JMcDM

A package for Multiple-criteria decision making techniques in Julia.

The problem

Suppose a decision process has $n$ alternatives and $m$ criteria which are either to be maximized or minimized. Each single criterion has a weight $0 <= w_i <= 1$ where sum of w_i is 1. f_i is either maximum or minimum. g_j(.) is evolution function and it is taken as g_j(x) = x in many methods. A multiple criteria decision problem can be represented using the decision table

Criteria C_1 C_2 ... C_m
Weights w_1 w_2 ... w_m
Functions f_1 f_2 ... f_m
A_1 g_1(A_1) g_2(A_1) ... g_m(S_A)
A_2 g_1(A_2) g_2(A_2) ... g_m(A_2)
⋮ ⋮ ⋮ ... ⋮
A_n g_1(A_n) g_2(A_n) ... g_m(A_n)

without loss of generality. When A_1, A_2, ..., A_n are alternatives and C_1, C_2, ..., C_m are different situations of a single criterion then the decision problem is said to be single criterion decision problem. If A_i and C_j are strategies of two game players then g_j(A_i) is the gain of the row player when she selects the strategy i and the column player selects the strategy C_j.

The package mainly focused on solving these kind of decision problems.

For whom?

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 development 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 analysis.

Installation

Please type

julia> ]
(@v1.5) pkg> add JMcDM

or

julia> using Pkg
julia> Pkg.add("JMcDM")

in Julia REPL.

Documentation

Please check out the reference manual here.

Implemented methods

MCDM Tools

  • TOPSIS (Technique for Order Preference by Similarity to Ideal Solutions)
  • ELECTRE (Elemination and Choice Translating Reality)
  • DEMATEL (The Decision Making Trial and Evaluation Laboratory)
  • MOORA (Multi-Objective Optimization By Ratio Analysis)
  • 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)

SCDM Tools

  • minimax
  • maximin
  • minimin
  • maximax
  • Savage
  • Hurwicz
  • MLE
  • Laplace
  • Expected Regret

Game

  • Game solver for zero sum games

Unimplemented methods

  • UTA

  • MAUT

  • STEM

  • PAPRIKA

  • ANP (Analytical Network Process)

  • Goal Programming

  • MACBETH

  • COMET

  • will be updated soon.

Example

julia> using JMcDM, DataFrames
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> 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 = makeminmax([minimum, maximum, minimum, minimum, maximum]);
julia> result = topsis(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(df, w, fns, TopsisMethod())

or

julia> setting = MCDMSetting(df, w, fns)
julia> result = topsis(setting)

or

julia> setting = MCDMSetting(df, w, fns)
julia> result = mcdm(setting, TopsisMethod())

Community guidelines

Do you want to contribute?

  • Please create an Issue first. In this issue, please specify the idea.
  • Let the community discuss the new contribution.

If the community decision is yes, please

  • Fork the repository
  • Send a pull request.

Please read the issue Welcome to newcomers! for implementation details.

Welcome!