function Type specifies the type of function for the
criterion (“linear”, “v-shape”, “usual”,“u-shape”, “level” and
“gaussian”). - Indifference Threshold is the indifference
threshold for the criterion. - Preference Threshold is the
preference threshold for the criterion. - Objective
specifies whether the criterion’s objective is to maximize (“max”) or
minimize (“min”). - Weight represents the weight of the
criterion in the analysis. The sum of the weights of all criteria must
be equal to 1.
The preference and indifference thresholds depend on the type of function selected. The preference threshold is non-zero for all functions except for “usual” and “u-shaped”. The indifference threshold is non-zero for “linear”, “level” and “u-shaped” functions.
Replace the placeholders with the actual names of your criteria and provide appropriate values for each parameter.
This is an example which shows you how to solve a ranking and sorting problem:
# Load the PrometheeTools library
library(PrometheeTools)
# Example code corresponds to 30 customers to be evaluated with five
# criteria for partial ranking (PROMETHEE I), complete ranking (PROMETHEE II) and
# sorting into four groups ordered by decision-maker preferences (GLNF sorting).
# Finally the silhouette quality index for sorting (`SILS`) is calculated.
# The evaluation matrix is defined, and five limiting profiles are included
# (r1,r2,r3,r4,r5) to define four categories.
#############
matrix_evaluation <- data.frame (
Alternative = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
21, 22, 23, 24, 25, 26, 27, 28, 29, 30,
"r1", "r2", "r3", "r4", "r5"),
Monetary = c(21.52, 68.09, 184.94, 237.62, 14.29, 12.78, 91.53, 11.39, 264.79, 12.74,
274.41, 3.75, 47.92, 34.5, 45.89, 39.92, 31.18, 273.23, 16.39, 3.91,
20.09, 6.52, 26.62, 28.47, 7.57, 69.2, 420.95, 12.01, 85.88, 8.78,
6816.80, 120, 40, 20, 0),
Recency = c(0, 0, 0, 0, 3, 5, 0, 6, 0, 3,
1, 0, 1, 0, 0, 0, 0, 0, 2, 1,
0, 0, 0, 0, 5, 1, 0, 0, 1, 4,
0, 1, 7, 8, 12),
Frequency = c(7, 5, 12, 12, 1, 3, 9, 2, 12, 4,
11, 3, 10, 10, 11, 11, 12, 12, 7, 1,
5, 2, 9, 11, 4, 10, 12, 3, 10, 2,
12, 10, 8, 4, 1),
Financial_score = c(66, 58, 83, 68, 68, 69, 77, 55, 77, 53,
78, 35, 84, 75, 71, 64, 56, 55, 52, 30,
66, 50, 65, 53, 54, 82, 68, 53, 62, 43,
100, 80, 75, 65, 0),
Length = c(4, 3, 3, 2, 2, 2, 2, 3, 2, 4,
3, 3, 1, 1, 2, 5, 4, 2, 2, 5,
4, 5, 1, 4, 2, 1, 5, 1, 1, 2,
5, 4, 3, 2, 1))
# The matrix with the criteria parameters is defined
data_criteria <- data.frame(
Parameter = c("Function Type", "Indifference Threshold",
"Preference Threshold","Objetive", "Weight"),
Frequency = c("linear", 0, 3, "max", 0.2),
Monetary = c("linear", 30.00, 120, "max", 0.4),
Recency = c("usual", 0.00, 0.00, "min", 0.1),
Financial_score = c("linear", 0.00, 10, "max", 0.2),
Length = c("usual", 0.00, 0.00, "max", 0.1))
#############
# The `PROMETHEEII` function is applied
RS <- PROMETHEEII(matrix_evaluation, data_criteria)
# Positive flows, negative flows and net flows
RS$NF
# Net flows by criteria
RS$NFC
#############
# The `GLNF` function is applied
RS <- GLNF(matrix_evaluation, data_criteria)
# Final classification of the 30 customers into four ordered groups
RS$Class
# It is possible to check the details of global and local searches.
# Show global classification results
RS$Global
# Show local classification results
RS$Local1
RS$Local2
#############
# Add the categories calculated with GLNF (or another method) to the last column
# of `matrix_evaluation`. The limiting profiles have not been assigned to any
# group.
matrix_evaluation$Category = c(3, 3, 1, 1, 4, 3, 2, 4, 1, 3,
1, 4, 2, 2, 2, 2, 2, 1, 3, 4,
3, 3, 3, 2, 4, 2, 1, 4, 3, 4,
NA, NA, NA, NA, NA)
# The number of categories or groups to be evaluated is defined.
k <- 4
# The function `SILS` is applied, where `SILS_plot = TRUE` to plot the results
# of the silhouettes.
RS <- SILS(matrix_evaluation, data_criteria, k, SILS_plot = TRUE)
#Print silhouette values
print(RS)