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https://github.com/refiaa/topsis-py

Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for multi-criteria decision
https://github.com/refiaa/topsis-py

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Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for multi-criteria decision

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# TOPSIS Multi-Criteria Decision Making



This project implements the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for multi-criteria decision making. The project is structured into three main Python scripts: `data_loader.py`, `model_ranker.py`, and `topsis.py`. These scripts work together to load data, process it using the TOPSIS method, and rank models based on multiple criteria.



## Introduction to TOPSIS



TOPSIS is a multi-criteria decision analysis method that ranks alternatives based on their distance from an ideal solution. The method involves the following steps:



1. **Normalize the Decision Matrix**:

   Each criterion value is normalized to ensure comparability.



   $R_{ij} = \frac{X_{ij}}{\sqrt{\sum_{i=1}^{n} X_{ij}^2}}$



2. **Calculate the Weighted Normalized Decision Matrix**:

   Apply the weights to the normalized criteria.



   $V_{ij} = w_j \cdot R_{ij}$



3. **Determine the Positive and Negative Ideal Solutions**:

   Identify the best and worst values for each criterion.



    $A^+ = \{ \max(V_{ij}) \, | \, j \in J \}, \, \min(V_{ij}) \, | \, j \in J' \$



    $A^- = \{ \min(V_{ij}) \, | \, j \in J \}, \, \max(V_{ij}) \, | \, j \in J' \$



4. **Calculate the Separation Measures**:

   Compute the distance of each alternative from the positive and negative ideal solutions.



   $S_i^+ = \sqrt{\sum_{j=1}^{m} (V_{ij} - A_j^+)^2}$



   $S_i^- = \sqrt{\sum_{j=1}^{m} (V_{ij} - A_j^-)^2}$



5. **Calculate the Relative Closeness to the Ideal Solution**:

   Determine the relative closeness of each alternative to the ideal solution.



   $C_i^* = \frac{S_i^-}{S_i^+ + S_i^-}$



6. **Rank the Alternatives**:

   Rank the alternatives based on the relative closeness to the ideal solution.



## Scripts Explanation



### data_loader.py



This script is responsible for loading and preprocessing the data. The criteria, weights, and benefit criteria are dynamically loaded from environment variables.



- **load_data**: Reads the CSV file and extracts the decision matrix and model names.

- **preprocess_data**: Retrieves weights and benefit criteria from the environment variables.



### model_ranker.py



This script orchestrates the data loading, model ranking, and saving the results.



- **load_and_prepare_data**: Loads the data and prepares the decision matrix, weights, and benefit criteria.

- **rank_models**: Uses the TOPSIS class to rank the models.

- **gather_rankings**: Collects the rankings and prepares them for saving.

- **save_rankings**: Saves the rankings to a CSV file.



### topsis.py



This script implements the TOPSIS method.



- **normalize**: Normalizes the decision matrix.

- **apply_weights**: Applies the weights to the normalized matrix.

- **determine_ideal_solutions**: Determines the positive and negative ideal solutions.

- **calculate_separation_measures**: Calculates the separation measures.

- **calculate_scores**: Computes the relative closeness to the ideal solution.

- **rank**: Ranks the alternatives based on the calculated scores.



## Example Usage



Here is an example of how to run the script with the given environment variables and CSV data.



1. Create a `.env` file with the following content:



    ```plaintext

    CRITERIA=index1,index2,index3,index4

    WEIGHTS=0.25,0.25,0.25,0.25

    BENEFIT_CRITERIA=False,False,True,True

    INPUT_FILE=./data/sample.csv

    OUTPUT_FILE=./data/sample_ranked.csv

    ```



2. Create a CSV file `sample.csv` with the following content:



    ```csv

    Model,index1,index2,index3,index4

    Model_1,5.0,0.1,0.9,0.8

    Model_2,6.0,0.15,0.85,0.75

    Model_3,4.5,0.2,0.8,0.7

    Model_4,5.5,0.12,0.88,0.78

    Model_5,6.1,0.11,0.87,0.79

    ```



3. Run the script:



    ```python

    if __name__ == "__main__":

        input_file = os.getenv("INPUT_FILE")

        output_file_path = os.getenv("OUTPUT_FILE")

        ranker = ModelRanker(input_file, output_file_path)

        ranker.run()

    ```



This will read the input file, process the data using the TOPSIS method, and save the ranked models to the specified output file.