defmodule Descisionex.AnalyticHierarchy do
@moduledoc """
https://en.wikipedia.org/wiki/Analytic_hierarchy_process
"""
alias Descisionex.{AnalyticHierarchy, Helper}
defstruct comparison_matrix: [],
normalized_comparison_matrix: [],
criteria_weights: [],
criteria_num: 0,
alternatives: [],
alternatives_matrix: %{},
alternatives_weights: [],
alternatives_weights_by_criteria: [],
alternatives_num: 0,
criteria: []
def set_criteria(%AnalyticHierarchy{} = _data, []) do
raise ArgumentError, message: "Criteria must be not empty!"
end
@doc """
Set criteria for analytic hierarchy.
## Examples
iex> %Descisionex.AnalyticHierarchy{} |> Descisionex.AnalyticHierarchy.set_criteria([])
** (ArgumentError) Criteria must be not empty!
iex> %Descisionex.AnalyticHierarchy{} |> Descisionex.AnalyticHierarchy.set_criteria(["some", "criteria"])
%Descisionex.AnalyticHierarchy{
alternatives: [],
alternatives_matrix: %{},
alternatives_num: 0,
alternatives_weights: [],
alternatives_weights_by_criteria: [],
comparison_matrix: [],
criteria: ["some", "criteria"],
criteria_num: 2,
criteria_weights: [],
normalized_comparison_matrix: []
}
"""
def set_criteria(%AnalyticHierarchy{} = data, criteria) do
data |> Map.put(:criteria, criteria) |> Map.put(:criteria_num, Enum.count(criteria))
end
def set_alternatives(%AnalyticHierarchy{} = _data, []) do
raise ArgumentError, message: "Alternatives must be not empty!"
end
@doc """
Set alternatives for analytic hierarchy.
## Examples
iex> %Descisionex.AnalyticHierarchy{} |> Descisionex.AnalyticHierarchy.set_alternatives([])
** (ArgumentError) Alternatives must be not empty!
iex> %Descisionex.AnalyticHierarchy{} |> Descisionex.AnalyticHierarchy.set_alternatives(["some", "alternatives"])
%Descisionex.AnalyticHierarchy{
alternatives: ["some", "alternatives"],
alternatives_matrix: %{},
alternatives_num: 2,
alternatives_weights: [],
alternatives_weights_by_criteria: [],
comparison_matrix: [],
criteria: [],
criteria_num: 0,
criteria_weights: [],
normalized_comparison_matrix: []
}
"""
def set_alternatives(%AnalyticHierarchy{} = data, alternatives) do
data
|> Map.put(:alternatives, alternatives)
|> Map.put(:alternatives_num, Enum.count(alternatives))
end
@doc """
Set alternatives matrix for analytic hierarchy (criteria must be set!).
## Examples
iex> %Descisionex.AnalyticHierarchy{} |> Descisionex.AnalyticHierarchy.set_alternatives_matrix([[1, 2], [3, 4]])
** (ArgumentError) Criteria must be set!
iex> %Descisionex.AnalyticHierarchy{} |> Descisionex.AnalyticHierarchy.set_criteria(["some", "criteria"]) |> Descisionex.AnalyticHierarchy.set_alternatives_matrix([[1, 2], [3, 4]])
%Descisionex.AnalyticHierarchy{
alternatives: [],
alternatives_matrix: %{"criteria" => [3, 4], "some" => [1, 2]},
alternatives_num: 0,
alternatives_weights: [],
alternatives_weights_by_criteria: [],
comparison_matrix: [],
criteria: ["some", "criteria"],
criteria_num: 2,
criteria_weights: [],
normalized_comparison_matrix: []
}
"""
def set_alternatives_matrix(%AnalyticHierarchy{} = data, matrix) do
if data.criteria_num == 0, do: raise(ArgumentError, message: "Criteria must be set!")
tagged =
Enum.map(Enum.with_index(data.criteria), fn {criteria, index} ->
{criteria, Enum.at(matrix, index)}
end)
|> Enum.into(%{})
data |> Map.put(:alternatives_matrix, tagged)
end
def set_tagged_alternatives_matrix(%AnalyticHierarchy{} = data, matrix) do
if data.criteria_num == 0, do: raise(ArgumentError, message: "Criteria must be set!")
if matrix == [] || matrix == %{}, do: raise(ArgumentError, message: "Incorrect matrix!")
data |> Map.put(:alternatives_matrix, matrix)
end
@doc """
Normalizes comparison matrix for analytic hierarchy (criteria must be set, such as comparison matrix!).
## Examples
iex> %Descisionex.AnalyticHierarchy{} |> Descisionex.AnalyticHierarchy.set_criteria(["some", "criteria"]) |> Descisionex.AnalyticHierarchy.normalize_comparison_matrix()
** (ArgumentError) Comparison matrix must be set!
iex> %Descisionex.AnalyticHierarchy{comparison_matrix: [[1, 2], [3, 4]]} |> Descisionex.AnalyticHierarchy.set_criteria(["some", "criteria"]) |> Descisionex.AnalyticHierarchy.normalize_comparison_matrix()
%Descisionex.AnalyticHierarchy{
alternatives: [],
alternatives_matrix: %{},
alternatives_num: 0,
alternatives_weights: [],
alternatives_weights_by_criteria: [],
comparison_matrix: [[1, 2], [3, 4]],
criteria: ["some", "criteria"],
criteria_num: 2,
criteria_weights: [],
normalized_comparison_matrix: [[0.25, 0.333], [0.75, 0.667]]
}
"""
def normalize_comparison_matrix(%AnalyticHierarchy{} = data) do
size = data.criteria_num
if size == 0, do: raise(ArgumentError, message: "Criteria must be set!")
if data.comparison_matrix == [],
do: raise(ArgumentError, message: "Comparison matrix must be set!")
normalized = Helper.normalize(data.comparison_matrix, size)
Map.put(data, :normalized_comparison_matrix, normalized)
end
@doc """
Calculates weights for normalized comparison matrix for analytic hierarchy (criteria must be set, such as comparison matrix!).
## Examples
iex> %Descisionex.AnalyticHierarchy{comparison_matrix: [[1, 2], [3, 4]]} |> Descisionex.AnalyticHierarchy.set_criteria(["some", "criteria"]) |> Descisionex.AnalyticHierarchy.calculate_criteria_weights()
** (ArgumentError) Comparison matrix must be normalized!
iex> %Descisionex.AnalyticHierarchy{comparison_matrix: [[1, 2], [3, 4]]} |> Descisionex.AnalyticHierarchy.set_criteria(["some", "criteria"]) |> Descisionex.AnalyticHierarchy.normalize_comparison_matrix() |> Descisionex.AnalyticHierarchy.calculate_criteria_weights()
%Descisionex.AnalyticHierarchy{
alternatives: [],
alternatives_matrix: %{},
alternatives_num: 0,
alternatives_weights: [],
alternatives_weights_by_criteria: [],
comparison_matrix: [[1, 2], [3, 4]],
criteria: ["some", "criteria"],
criteria_num: 2,
criteria_weights: [[0.291], [0.709]],
normalized_comparison_matrix: [[0.25, 0.333], [0.75, 0.667]]
}
"""
def calculate_criteria_weights(%AnalyticHierarchy{} = data) do
size = data.criteria_num
if size == 0, do: raise(ArgumentError, message: "Criteria must be set!")
if data.normalized_comparison_matrix == [],
do: raise(ArgumentError, message: "Comparison matrix must be normalized!")
criteria_weights = Helper.calculate_weights(data.normalized_comparison_matrix, size)
Map.put(data, :criteria_weights, criteria_weights)
end
@doc """
Calculates alternatives weights by criteria for analytic hierarchy (criteria must be set, such as comparison matrix!).
## Examples
iex> %Descisionex.AnalyticHierarchy{comparison_matrix: [[1, 2], [3, 4]]} |> Descisionex.AnalyticHierarchy.set_criteria(["some", "criteria"]) |> Descisionex.AnalyticHierarchy.calculate_alternatives_weights_by_criteria()
** (ArgumentError) Alternatives matrix must be set!
iex> %Descisionex.AnalyticHierarchy{} |> Descisionex.AnalyticHierarchy.set_criteria(["some", "criteria"]) |> Descisionex.AnalyticHierarchy.set_alternatives(["some", "alternatives"]) |> Descisionex.AnalyticHierarchy.set_alternatives_matrix([[[1, 2, 3]], [[4, 5, 6]]]) |> Descisionex.AnalyticHierarchy.calculate_alternatives_weights_by_criteria()
%Descisionex.AnalyticHierarchy{
alternatives: ["some", "alternatives"],
alternatives_matrix: %{"criteria" => [[4, 5, 6]], "some" => [[1, 2, 3]]},
alternatives_num: 2,
alternatives_weights: [],
alternatives_weights_by_criteria: [[3.0, 3.0]],
comparison_matrix: [],
criteria: ["some", "criteria"],
criteria_num: 2,
criteria_weights: [],
normalized_comparison_matrix: []
}
"""
def calculate_alternatives_weights_by_criteria(%AnalyticHierarchy{} = data) do
if data.criteria_num == 0, do: raise(ArgumentError, message: "Criteria must be set!")
if data.alternatives_matrix == %{},
do: raise(ArgumentError, message: "Alternatives matrix must be set!")
alternatives_weights_by_criteria =
Enum.map(data.criteria, fn criteria ->
matrix = data.alternatives_matrix[criteria]
size = Enum.count(matrix)
weights =
matrix
|> Helper.normalize(size)
|> Helper.calculate_weights(size)
weights
end)
result = alternatives_weights_by_criteria |> Matrix.transpose() |> Enum.map(&List.flatten/1)
Map.put(data, :alternatives_weights_by_criteria, result)
end
@doc """
Calculates alternatives weights for analytic hierarchy (criteria must be set, such as comparison matrix and weights before must be calculated!).
## Examples
iex> %Descisionex.AnalyticHierarchy{comparison_matrix: [[1, 2], [3, 4]]} |> Descisionex.AnalyticHierarchy.set_criteria(["some", "criteria"]) |> Descisionex.AnalyticHierarchy.normalize_comparison_matrix() |> Descisionex.AnalyticHierarchy.set_alternatives(["some", "alternatives"]) |> Descisionex.AnalyticHierarchy.set_alternatives_matrix([[[1, 2, 3]], [[4, 5, 6]]]) |> Descisionex.AnalyticHierarchy.calculate_alternatives_weights_by_criteria() |> Descisionex.AnalyticHierarchy.calculate_alternatives_weights()
** (ArgumentError) Weights must be calculated before!
iex> %Descisionex.AnalyticHierarchy{comparison_matrix: [[1, 2], [3, 4]]} |> Descisionex.AnalyticHierarchy.set_criteria(["some", "criteria"]) |> Descisionex.AnalyticHierarchy.normalize_comparison_matrix() |> Descisionex.AnalyticHierarchy.calculate_criteria_weights() |> Descisionex.AnalyticHierarchy.set_alternatives(["some", "alternatives"]) |> Descisionex.AnalyticHierarchy.set_alternatives_matrix([[[1, 2, 3]], [[4, 5, 6]]]) |> Descisionex.AnalyticHierarchy.calculate_alternatives_weights_by_criteria() |> Descisionex.AnalyticHierarchy.calculate_alternatives_weights()
%Descisionex.AnalyticHierarchy{
alternatives: ["some", "alternatives"],
alternatives_matrix: %{"criteria" => [[4, 5, 6]], "some" => [[1, 2, 3]]},
alternatives_num: 2,
alternatives_weights: [3.0],
alternatives_weights_by_criteria: [[3.0, 3.0]],
comparison_matrix: [[1, 2], [3, 4]],
criteria: ["some", "criteria"],
criteria_num: 2,
criteria_weights: [[0.291], [0.709]],
normalized_comparison_matrix: [[0.25, 0.333], [0.75, 0.667]]
}
"""
def calculate_alternatives_weights(%AnalyticHierarchy{} = data) do
weights = data.criteria_weights
if weights == [], do: raise(ArgumentError, message: "Weights must be calculated before!")
alternatives_weights =
Enum.reduce(data.alternatives_weights_by_criteria, [], fn column, acc ->
product =
Enum.map(Enum.with_index(column), fn {number, index} ->
[weight | _] = Enum.at(weights, index)
Float.round(number * weight, 3)
end)
|> Enum.sum()
acc ++ [product]
end)
Map.put(data, :alternatives_weights, alternatives_weights)
end
end
