A package for Multiple-criteria decision-making techniques in Julia.
Suppose a decision process has n alternatives and m criteria which are either to be maximized or minimized. Each single criterion has a weight 0 ≤ wᵢ ≤ 1 where sum of wᵢ is 1. fᵢ is either maximum or minimum. gⱼ(.) is the evolution function and it is choosen as gⱼ(x) = x in many methods. A multiple criteria decision problem can be represented using the decision table
without loss of generality. When A₁, A₂, ..., Aₙ are alternatives and C₁, C₂, ..., Cₙ are different situations of a single criterion then the decision problem is said to be single criterion decision problem. If Cⱼ are strategies of two game players then gⱼ(Aᵢ) is the gain of the row player when she selects the strategy i and the column player selects the strategy Cⱼ.
The package mainly focuses on solving these kinds of decision problems.
Multiple-criteria decision-making is an inter-discipline subject and there is a vast amount of research in the literature in this area. However, the existing software packages in this area are generally focused on a small subset of tools. JMcDM is a developer and researcher-friendly Julia package that combines the developed methods, utility functions for implementing new ones, and serves an environment for comparing results of multiple analyses.
Please type
julia> ]
(@v1.7) pkg> add JMcDM
or
julia> using Pkg
julia> Pkg.add("JMcDM")
in Julia REPL to install package in the standard way, otherwise, you can clone the repository and type
julia> ]
(@v1.7) pkg> develop .
to start developing new methods.
Since the Julia package manager installs all of the dependencies automatically, a standard user doesn't need to install them manually. The package dependencies are listed below:
- Requires.jl
for the main functionality. You can also install the
- GLPK
- JuMP
for zero-sum game problem solving and the data envelopment problem for the efficiency. You can also import
- DataFrames
manually for user-friendly interactions. All of the methods require a decision matrix in type of Matrix which can be converted from a DataFrame using the code
Matrix(df)
before calling any method.
Please check out the reference manual here.
- TOPSIS (Technique for Order Preference by Similarity to Ideal Solutions)
- ELECTRE (Elimination and Choice Translating Reality)
- DEMATEL (The Decision Making Trial and Evaluation Laboratory)
- MOORA Reference (Multi-Objective Optimization By Ratio Analysis)
- MOORA Ratio
- VIKOR (VlseKriterijumska Optimizcija I Kaompromisno Resenje in Serbian)
- AHP (Analytic Hierarchy Process)
- DEA (Data Envelopment Analysis)
- GRA (Grey Relational Analysis)
- Non-dominated Sorting
- SAW (Simple Additive Weighting) (aka WSM)
- ARAS (Additive Ratio Assessment)
- WPM (Weighted Product Model)
- WASPAS (Weighted Aggregated Sum Product ASsessment)
- EDAS (Evaluation based on Distance from Average Solution)
- MARCOS (Measurement Alternatives and Ranking according to COmpromise Solution)
- MABAC (Multi-Attributive Border Approximation area Comparison)
- MAIRCA (Multi Attributive Ideal-Real Comparative Analysis)
- COPRAS (COmplex PRoportional ASsessment)
- PROMETHEE (Preference Ranking Organization METHod for Enrichment of Evaluations)
- CoCoSo (Combined Compromise Solution)
- CRITIC (CRiteria Importance Through Intercriteria Correlation)
- Entropy
- CODAS (COmbinative Distance-based ASsessment)
- Copeland (For combining multiple ordering results)
- SD Method for determining weights of criteria
- ROV (Range of Value) Method
- PSI (Preference Selection Index) Method
- MOOSRA (Multi-Objective Optimization on the basis of Simple Ratio Analysis) Method
- MEREC (MEthod based on the Removal Effects of Criteria) for determining weights
- PIV (Proximity Indexed Value) method
- minimax
- maximin
- minimin
- maximax
- Savage
- Hurwicz
- MLE
- Laplace
- Expected Regret
- Game solver for zero sum games
-
UTA
-
MAUT
-
STEM
-
PAPRIKA
-
ANP (Analytical Network Process)
-
Goal Programming
-
MACBETH
-
COMET
-
SWARA
-
ORESTE
-
SMAA
-
TODIM
-
will be updated soon.
julia> using JMcDM
julia> df = DataFrame(
:age => [6.0, 4, 12],
:size => [140.0, 90, 140],
:price => [150000.0, 100000, 75000],
:distance => [950.0, 1500, 550],
:population => [1500.0, 2000, 1100]);
julia> using DataFrames
julia> df
3×5 DataFrame
Row │ age size price distance population
│ Float64 Float64 Float64 Float64 Float64
─────┼──────────────────────────────────────────────────
1 │ 6.0 140.0 150000.0 950.0 1500.0
2 │ 4.0 90.0 100000.0 1500.0 2000.0
3 │ 12.0 140.0 75000.0 550.0 1100.0
julia> w = [0.35, 0.15, 0.25, 0.20, 0.05];
julia> fns = [minimum, maximum, minimum, minimum, maximum];
julia> result = topsis(Matrix(df), w, fns);
julia> result.scores
3-element Array{Float64,1}:
0.5854753145549456
0.6517997936899308
0.41850223305822903
julia> result.bestIndex
2
alternatively
julia> result = mcdm(Matrix(df), w, fns, TopsisMethod())
or
julia> setting = MCDMSetting(Matrix(df), w, fns)
julia> result = topsis(setting)
or
julia> setting = MCDMSetting(Matrix(df), w, fns)
julia> result = mcdm(setting, TopsisMethod())
Here is a Jupyter Notebook for basic usage:
https://github.com/jbytecode/JMcDM/blob/main/notebook/basic-usage.ipynb
Please use the BibTeX entry:
@article{Satman2021,
doi = {10.21105/joss.03430},
url = {https://doi.org/10.21105/joss.03430},
year = {2021},
publisher = {The Open Journal},
volume = {6},
number = {65},
pages = {3430},
author = {Mehmet Hakan Satman and Bahadır Fatih Yıldırım and Ersagun Kuruca},
title = {JMcDM: A Julia package for multiple-criteria decision-making tools},
journal = {Journal of Open Source Software}
}
or citation string
Satman et al., (2021). JMcDM: A Julia package for multiple-criteria decision-making tools. Journal of Open Source Software, 6(65), 3430, https://doi.org/10.21105/joss.03430
to cite this software.
Do you want to contribute?
- Please create an issue first. In this issue, please specify the idea.
- Let the community discuss the new contribution in our Slack channel or the created issue.
If the community decision is yes, please
- Fork the repository
- Add the new code to this forked repository
- Make sure the tests are passed
- Send a pull request with a good description of functionality.
The TOPSIS method, defined in topsis.jl, is a basis for many methods and it can be followed before implementing a new one.
topsis()
takes the decision matrix, weights, and vector of directions of optimization as arguments. This function is defined intopsis.jl
.
function topsis(decisionMat::Matrix, weights::Array{Float64,1}, fns::Array{Function,1})::TopsisResult
topsis()
method has a return type ofTopsisResult
. Thisstruct
is defined intypes.jl
struct TopsisResult <: MCDMResult
decisionMatrix::Matrix
weights::Array{Float64,1}
normalizedDecisionMatrix::DataFrame
normalizedWeightedDecisionMatrix::DataFrame
bestIndex::Int64
scores::Array{Float64,1}
end
- Optionally, a
show
function can be derived for pretty-printing the result. These functions are defined inprint.jl
function Base.show(io::IO, result::TopsisResult)
println(io, "Scores:")
println(io, result.scores)
println(io, "Best indices:")
println(io, result.bestIndex)
end
Please read the issue Welcome to newcomers! for other implementation details.
If you find a bug or error, first report the problem in a new issue. If the problem is already addressed in an existing issue please follow the existing one.
Our Slack channel is JMcDM Slack Channel. Please feel free to ask about any problem using our Slack channel or issues. Julia Discourse is the JMcDM entry in Julia Discourse site and any thoughts, problems, and issues can also be discussed there.
Welcome!