added semielliptic membership functions (#25)

Author: lucaferranti

docs/src/changelog.md

@@ -2,6 +2,10 @@
 
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/), and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## Unreleased
+
+- ![](https://img.shields.io/badge/new%20feature-green.svg) added semi-elliptic membership functions
+
 ## v0.1.2 -- 2023-03-12
 
 [view release on GitHub](https://github.com/lucaferranti/FuzzyLogic.jl/releases/tag/v0.1.2)

src/FuzzyLogic.jl

@@ -18,7 +18,7 @@ include("readwrite.jl")
 
 export DifferenceSigmoidMF, LinearMF, GeneralizedBellMF, GaussianMF, ProductSigmoidMF,
        SigmoidMF, TrapezoidalMF, TriangularMF, SShapeMF, ZShapeMF, PiShapeMF,
-       PiecewiseLinearMF, WeightedMF, Type2MF, ..,
+       SemiEllipticMF, PiecewiseLinearMF, WeightedMF, Type2MF, ..,
        ProdAnd, MinAnd, LukasiewiczAnd, DrasticAnd, NilpotentAnd, HamacherAnd, EinsteinAnd,
        ProbSumOr, MaxOr, BoundedSumOr, DrasticOr, NilpotentOr, EinsteinOr, HamacherOr,
        MinImplication, ProdImplication,

src/membership_functions.jl

@@ -278,6 +278,31 @@ function (p::PiShapeMF)(x::T) where {T <: Real}
     return 2 * ((x - p.d) / (p.d - p.c))^2
 end
 
+"""
+Semi-elliptic membership function.
+
+### Fields
+
+$(TYPEDFIELDS)
+
+### Example
+
+```julia
+mf = SemiEllipticMF(5.0, 4.0)
+```
+"""
+struct SemiEllipticMF{T <: Real} <: AbstractMembershipFunction
+    "center."
+    cd::T
+    "semi-axis."
+    rd::T
+end
+function (semf::SemiEllipticMF)(x::Real)
+    cd, rd = semf.cd, semf.rd
+    cd - rd <= x <= cd + rd || return zero(x)
+    sqrt(1 - (cd - x)^2 / rd^2)
+end
+
 """
 Piecewise linear membership function.
 

test/test_membership_functions.jl

@@ -117,6 +117,15 @@ end
     @test mf(10) == eval(to_expr(mf, 10)) == 0
 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
+end
+
 @testset "Piecewise linear Membership function" begin
     mf = PiecewiseLinearMF([(1, 0), (2, 1), (3, 0), (4, 0.5), (5, 0), (6, 1)])
     @test mf(0.0) == eval(to_expr(mf, 0.0)) == 0