Utility functions

struct MCDMSetting
    df::Matrix
    weights::Array{Float64, 1}
    fns::Array{Function, 1}
end

Immutable data structure for a MCDM setting.

Arguments

• df::Matrix: The decision matrix in type of Matrix.
• weights::Array{Float64,1}: Array of weights for each criterion.
• fns::Array{<:Function, 1}: Array of functions. The elements are either minimum or maximum.

Description

Many methods including Topsis, Electre, Waspas, etc., use a decision matrix, weights, and directions of optimizations in types of Matrix and Vector, respectively. The type MCDMSetting simply holds these information to pass them into methods easly. Once a MCDMSetting object is created, the problem can be passed into several methods like topsis(setting), electre(setting), waspas(setting), etc.

# Examples

julia> df = DataFrame();
julia> df[:, :x] = Float64[9, 8, 7];
julia> df[:, :y] = Float64[7, 7, 8];
julia> df[:, :z] = Float64[6, 9, 6];
julia> df[:, :q] = Float64[7, 6, 6];

julia> w = Float64[4, 2, 6, 8];

julia> fns = [maximum, maximum, maximum, maximum];

julia> setting = MCDMSetting(Matrix(df), w, fns)

julia> result = topsis(setting);
julia> # Same result can be obtained using
julia> result2 = mcdm(setting, TopsisMethod())

    mcdm(df, w, fns, method)

Perform selected method for a given decision matrix, weight vector, and function list.

Arguments:

• df::Matrix: n × m matrix of decision matrix in type of Matrix.
• weights::Array{Float64, 1}: m-vector of weights for criteria.
• fs::Array{Function, 1}: m-vector of functions that are either maximize or minimize for each single criterion.
• method::MCDMMethod: Preferred MCDMMethod.

Description

The method is one of the subtypes of MCDMMethod type. See examples.

Output

• ::MCDMResult: An object derived from subtypes of MCDMResult type.

Examples

julia> subtypes(MCDMMethod)
23-element Vector{Any}:
 ArasMethod
 CocosoMethod
 CodasMethod
 CoprasMethod
 CriticMethod
 EdasMethod
 ElectreMethod
 GreyMethod
 LMAWMethod
 LOPCOWMethod
 MabacMethod
 MaircaMethod
 MarcosMethod
 MERECMethod
 MooraMethod
 MoosraMethod
 OCRAMethod
 PIVMethod
 PrometheeMethod
 PSIMethod
 ROVMethod
 SawMethod
 TopsisMethod
 VikorMethod
 WaspasMethod
 WPMMethod


julia> # mcdm() for Topsis:
julia> # mcdm(df, w, fns, TopsisMethod())

julia> # mcdm() for Saw:
julia> # mcdm(df, w, fns, SawMethod())

julia> # mcdm() with optional parameters:
julia> # mcdm(df, w, fns, GreyMethod(0.6))

mcdm(setting, method = TopsisMethod())

Perform selected method for a given decision matrix, weight vector, and function list.

Arguments:

• setting::MCDMSetting: MCDMSetting object that holds the decision matrix, weight vector, and functions.
• method::MCDMMethod: Preferred MCDMMethod. The default is TopsisMethod().

Description

The method is one of the subtypes of MCDMMethod type. See examples.

Output

• ::MCDMResult: An object derived from subtypes of MCDMResult type.

Examples

julia> # mcdm() for Topsis:
julia> # mcdm(setting, TopsisMethod())

julia> # mcdm() for Saw:
julia> # mcdm(setting, SawMethod())

julia> # mcdm() with optional parameters:
julia> # mcdm(setting, GreyMethod(0.6))

    summary(decisionMat, weights, fns, methods)

Apply more methods for a given decision problem. The methods accept standart number of arguments.

Arguments:

• decisionMat::Matrix: n × m matrix of objective values for n candidate (or strategy) and m criteria
• weights::Array{Float64, 1}: m-vector of weights that sum up to 1.0. If the sum of weights is not 1.0, it is automatically normalized.
• fns::Array{<:Function, 1}: m-vector of function that are either minimize or maximize.
• methods::Array{Symbol, 1}: Array of symbols. The elements can be :topsis, :electre, :cocoso, :copras, :moora, :vikor, :grey, :aras, :saw, :wpm, :waspas, :edas, :marcos, :mabac, :mairca, :copras, :critic

Description

This method outputs a summarized output using more than MCDM methods in a comparable way. 

# Output

• ::Matrix: A DataFrame object, methods in columns, and alternatives in rows. Green check symbol indicates the selected alternative as the best by the corresponding method.

Examples

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> methods = [:topsis, :electre, :vikor, :moora, :cocoso, :wpm, :waspas]

julia> w  = [0.036, 0.192, 0.326, 0.326, 0.12];

julia> fns = [maximum, minimum, maximum, maximum, maximum];


julia> result = summary(Matrix(df), w, fns, methods)
3×7 DataFrame
 Row │ topsis  electre  cocoso  moora   vikor   wpm     waspas 
     │ String  String   String  String  String  String  String 
─────┼─────────────────────────────────────────────────────────
   1 │                           ✅      ✅
   2 │  ✅      ✅       ✅                      ✅      ✅
   3 │

    summary(setting, methods)

Apply more methods for a given decision problem. The methods accept standart number of arguments.

Arguments:

• setting::MCDMSetting: MCDMSetting object.
• methods::Array{Symbol, 1}: Array of symbols. The elements can be :topsis, :electre, :cocoso, :copras, :moora, :vikor, :grey, :aras, :saw, :wpm, :waspas, :edas, :marcos, :mabac, :mairca, :copras, :critic

Description

This method outputs a summarized output using more than MCDM methods in a comparable way.