SILS: Quality Index of Silhouette for Sorting

In PrometheeTools: PROMETHEE and GLNF for Ranking and Sorting Problems

Quality Index of Silhouette for Sorting

Description

This function computes the quality index for SILS (Silhouette for Sorting), which relies on PROMETHEE II net flows to assess the classifications generated by PROMETHEE-based ordered sorting methods.

Usage

SILS(matrix_evaluation, data_criteria, k, SILS_plot = FALSE)

Arguments

matrix_evaluation	The matrix includes the values for all alternatives and limiting profiles are rows and columns correspond to the evaluation criteria. The last column indicates the alternative classification.
data_criteria	Matrix with the parameter information (rows) for each criterion (columns). The rows of parameters are in the following order: Function Type, Indifference Threshold, Preference Threshold, Objective and Weight.
k	The number of categories to be evaluated.
SILS_plot	Boolean value indicating whether to generate a stacked bar chart representing the SILS values.

Details

• The categories corresponding to the classifications to be assessed should be indicated in the last column of matrix_evaluation in ordinal numbers, where 1 is the most preferred group.

• Enter the same criteria parameters and limiting profiles that you used to obtain the classifications with PROMETHEE II.

• The Limiting Profiles used must be presented as rows in the matrix_evaluation. The name must start with the letter "r" followed by the profile number (e.g., "r1", "r2"). For k categories, there should define k + 1 limiting profiles.

• The types of preference function are as follows: "linear", "v-shape", "usual", "u-shape", "level" and "gaussian".

• The preference and indifference thresholds depend on the type of function selected. The preference threshold requires definition (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.

• In the objective write "max" to maximize or "min" to minimize.

• The sum of the weights of all criteria must be equal to 1.

Value

• A data frame with the SILS values for each alternative according to the classification entered.

• Stacked bar chart representing the SILS values for each alternative with horizontal control limits.

References

Barrera, F., Segura, M., & Maroto, C. (2023) Online. Multicriteria sorting method based on global and local search for supplier segmentation. International Transactions in Operational Research. DOI:10.1111/itor.13288

See Also

PROMETHEEII

Examples

k <- 4
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),
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))
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))
RS <- SILS(matrix_evaluation, data_criteria, k, SILS_plot = TRUE)
print(RS)

PrometheeTools documentation built on Sept. 1, 2023, 5:08 p.m.