Membership functions

struct DifferenceSigmoidMF{Ta1<:Real, Tc1<:Real, Ta2<:Real, Tc2<:Real} <: FuzzyLogic.AbstractMembershipFunction

Difference of two sigmoids. See also SigmoidMF.

Fields

• a1::Real: slope of the first sigmoid.

• c1::Real: center of the first sigmoid.

• a2::Real: slope of the second sigmoid.

• c2::Real: center of the second sigmoid.

Example

mf = DifferenceSigmoidMF(5, 2, 5, 7)

struct GaussianMF{Tm<:Real, Ts<:Real} <: FuzzyLogic.AbstractMembershipFunction

Gaussian membership function $e^{-\frac{(x-μ)²}{2σ²}}$.

Fields

• mu::Real: mean $μ$.

• sig::Real: standard deviation $σ$.

Example

mf = GaussianMF(5.0, 1.5)

struct GeneralizedBellMF{Ta<:Real, Tb<:Real, Tc<:Real} <: FuzzyLogic.AbstractMembershipFunction

Generalized Bell membership function $\frac{1}{1+\vert\frac{x-c}{a}\vert^{2b}}$.

Fields

• a::Real: Width of the curve, the bigger the wider.

• b::Real: Slope of the curve, the bigger the steeper.

• c::Real: Center of the curve.

Example

mf = GeneralizedBellMF(2, 4, 5)

struct LinearMF{Ta<:Real, Tb<:Real} <: FuzzyLogic.AbstractMembershipFunction

Linear membership function. If $a < b$, it is increasing (S-shaped), otherwise it is decreasing (Z-shaped).

Fields

• a::Real: foot.

• b::Real: shoulder.

Example

mf = LinearMF(2, 8)

struct PiShapeMF{Ta<:Real, Tb<:Real, Tc<:Real, Td<:Real} <: FuzzyLogic.AbstractMembershipFunction

Π-shaped membership function.

Fields

• a::Real: left foot.

• b::Real: left shoulder.

• c::Real: right shoulder.

• d::Real: right foot.

Example

mf = PiShapeMF(1, 4, 5, 10)

struct PiecewiseLinearMF{T<:Real, S<:Real} <: FuzzyLogic.AbstractMembershipFunction

Piecewise linear membership function.

Fields

• points::Array{Tuple{T, S}, 1} where {T<:Real, S<:Real}

Notes

If the input is between two points, its membership degree is computed by linear interpolation. If the input is before the first point, it has the same membership degree of the first point. If the input is after the last point, it has the same membership degree of the first point.

Example

mf = PiecewiseLinearMF([(1, 0), (2, 1), (3, 0), (4, 0.5), (5, 0), (6, 1)])

struct ProductSigmoidMF{T<:Real} <: FuzzyLogic.AbstractMembershipFunction

Product of two sigmoids. See also SigmoidMF.

Fields

• a1::Real: slope of the first sigmoid.

• c1::Real: center of the first sigmoid.

• a2::Real: slope of the second sigmoid.

• c2::Real: center of the second sigmoid.

Example

mf = ProductSigmoidMF(2, 3, -5, 8)

struct SShapeMF{Ta<:Real, Tb<:Real} <: FuzzyLogic.AbstractMembershipFunction

S-shaped membership function.

Fields

• a::Real: foot.

• b::Real: shoulder.

Example

mf = SShapeMF(1, 8)

struct SemiEllipticMF{Tcd<:Real, Trd<:Real} <: FuzzyLogic.AbstractMembershipFunction

Semi-elliptic membership function.

Fields

• cd::Real: center.

• rd::Real: semi-axis.

Example

mf = SemiEllipticMF(5.0, 4.0)

struct SigmoidMF{Ta<:Real, Tc<:Real} <: FuzzyLogic.AbstractMembershipFunction

Sigmoid membership function $\frac{1}{1+e^{-a(x-c)}}$.

Fields

• a::Real: parameter controlling the slope of the curve.

• c::Real: center of the slope.

Example

mf = SigmoidMF(2, 5)

struct SingletonMF{T<:Real} <: FuzzyLogic.AbstractMembershipFunction

Singleton membership function. Equal to one at a single point and zero elsewhere.

Fields

• c::Real: Point at which the membership function has value 1.

Example

mf = SingletonMF(4)

struct TrapezoidalMF{Ta<:Real, Tb<:Real, Tc<:Real, Td<:Real} <: FuzzyLogic.AbstractMembershipFunction

Trapezoidal membership function.

Fields

• a::Real: left foot.

• b::Real: left shoulder.

• c::Real: right shoulder.

• d::Real: right foot.

Example

mf = TrapezoidalMF(1, 3, 7, 9)

struct TriangularMF{Ta<:Real, Tb<:Real, Tc<:Real} <: FuzzyLogic.AbstractMembershipFunction

Triangular membership function.

Fields

• a::Real: left foot.

• b::Real: peak.

• c::Real: right foot.

Example

mf = TriangularMF(3, 5, 7)

struct Type2MF{MF1<:FuzzyLogic.AbstractMembershipFunction, MF2<:FuzzyLogic.AbstractMembershipFunction} <: FuzzyLogic.AbstractMembershipFunction

A type-2 membership function.

• lo::FuzzyLogic.AbstractMembershipFunction: lower membership function.

• hi::FuzzyLogic.AbstractMembershipFunction: upper membership function.

Example

mf = 0.7 * TriangularMF(3, 5, 7) .. TriangularMF(1, 5, 9)

struct WeightedMF{MF<:FuzzyLogic.AbstractMembershipFunction, T<:Real} <: FuzzyLogic.AbstractMembershipFunction

A membership function scaled by a parameter $0 ≤ w ≤ 1$.

• mf::FuzzyLogic.AbstractMembershipFunction: membership function.

• w::Real: scaling factor.

Example

mf = 0.5 * TriangularMF(1, 2, 3)

struct ZShapeMF{Ta<:Real, Tb<:Real} <: FuzzyLogic.AbstractMembershipFunction

Z-shaped membership function.

Fields

• a::Real: shoulder.

• b::Real: foot.

Example

mf = ZShapeMF(3, 7)