The ELECTRE (Elimination Et Choix Traduisant la Realité) method is a powerful approach to multi-criteria decision making. In an era where complex decisions often have to be taken, this method has proven its value in assisting decision making by considering various factors.
By using a systematic approach and analytical structure, the ELECTRE method allows decision makers to overcome the complexity and uncertainty often associated with various options.
In this article, we will explain the basic principles of the ELECTRE method, the steps for its implementation, as well as examples of how this method can be applied in various real contexts.
What is the Electre Method
The ELECTRE method (Elimination Et Choix Traduisant la Realité) is an approach to multi-criteria decision making used to select the best alternative from a number of available options.
By considering several criteria, this method eliminates less suitable alternatives and selects the ones that best match predetermined preferences.
ELECTRE provides a systematic framework for analyzing decision complexity by integrating diverse information and supporting decision makers in dealing with uncertainty.
Electre Method Steps
- Conduct pairwise comparisons between each alternative on each criterion, then the results are normalized on a comparable scale.
- Give weight to each criterion to describe the relative level of importance (wi). This is done by multiplying each column of the X matrix by the weights set by the decision maker.
- Determine the set of concordance and discordance.
For each pair of alternatives k and l (with kl = 1, 2, 3, …, m and k ≠ l), the set of criteria j is divided into two groups: concordance and discordance. A criterion in an alternative is considered concordance if:
On the other hand, a complementary group of these is discordance, which is when:
- Determine the concordance and discordance matrices.
To calculate the value of the elements in the concordance matrix, it is done by adding up the weights included in the concordance group. Mathematically, this step can be explained as follows:
In determining the values of the elements in the discordance matrix, the step is to divide the maximum difference in the value of the criteria included in the discordance group by the maximum difference in the values of all existing criteria. Mathematically, this step can be described as follows:
- Next, the next step is to determine the dominant concordance and discordance matrices.
Dominance in the concordance matrix is applied using a threshold value for the concordance index. This is done by comparing each element value in the concordance matrix with that threshold value. For example, an element Ak will dominate the element Al if the corresponding concordance index value Ckl exceeds a certain threshold value, namely c.
Ckl ≥ c
The threshold value can be set as the average of the concordance index, with the c value calculated as follows:
Based on the threshold value, the value of each element in the F matrix as the dominant concordance matrix can be determined as follows:
Similarly, dominance in the discordance matrix G is defined by utilizing the threshold value d. The d value is defined as follows:
Where the value of each element of matrix G as the dominant discordance matrix can be determined as follows:
- Next, the next step is to determine the aggregate dominant matrix (matrix E), using the following formula:
- After that, alternative elimination is carried out.
Matrix E gives a preference order for each alternative, where if ekl = 1, then alternative Ak is considered better than Al. Therefore, the row in matrix E that has the least number of ekl = 1 can be eliminated. Thus, the best alternative is the one that dominates the other alternatives.
Advantages of the Electre Method
The ELECTRE (Elimination Et Choix Traduisant la Realité) method is a powerful approach to multi-criteria decision making that has a number of significant advantages. The following is a more in-depth explanation of the advantages of the ELECTRE Method:
1. Focus on Preferences
One of the main advantages of the ELECTRE Method is its focus on preferences or relative preferences between alternatives. This method allows decision makers to express their level of preference for one alternative compared to another, which better reflects the complexity of the real world.
2. Multi-Criteria Handling Capability
ELECTRE is specifically designed to address situations where there are many criteria to consider in decision making. In this context, this method is very useful because it can integrate various important aspects or factors in one framework.
3. Uncertainty and Ambiguity
Decisions often have to be taken in situations full of uncertainty and ambiguity. ELECTRE can help decision makers overcome this uncertainty by providing a systematic and analytical framework, so they can feel more confident in choosing alternatives.
4. Ability to Handle Different Scales
This method is able to handle criteria with different scales, including interval and ordinal scales. This allows decision makers to incorporate different types of information into the decision-making process.
5. Grouping Concordance and Discordance
ELECTRE allows grouping between criteria that are “concordance” (concordance) and “discordance” (not appropriate). This helps in dealing with cases where some criteria may be more important than others or may conflict with each other.
6. Flexibility and Customization
This method is quite flexible and can be adapted to the preferences and needs of decision makers. In ELECTRE, parameters such as criteria weights, thresholds, etc. can be adjusted according to the relevant context.
7. Decision Transparency
ELECTRE provides transparency in the decision-making process. Final decisions are made based on clear and logical mathematical calculations, which enable decision makers to understand and explain the reasons behind the decision.
8. Take into account the threshold value
The use of threshold values in concordance and discordance dominance helps in controlling the level of decision sensitivity. This allows decision makers to adjust the extent to which they want to consider the differences between alternatives.
9. Eliminate Alternatives Gradually
The ELECTRE method allows the gradual elimination of alternatives through a dominant matrix calculation process. This helps in generating an increasingly relevant and shortlisted list of alternatives, according to defined preferences and criteria.
Disadvantages of the Electre Method
Like other approaches, the ELECTRE (Elimination Et Choix Traduisant la Realité) Method also has some drawbacks that need to be considered. Here are some disadvantages of this method:
1. Calculation Complexity
The ELECTRE method involves calculating dominant matrices, thresholds, and a fairly complicated elimination process. This can require significant time and effort in collecting data, calculating, and interpreting results.
2. Sensitivity to Parameters
Results from the ELECTRE Method may vary depending on how parameters such as criteria weights, thresholds, and threshold values are set. Errors in determining these parameters can lead to less accurate and relevant results.
3. Limitations on Subjective Comparisons
The pairwise comparison process in this method requires subjective comparisons between alternatives based on specified criteria. This can be a problem if decision makers do not have enough knowledge or if their preferences are unstable.
4. Possibility of Domination Effect is Lower
This method tends to give considerable weight to criteria that have lower dominance in the concordance and discordance groups. This can cause alternatives that are actually better in some aspects but less dominant, to be ignored.
5. Difficulty in Determining Thresholds
Determining threshold values for concordance and discordance dominance can be challenging. Incorrect threshold values can affect the final results and the interpretation of decisions.
6. Doesn’t Handle Criterion Interactions
The ELECTRE method does not explicitly handle interactions between criteria. This means that the impact of certain criteria on other criteria is not always recognized, which can result in decisions that do not fully reflect reality.
7. Possibility of Inconsistent Weighting
Assigning weights to criteria can be subjective and difficult to be consistent. Decision makers’ decisions in assigning weights can change over time or depend on certain situations.
8. Not Handling New Alternatives Well
If new alternatives emerge after the ELECTRE design stage, integration of these new alternatives into the method can become complicated and require significant recalculation.
9. Not taking into account the threshold value in all cases
In the elimination stage, this method only considers alternatives that have the least number of ekl = 1. However, this may not always produce optimal results in some contexts.
Example of Electre Method
The following is an example of applying the ELECTRE Method in multi-criteria decision making:
Context: You are a manager who has to choose a new official car for your company. You have four alternatives to evaluate: Car A, Car B, Car C, and Car D. You have three criteria to consider: Price, Fuel Consumption, and Safety.
Stage 1: Determining Criteria Weights: You assign weights to each criterion according to its level of importance. For example, you assign a weight of 0.4 to Price, 0.3 to Fuel Consumption, and 0.3 to Safety.
Stage 2: Pairwise Comparison: You perform a pairwise comparison between each alternative based on each criterion. For example, you compare the prices of Car A with Car B, Car A with Car C, and so on. You assign preference values based on a scale such as 1 (more important) to 7 (less important).
Stage 3: Normalization and Weighting: After pairwise comparison, the values are normalized and multiplied by the predetermined criteria weights. This produces a matrix that describes the relative preferences for each alternative and criterion.
Stage 4: Calculating Concordance and Discordance: You divide the alternatives into concordance and discordance groups based on differences in preferences. You calculate the concordance value by adding up the weights of the criteria included in the concordance group. Next, you calculate the discordance value by comparing the difference in the criteria values in the discordance group with the maximum existing difference.
Stage 5: Dominance and Threshold Matrix: You compare the concordance and discordance values with a predetermined threshold value. Alternatives with concordance values above the threshold and discordance values below the threshold will become part of the dominant matrix of concordance and discordance.
Stage 6: Aggregate Dominance Matrix (E Matrix): You combine the results of the concordance and discordance dominant matrices to produce an aggregate dominance matrix (E matrix), which ranks each alternative based on its dominance.
Stage 7: Elimination of Alternatives: You eliminate the alternative with the least amount of dominance in matrix E. The alternative with the lesser amount of dominance is considered the best alternative.
By following these steps, you can choose the alternative that best suits your preferences and established criteria. Keep in mind that the above example is a simplification and in practice, this process can be more complex depending on many factors.