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Implement Cradis method
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‎CHANGELOG.md‎

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@@ -4,6 +4,7 @@
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- Remove redundant code in `saw`.
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- Add Julia v1.12 to GitHub workflows.
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- Add Borda count method.
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- Add CRADIS method.
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### 0.8.2

‎docs/src/mcdms.md‎

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@@ -202,4 +202,9 @@ JMcDM.bestworst
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## RAM
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```@docs
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JMcDM.ram
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```
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## CRADIS
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```@docs
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JMcDM.cradis
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```

‎src/JMcDM.jl‎

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@@ -134,6 +134,7 @@ include("ram.jl")
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include("copeland.jl")
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include("borda.jl")
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include("cradis.jl")
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include("fuzzy/fuzzy.jl")
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@@ -174,6 +175,7 @@ import .TODIM: todim, TODIMResult, TODIMMethod
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import .CILOS: cilos, CILOSResult
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import .IDOCRIW: idocriw, IDOCRIWResult
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import .RAM: ram, RAMResult, RAMMethod
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import .CRADIS: cradis, CRADISMethod, CRADISResult
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import .Borda: borda
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import .SCDM: LaplaceResult, MaximinResult, MaximaxResult, MinimaxResult, MiniminResult
@@ -219,6 +221,7 @@ export OCRAMethod
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export LMAWMethod
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export TODIMMethod
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export RAMMethod
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export CradisMethod
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export MCDMSetting
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export CILOSResult
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export IDOCRIWResult
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export RAMResult
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export CRADISResult
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#  export SCDM types
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export SCDMResult
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export idocriw
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export ram
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export borda
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export cradis
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#  export SCDM tools
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export laplace

‎src/cradis.jl‎

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module CRADIS
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import ..MCDMMethod, ..MCDMResult, ..MCDMSetting
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import ..Normalizations
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using ..Utilities: weightise, colmins, colmaxs, rowsums
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struct CradisMethod <: MCDMMethod
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normalization::G where {G<:Function}
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end
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CradisMethod() = CradisMethod(Normalizations.dividebycolumnmaxminnormalization)
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const CRADISMethod = CradisMethod
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struct CRADISResult <: MCDMResult
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decisionMat::Matrix
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normalizedDecisionMat::Matrix
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weights::Vector{Float64}
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weightedNormalizedDecisionMat::Matrix{Float64}
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tideal::Float64
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tantiideal::Float64
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idealAlternative::Vector{Float64}
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antiIdealAlternative::Vector{Float64}
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dplus::Matrix{Float64}
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dminus::Matrix{Float64}
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splus::Vector{Float64}
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sminus::Vector{Float64}
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splus0::Float64
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sminus0::Float64
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kplus::Vector{Float64}
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kminus::Vector{Float64}
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q::Vector{Float64}
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scores::Vector{Float64}
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ranking::Vector{Int64}
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bestIndex::Int64
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end
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export cradis, CRADISMethod, CRADISResult
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"""
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cradis(decisionMat::Matrix, weights::Array{Float64,1}, fs::Array{F,1}; normalization::G=Normalizations.dividebycolumnmaxminnormalization) where {F<:Function,G<:Function}
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# Description
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The CRADIS (Criteria Ranking and Decision Support) method is a multi-criteria decision-making
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technique that evaluates alternatives based on multiple criteria. It normalizes the decision
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matrix, applies weights to the criteria, and calculates scores for each alternative to determine
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their ranking.
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# Arguments
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- `decisionMat::Matrix`: A matrix representing the decision matrix, where rows correspond to
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alternatives and columns correspond to criteria.
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- `weights::Array{Float64,1}`: An array of weights for each criterion, indicating their relative
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importance.
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- `fs::Array{F,1}`: An array of functions that define the direction of optimization for each criterion
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(e.g., `maximum` for benefit criteria, `minimum` for cost criteria).
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- `normalization::G`: An optional normalization function to be applied to the decision matrix.
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Default is `Normalizations.dividebycolumnmaxminnormalization`.
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# References
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- Puška, A., I. Hodžić, and A. Štilić. "Evaluating the knowledge economies within the European
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Union: A global knowledge index ranking via entropy and CRADIS methodologies." International
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Journal of Knowledge and Innovation Studies 1.2 (2023): 103-115.
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"""
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function cradis(
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decisionMat::Matrix,
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weights::Array{Float64,1},
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fs::Array{F,1};
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normalization::G=Normalizations.dividebycolumnmaxminnormalization)::CRADISResult where {F<:Function,G<:Function}
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n, p = size(decisionMat)
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normalizedDecisionMat = normalization(decisionMat, fs)
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weightedNormalizedDecisionMat = weightise(normalizedDecisionMat, weights)
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t_ideal = maximum(weightedNormalizedDecisionMat)
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t_anti_ideal = minimum(weightedNormalizedDecisionMat)
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idealAlternative = colmaxs(weightedNormalizedDecisionMat)
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antiIdealAlternative = colmins(weightedNormalizedDecisionMat)
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dplus = Array{Float64,2}(undef, n, p)
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dminus = Array{Float64,2}(undef, n, p)
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for i in 1:n
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for j in 1:p
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dplus[i, j] = t_ideal - weightedNormalizedDecisionMat[i, j]
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dminus[i, j] = weightedNormalizedDecisionMat[i, j] - t_anti_ideal
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end
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end
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splus = rowsums(dplus)
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sminus = rowsums(dminus)
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splus0 = sum(t_ideal .- idealAlternative)
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sminus0 = sum(idealAlternative .- t_anti_ideal)
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kplus = splus0 ./ splus
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kminus = sminus ./ sminus0
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q = (kplus .+ kminus) ./ 2
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ranking = sortperm(q)
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bestIndex = ranking |> last
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return CRADISResult(
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decisionMat,
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normalizedDecisionMat,
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weights,
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weightedNormalizedDecisionMat,
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t_ideal,
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t_anti_ideal,
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idealAlternative,
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antiIdealAlternative,
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dplus,
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dminus,
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splus,
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sminus,
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splus0,
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sminus0,
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kplus,
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kminus,
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q,
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q,
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ranking,
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bestIndex)
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end
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function cradis(setting::MCDMSetting; normalization::G=Normalizations.dividebycolumnmaxminnormalization)::CRADISResult where {G<:Function}
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cradis(setting.df, setting.weights, setting.fns, normalization=normalization)
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end
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end # end of module CRADIS

‎test/mcdm/testcradis.jl‎

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@testset "Cradis" begin
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# This test data is taken from the paper
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# Puška, A., I. Hodžić, and A. Štilić. "Evaluating the knowledge economies within the European
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# Union: A global knowledge index ranking via entropy and CRADIS methodologies." International
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# Journal of Knowledge and Innovation Studies 1.2 (2023): 103-115.
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#
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# The implementation is also based on the same paper.
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eps = 0.01
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decmat = [
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79.60 67.40 64.70 43.50 66.10 67.80 79.40;
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84.00 64.90 63.20 43.70 59.80 67.60 78.00;
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69.80 58.70 58.60 34.10 56.50 55.80 61.60;
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77.50 50.60 67.10 41.70 65.10 55.30 68.90;
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74.00 60.70 59.50 32.10 57.60 58.30 68.40;
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83.10 63.40 59.10 39.10 55.80 65.70 73.90;
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79.80 57.50 63.50 50.30 70.80 73.60 83.40;
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79.90 64.20 62.50 43.30 71.10 63.40 76.50;
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84.30 68.20 61.30 50.70 71.80 66.70 85.80;
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78.50 55.20 53.50 45.70 65.20 65.50 75.30;
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75.70 63.70 61.10 47.30 61.90 66.50 79.40;
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72.80 47.00 47.20 34.80 53.00 52.50 63.90;
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70.60 67.10 47.80 34.90 56.70 66.20 67.00;
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70.40 60.30 55.30 42.90 62.40 72.30 81.80;
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75.40 62.40 52.40 42.30 55.50 59.70 68.70;
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80.50 62.80 59.30 32.60 63.10 63.30 71.70;
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79.30 58.20 56.90 32.60 62.20 62.40 73.90;
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77.20 64.10 66.40 45.90 72.60 65.40 82.40;
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78.20 52.70 58.00 46.70 71.50 68.50 73.80;
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83.80 68.10 63.00 48.80 71.60 65.60 80.60;
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83.40 55.30 54.80 31.60 57.90 57.80 69.30;
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85.70 62.10 63.30 34.90 57.30 59.50 77.20;
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60.20 57.70 55.00 32.00 54.20 58.90 64.60;
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80.10 69.10 58.30 30.50 54.20 56.60 69.00;
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82.40 65.50 61.40 39.80 63.70 62.60 75.50;
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79.10 59.70 55.40 37.40 62.00 60.40 73.10;
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82.30 61.20 62.40 54.70 72.40 68.10 85.70
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]
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normalized_expected = [
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0.929 0.975 0.964 0.795 0.910 0.921 0.925;
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0.980 0.939 0.942 0.799 0.824 0.918 0.909;
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0.814 0.849 0.873 0.623 0.778 0.758 0.718;
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0.904 0.732 1.000 0.762 0.897 0.751 0.803;
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0.863 0.878 0.887 0.587 0.793 0.792 0.797;
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0.970 0.918 0.881 0.715 0.769 0.893 0.861;
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0.931 0.832 0.946 0.920 0.975 1.000 0.972;
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0.932 0.929 0.931 0.792 0.979 0.861 0.892;
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0.984 0.987 0.914 0.927 0.989 0.906 1.000;
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0.916 0.799 0.797 0.835 0.898 0.890 0.878;
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0.883 0.922 0.911 0.865 0.853 0.904 0.925;
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0.849 0.680 0.703 0.636 0.730 0.713 0.745;
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0.824 0.971 0.712 0.638 0.781 0.899 0.781;
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0.821 0.873 0.824 0.784 0.860 0.982 0.953;
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0.880 0.903 0.781 0.773 0.764 0.811 0.801;
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0.939 0.909 0.884 0.596 0.869 0.860 0.836;
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0.925 0.842 0.848 0.596 0.857 0.848 0.861;
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0.901 0.928 0.990 0.839 1.000 0.889 0.960;
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0.912 0.763 0.864 0.854 0.985 0.931 0.860;
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0.978 0.986 0.939 0.892 0.986 0.891 0.939;
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0.973 0.800 0.817 0.578 0.798 0.785 0.808;
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1.000 0.899 0.943 0.638 0.789 0.808 0.900;
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0.702 0.835 0.820 0.585 0.747 0.800 0.753;
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0.935 1.000 0.869 0.558 0.747 0.769 0.804;
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0.961 0.948 0.915 0.728 0.877 0.851 0.880;
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0.923 0.864 0.826 0.684 0.854 0.821 0.852;
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0.960 0.886 0.930 1.000 0.997 0.925 0.999
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]
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weighted_normalized_expected = [
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0.0260 0.0878 0.0990 0.2943 0.1216 0.1365 0.1179;
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0.0275 0.0845 0.0967 0.2957 0.1100 0.1361 0.1158;
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0.0228 0.0765 0.0896 0.2307 0.1040 0.1124 0.0915;
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0.0253 0.0659 0.1027 0.2821 0.1198 0.1114 0.1023;
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0.0242 0.0791 0.0910 0.2172 0.1060 0.1174 0.1016;
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0.0272 0.0826 0.0904 0.2645 0.1027 0.1323 0.1097;
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0.0261 0.0749 0.0971 0.3403 0.1303 0.1482 0.1239;
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0.0261 0.0836 0.0956 0.2930 0.1308 0.1277 0.1136;
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0.0276 0.0888 0.0938 0.3430 0.1321 0.1343 0.1274;
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0.0257 0.0719 0.0818 0.3092 0.1200 0.1319 0.1118;
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0.0247 0.0830 0.0935 0.3200 0.1139 0.1339 0.1179;
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0.0238 0.0612 0.0722 0.2354 0.0975 0.1057 0.0949;
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0.0231 0.0874 0.0731 0.2361 0.1043 0.1333 0.0995;
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0.0230 0.0785 0.0846 0.2902 0.1148 0.1456 0.1215;
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0.0246 0.0813 0.0802 0.2862 0.1021 0.1202 0.1020;
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0.0263 0.0818 0.0907 0.2206 0.1161 0.1275 0.1065;
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0.0259 0.0758 0.0870 0.2206 0.1145 0.1257 0.1097;
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0.0252 0.0835 0.1016 0.3105 0.1336 0.1317 0.1224;
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0.0256 0.0686 0.0887 0.3160 0.1316 0.1380 0.1096;
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0.0274 0.0887 0.0964 0.3302 0.1318 0.1321 0.1197;
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0.0273 0.0720 0.0838 0.2138 0.1066 0.1164 0.1029;
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0.0280 0.0809 0.0968 0.2361 0.1054 0.1198 0.1146;
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0.0197 0.0752 0.0841 0.2165 0.0997 0.1186 0.0959;
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0.0262 0.0900 0.0892 0.2064 0.0997 0.1140 0.1025;
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0.0269 0.0853 0.0939 0.2693 0.1172 0.1261 0.1121;
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0.0259 0.0778 0.0848 0.2530 0.1141 0.1216 0.1086;
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0.0269 0.0797 0.0955 0.3701 0.1332 0.1371 0.1273
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]
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s_plus_expected = [
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1.7074, 1.7242, 1.8631, 1.7811, 1.8541, 1.7811, 1.6498, 1.7201, 1.6435, 1.7383,
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1.7036, 1.8997, 1.8337, 1.7323, 1.7939, 1.8211, 1.8314, 1.6820, 1.7126, 1.6644,
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1.8678, 1.8088, 1.8808, 1.8626, 1.7597, 1.8049, 1.6208
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]
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s_minus_expected = [
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0.7454, 0.7286, 0.5897, 0.6718, 0.5987, 0.6717, 0.8031, 0.7327, 0.8093, 0.7146,
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0.7492, 0.5531, 0.6191, 0.7206, 0.6589, 0.6317, 0.6215, 0.7708, 0.7403, 0.7885,
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0.5850, 0.6440, 0.5720, 0.5902, 0.6931, 0.6479, 0.8321
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]
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k_plus_expected = [
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0.9316, 0.9225, 0.8537, 0.8930, 0.8579, 0.8930, 0.9641, 0.9247, 0.9678, 0.9150,
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0.9336, 0.8373, 0.8674, 0.9182, 0.8867, 0.8734, 0.8685, 0.9456, 0.9288, 0.9557,
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0.8516, 0.8794, 0.8457, 0.8539, 0.9039, 0.8813, 0.9814
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]
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k_minus_expected = [
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0.8645, 0.8450, 0.6839, 0.7791, 0.6943, 0.7790, 0.9314, 0.8497, 0.9386, 0.8287,
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0.8689, 0.6414, 0.7181, 0.8357, 0.7642, 0.7326, 0.7207, 0.8939, 0.8585, 0.9144,
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0.6785, 0.7469, 0.6634, 0.6845, 0.8039, 0.7515, 0.9650
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]
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q_expected = [
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0.8981, 0.8838, 0.7688, 0.8361, 0.7761, 0.8360, 0.9477, 0.8872, 0.9532, 0.8719,
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0.9013, 0.7393, 0.7927, 0.8769, 0.8254, 0.8030, 0.7946, 0.9198, 0.8937, 0.9350,
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0.7650, 0.8131, 0.7545, 0.7692, 0.8539, 0.8164, 0.9732
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]
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rank_expected = [
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7, 10, 24, 14, 22, 15, 3, 9, 2, 12, 6, 27, 21, 11, 16, 19, 20, 5, 8, 4, 25, 18, 26, 23, 13, 17, 1
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]
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weights = [0.0280, 0.0900, 0.1027, 0.3701, 0.1336, 0.1482, 0.1274]
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dirs = [maximum for i in 1:7]
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result = cradis(decmat, weights, dirs)
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@test isapprox(result.normalizedDecisionMat, normalized_expected, atol=eps)
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@test isapprox(result.weightedNormalizedDecisionMat, weighted_normalized_expected, atol=eps)
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@test isapprox(result.splus, s_plus_expected, atol=eps)
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@test isapprox(result.sminus, s_minus_expected, atol=eps)
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@test isapprox(result.kplus, k_plus_expected, atol=eps)
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@test isapprox(result.kminus, k_minus_expected, atol=eps)
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@test isapprox(result.q, q_expected, atol=eps)
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@test result.scores == result.q
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@test result.bestIndex == 27
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ranks = similar(result.ranking)
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for (r, idx) in enumerate(reverse(result.ranking))
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ranks[idx] = r
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end
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@test ranks == rank_expected
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end

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