# promethee123: PROMETHEE I, II, and III Methods In promethee123: PROMETHEE I, II, and III Methods

## Description

The PROMETHEE method is a multti-criteria decision-making method addressing with outranking problems. The method establishes a preference structure between the alternatives, having a preference function for each criterion. IN this context, three variants of the method is carried out: PROMETHEE I (Partial pre-ordering), PROMETHEE II (Total pre-ordering), and PROMETHEE III (pre-ordering by inervals).

## Usage

 ```1 2``` ``` promethee123(alternatives, criteria, decision_matrix, min_max, normalization_function, q_indifference, p_preference, s_curve_change, criteria_weights) ```

## Arguments

 `alternatives` The names respective to set of alternatives in evaluation `criteria` The names respective to set of criteria in evaluation `decision_matrix` A matrix where rows correspond to the criteria and columns correspond to alternatives, there is inputed the performance of alternatives in each criterion `min_max` A vector with objectives, minimize or maximize, to each criteria. `normalization_function` Numerical description relative to each type of normalization function to each criterion `q_indifference` Indifference threshold `p_preference` Preference threshold `s_curve_change` Threshold of changing in the curve `criteria_weights` Numerical representation of the respective importance for each criterion

## Details

- For normalization function we have six types: [ 1 ] for USUAL (0 or 1) — [ 2 ] for U-SHAPE (0 or 1) q [ 3 ] for V-SHAPE (x/p or 1) p [ 4 ] for LEVEL (0, 0.5 or 1) q , p [ 5 ] for V-SHAPE I (0, (x-q)/(p-q) or 1) q , p [ 6 ] for GAUSSIAN (0 or 1-e^(-x^2/2*s^2)) s ———————————- q = indifference parameter p = preference parameter s = parameter to indicate change in the preference curve

- The input of thresholds depends of the type of preference function used;

- The sum of weights must be 1;

## Value

- Performance in each criterion;

- Global Index of Importance;

- Importance Flows (Positive, Negative, and Net);

- Preference relations in PROMETHEE I;

- Total Outranking in PROMETHEE II;

- Preference relations in PROMETHEE III;

- Graphical representations of PROMETHEE I, II, and III.

## Author(s)

Miguel Angelo Lellis Moreira miguellellis@hotmail.com, Marcos dos Santos marcosdossantos_doutorado_uff@yahoo.com.br, Carlos Francisco Simoes Gomes cfsg1@bol.com.br

## References

BRANS, Jean-Pierre; DE SMET, Yves. PROMETHEE methods. In: Multiple criteria decision analysis. Springer, New York, NY, 2016. p. 187-219. DOI: 10.1007/978-1-4939-3094-4_6. <https://link.springer.com/chapter/10.1007/978-1-4939-3094-4_6>

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```alternatives <- c("SARP", "ORAC", "TOTS", "MICRO", "IBRP") criteria <- c("Price", "Complexity", "Security", "Performance") decision_matrix <- matrix(c(15, 29, 38, 24, 25.5, 7.5, 9, 8.5, 8, 7, 1, 2, 4, 3, 3, 50, 110, 90, 75, 85), ncol = length(alternatives), nrow = length(criteria), byrow = TRUE) min_max <- c("min", "min", "max", "max") normalization_function <- c( 5 , 5 , 5 , 5 ) q_indifference <- c(2, 0.5 , 1 , 10) p_preference <- c(5 , 1 , 2 , 20) s_curve_change <- c("","","","") criteria_weights <- c(0.2 , 0.2 , 0.3 , 0.3) promethee123(alternatives, criteria, decision_matrix, min_max, normalization_function, q_indifference, p_preference, s_curve_change, criteria_weights) ```

promethee123 documentation built on Dec. 21, 2020, 5:06 p.m.