PROMETHEEII {PrometheeTools}

The PROMETHEE Outranking Method

Description

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 (full ranking). This function can handle a large number of alternatives.

Usage

PROMETHEEII(matrix_evaluation, data_criteria)

Arguments

matrix_evaluation

The matrix includes the values for all alternatives. The alternatives profiles are rows and columns correspond to the evaluation criteria.

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.

Details

• 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.

• This implementation of PROMETHEEII is designed to handle a large number of alternatives (it has been tested with 10,000 alternatives) much higher than the previous implementations in R (promethee123 and PROMETHEE).

Value

-NF Matrix with positive and negative flows (PROMETHEE I) and net flows for complete ranking (PROMETHEE II).

-NFC Net flows matrix by criterion.

References

Brans, J.P.; De Smet, Y., (2016). PROMETHEE Methods. In: Multiple Criteria Decision Analysis. State of the Art Surveys, Figuera, J., Greco, S., Ehrgott, M.; Springer: New York, USA, pp. 187-219. DOI: 10.1007/978-1-4939-3094-4_6.

Examples

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),
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),
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),
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),
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),
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))
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 <- PROMETHEEII(matrix_evaluation, data_criteria)
RS$NF
RS$NFC