add singleton mf and missing code generation function for semielliptic mf (#32)

Author: lucaferranti

docs/src/changelog.md

@@ -4,7 +4,7 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 
 ## Unreleased
 
-- ![](https://img.shields.io/badge/new%20feature-green.svg) added semi-elliptic membership functions
+- ![](https://img.shields.io/badge/new%20feature-green.svg) added semi-elliptic and singleton membership functions
 - ![](https://img.shields.io/badge/new%20feature-green.svg) added `gensurf` to plot generating surface
 - ![](https://img.shields.io/badge/bugfix-purple.svg) fix plotting of systems with several rules and membership functions.
 

src/FuzzyLogic.jl

@@ -17,7 +17,7 @@ include("tojulia.jl")
 include("readwrite.jl")
 
 export DifferenceSigmoidMF, LinearMF, GeneralizedBellMF, GaussianMF, ProductSigmoidMF,
-       SigmoidMF, TrapezoidalMF, TriangularMF, SShapeMF, ZShapeMF, PiShapeMF,
+       SigmoidMF, SingletonMF, TrapezoidalMF, TriangularMF, SShapeMF, ZShapeMF, PiShapeMF,
        SemiEllipticMF, PiecewiseLinearMF, WeightedMF, Type2MF, ..,
        ProdAnd, MinAnd, LukasiewiczAnd, DrasticAnd, NilpotentAnd, HamacherAnd, EinsteinAnd,
        ProbSumOr, MaxOr, BoundedSumOr, DrasticOr, NilpotentOr, EinsteinOr, HamacherOr,

src/membership_functions.jl

@@ -2,6 +2,26 @@
 abstract type AbstractPredicate end
 abstract type AbstractMembershipFunction <: AbstractPredicate end
 
+"""
+Singleton membership function. Equal to one at a single point and zero elsewhere.
+
+### Fields
+
+$(TYPEDFIELDS)
+
+### Example
+
+```julia
+mf = SingletonMF(4)
+```
+
+"""
+struct SingletonMF{T <: Real} <: AbstractMembershipFunction
+    "Point at which the membership function has value 1."
+    c::T
+end
+(mf::SingletonMF)(x::Real) = mf.c == x ? one(x) : zero(x)
+
 """
 Generalized Bell membership function ``\\frac{1}{1+\\vert\\frac{x-c}{a}\\vert^{2b}}``.
 

src/plotting.jl

@@ -6,6 +6,16 @@ using RecipesBase
     x -> mf(x), low, high
 end
 
+# special case: singleton mf
+@recipe function f(mf::SingletonMF, low::Real, high::Real)
+    legend --> nothing
+    line --> :stem
+    marker --> :circle
+    markersize --> 10
+    xlims --> (low, high)
+    [mf.c], [1]
+end
+
 @recipe function f(mf::Type2MF, low::Real, high::Real)
     legend --> nothing
     @series begin

src/tojulia.jl

@@ -126,6 +126,8 @@ end
 # MEMBERSHIP FUNCTIONS CODE GENERATION #
 ########################################
 
+to_expr(mf::SingletonMF, x = :x) = :($x == $(mf.c) ? one($x) : zero($x))
+
 to_expr(mf::GaussianMF, x = :x) = :(exp(-($x - $(mf.mu))^2 / $(2 * mf.sig^2)))
 function to_expr(mf::TriangularMF, x = :x)
     :(max(min(($x - $(mf.a)) / $(mf.b - mf.a), ($(mf.c) - $x) / $(mf.c - mf.b)), 0))
@@ -196,6 +198,14 @@ function to_expr(p::PiShapeMF, x = :x)
       end)
 end
 
+function to_expr(se::SemiEllipticMF, x = :x)
+    :(if $(se.cd - se.rd) <= $x <= $(se.cd + se.rd)
+          sqrt(1 - ($(se.cd) - $x)^2 / $(se.rd)^2)
+      else
+          zero($x)
+      end)
+end
+
 function to_expr(plmf::PiecewiseLinearMF, x = :x)
     :(if $x <= $(plmf.points[1][1])
           $(float(plmf.points[1][2]))

test/test_membership_functions.jl

@@ -60,6 +60,15 @@ end
     @test f(2) == eval(to_expr(f, 2)) == 1 / (1 + exp(4))
 end
 
+@testset "Singleton MF" begin
+    f = SingletonMF(4)
+    @test f(4) === eval(to_expr(f, 4)) === 1
+    @test f(4.0) === eval(to_expr(f, 4.0)) === 1.0
+    @test iszero(f(3))
+    @test iszero(eval(to_expr(f, 3)))
+    @test iszero(f(5))
+end
+
 @testset "Trapezoidal MF" begin
     f = TrapezoidalMF(1, 5, 7, 8)
     @test f(0) == eval(to_expr(f, 0)) == 0
@@ -119,11 +128,11 @@ end
 
 @testset "Semi-Elliptic MF" begin
     mf = SemiEllipticMF(5.0, 4.0)
-    @test mf(0) == 0
-    @test mf(1) == 0
-    @test mf(5) == 1
-    @test mf(9) == 0
-    @test mf(10) == 0
+    @test mf(0) == eval(to_expr(mf, 0)) == 0
+    @test mf(1) == eval(to_expr(mf, 1)) == 0
+    @test mf(5) == eval(to_expr(mf, 5)) == 1
+    @test mf(9) == eval(to_expr(mf, 9)) == 0
+    @test mf(10) == eval(to_expr(mf, 10)) == 0
 end
 
 @testset "Piecewise linear Membership function" begin