🤔 mcdm

mcdm is a Rust library to assist with solving Multiple-Criteria Decision Making (MCDM) problems. It provides a comprehensive set of tools for decision analysis, including normalization techniques, weighting methods, and ranking algorithms.

✨ Features

MCDM involves evaluating multiple conflicting criteria when making decisions. This library aims to provide various techniques to normalize data, assign weights to criteria, and rank alternatives. Below is a list of the components that have been implemented.

🔄 Normalization

Normalization ensures that criteria with different units of measurement can be compared on a common scale. Each method has a specific use case depending on the decision problem.

🌟 Name	📝 Description
Enhanced Accuracy	Technique proposed by Zeng and Yang in 2013 incorporating criterion's minimums and maximums into the computation.
Linear	Similiar to Max normalization, where profit criteria depend on the critions maximum value and cost criteria depend on criterion minimum value.
Logarithmic	Uses natural logarithm in the normalization.
Min-Max	Scales the values of each criterion between 0 and 1 (or another range) by using the minimum and maximum values of that criterion.
Max	Similiar to MinMax, but here each element is divided by the maximum value in the column
Nonlinear	Similiar to linear normalization, but relies on exponentiation of the criteria to help capture more complexitities in the criteria or when data distributions are skewed.
Sum	Uses the sum of each alternatives criterion.
Vector	Considers the root of the sum of squares for each criterion.
Zavadskas-Turskis	Convert different criteria into comparable units.

⚖️ Weighting

Weights reflect the relative importance of each criterion. Different weighting techniques help balance criteria appropriately in the decision-making process.

📊 Name	📝 Description
Entropy	Weights each criterion based on the entropy of all alternatives for the given criterion.
Equal	Assumes all criteria are of equal importance. Each criterion is assigned the same weight.
Method Based on the Removal Effects of Criiteria (MEREC)	Considers the redundancy or "information loss" when a criterion is removed. General idea assigns higher weights to criteria that cause more variation in the overall evaluation when excluded.
Standard Deviation	Criteria weights are derived from standard deviation across the criteria. This method leads to smaller weights for criteria that have similiar values.

📈 Ranking Methods

Ranking algorithms combine normalized data and weights to determine the best alternative. These methods aim to provide a clear ranking of alternatives based on the decision-maker's preferences.

🥇 Name	📝 Description
Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)	Conceptually says the best alternative should have the shortest geometric distance from the postivei ideal solution and the longest distance form the negative ideal solution.
Weighted Product Model	Ranks alternatives based on product of each weighted alternative.
Weighted Sum	Ranks alternatives based on the weighted sum of the alternatives criteria values.

🚀 Usage

To start using mcdm, add this to your Cargo.toml:

[dependencies]
mcdm = "0.1"

🧪 Example

Here’s an example demonstrating how to use the mcdm library for decision-making with the TOPSIS method:

use mcdm::{
    errors::McdmError,
    methods::{Rank, TOPSIS},
    normalization::{MinMax, Normalize},
    weights::{Equal, Weight},
    CriteriaType,
};
use ndarray::array;

fn main() -> Result<(), McdmError> {
    // Define the decision matrix (alternatives x criteria)
    let alternatives = array![[4.0, 7.0, 8.0], [2.0, 9.0, 6.0], [3.0, 6.0, 9.0]];
    let criteria_types = CriteriaType::from_vec(vec![-1, 1, 1])?;
    // Apply normalization using Min-Max
    let normalized_matrix = MinMax::normalize(&alternatives, &criteria_types)?;
    // Alternatively, use equal weights
    let equal_weights = Equal::weight(&normalized_matrix)?;
    // Apply the TOPSIS method for ranking
    let ranking = TOPSIS::rank(&normalized_matrix, &equal_weights)?;
    // Output the ranking
    println!("Ranking: {:.3?}", ranking);
    Ok(())
}

🤝 Contributing

Contributing is what makes the open source community thrive. Any contributions to enhance mcdm are welcome and greatly apprecaited!

If you have any suggestions that could make this project better, please feel free to fork the repo and create a pull request. You can also simply open an issue with the tag "enhancement".

Fork this repo
Create your feature branch (git checkout -b feature/new-decision-method)
Commit your changes (git commit -m 'Add new decision method')
Push to the remote branch (git push origin feature/new-decision-method)
Open a pull request

📄 License

Distributed under the MIT license. See LICENSE-MIT.txt for more information.

mcdm 0.1.5