sov-trotter / fuzzy.jl

Fuzzy Inference System in julia

Fuzzy

=============

Mamdani and Sugeno type Fuzzy Inference System in julia. This code is based in Lepisma.

Install

pkg> add Fuzzy

QuickStart

julia> using Fuzzy

Mamdani FIS

• Create input, output membership functions and rules

julia> input_a = Dict("small" => TriangularMF(1, 2, 3), "large" => TriangularMF(4, 5, 6))
julia> input_b = Dict("small" => TriangularMF(1, 2, 3))

julia> inputs = [input_a, input_b]
julia> output = Dict("small" => TriangularMF(1, 2, 3))

julia> rule = Rule(["large", "small"], "small")
julia> rules = [rule]

• Create FIS

julia> fis = FISMamdani(inputs, output, rules)

• Find output

julia> in_vals = [4.7, 2.3]
julia> eval_fis(fis, in_vals)

Sugeno FIS

• Create input membership functions and rules with consequence coefficients

julia> input_a = Dict("small" => TriangularMF(1, 2, 3), "large" => TriangularMF(5, 6, 7))
julia> input_b = Dict("small" => TriangularMF(1, 2, 3))

julia> inputs = [input_a, input_b]

julia> rule1 = Rule(["large", "small"], [1.0, 1.0, 1.0])
julia> rule2 = Rule(["small", "small"], [0.0, 0.0, 5.0])
julia> rules = [rule]

• Create FIS

julia> fis = FISSugeno(inputs, rules)

• Find output

julia> in_vals = [2.3, 1.2]
julia> eval_fis(fis, in_vals)

Features

• FIS

  • Mamdani
  • Sugeno

• Membership functions

  • Triangular
  • Gaussian
  • Bell
  • Trapezoidal
  • Sigmoid

• Defuzzification

  • Mean of Maximum
  • Weighted Average (default)
  • Centroid (coming soon)

• T-Norm

  • Minimum (MIN)
  • Algebraic product (A-PROD)
  • Bounded difference (B-DIF)
  • Drastic product (D-PROD)
  • Einstein product (E-PROD)
  • Hamacher product (H-PROD)

• S-Norm

  • Maximum (MAX)
  • Algebraic sum (A-SUM)
  • Bounded sum (B-SUM)
  • Drastic sum (D-SUM)
  • Einstein sum (E-SUM)
  • Hamacher sum (H-SUM)

Prepare to plot your Fuzzy sets

• Create points to use in plot packages using the chart_prepare

julia> input_a = Dict("small" => TriangularMF(1, 2, 3), "large" => TriangularMF(5, 6, 7));
julia> x = range(0, 8, length = 100);
julia> data = chart_prepare(input_a, x)
julia> using Plots
julia> plot(x, data["values"], label = data["names"])

License

MIT