Variable: FuzzyShape

@kortexya/reasoninglayer

---

@kortexya/reasoninglayer / FuzzyShape

Variable: FuzzyShape

const FuzzyShape: object

Defined in: src/builders/value.ts:587

Builder namespace for fuzzy membership function shapes.

Produces JSON using the "kind" discriminator (NOT "type"): {"kind": "Triangular", "a": 20, "b": 22, "c": 24}.

Type Declaration

bell()

readonly bell(center, width, slope): BellShape

Create a generalized bell fuzzy membership function.

Tunable flat-top bell: μ(x) = 1 / (1 + |((x - center) / width)|^(2*slope)). Unlike Gaussian, the slope controls how sharply the curve drops off.

Parameters

center

number

Center of the bell (membership = 1).

width

number

Half-width of the bell at the crossover point.

slope

number

Controls steepness of the sides. Higher = sharper edges.

Returns

BellShape

A BellShape.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

FuzzyShape.bell(100, 15, 3)
// {"kind": "Bell", "center": 100, "width": 15, "slope": 3}

cauchy()

readonly cauchy(center, gamma): CauchyShape

Create a Cauchy (Lorentzian) fuzzy membership function.

μ(x) = 1 / (1 + ((x - center) / gamma)^2). Heavy-tailed bell whose tails never reach zero.

Parameters

center

number

Center of the Cauchy curve (membership = 1).

gamma

number

Half-width at half-maximum, controlling the spread.

Returns

CauchyShape

A CauchyShape.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

FuzzyShape.cauchy(0, 1)
// {"kind": "Cauchy", "center": 0, "gamma": 1}

cosine()

readonly cosine(center, width): CosineShape

Create a cosine fuzzy membership function with compact support.

μ(x) = 0.5 * (1 + cos(2π/width * (x - center))) for |x - center| <= width/2, μ(x) = 0 otherwise.

Parameters

center

number

Center of the cosine curve (membership = 1).

width

number

Full width of the support region.

Returns

CosineShape

A CosineShape.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

FuzzyShape.cosine(50, 10)
// {"kind": "Cosine", "center": 50, "width": 10}

cyclicGaussian()

readonly cyclicGaussian(mean, stdDev, period): CyclicGaussianShape

Create a cyclic Gaussian fuzzy membership function with periodic wrapping.

Parameters

mean

number

Center of the Gaussian curve.

stdDev

number

Standard deviation controlling width.

period

number

Period of the cyclic wrapping (e.g., 360 for degrees).

Returns

CyclicGaussianShape

A CyclicGaussianShape.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

FuzzyShape.cyclicGaussian(180, 30, 360)

gaussian()

readonly gaussian(mean, stdDev): GaussianShape

Create a Gaussian fuzzy membership function.

Parameters

mean

number

Center of the Gaussian curve (membership = 1).

stdDev

number

Standard deviation controlling width.

Returns

GaussianShape

A GaussianShape.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

FuzzyShape.gaussian(100, 15)

gaussianProduct()

readonly gaussianProduct(mean1, stdDev1, mean2, stdDev2): GaussianProductShape

Create a Gaussian product (gauss2mf) fuzzy membership function.

Asymmetric flat-top bell: left Gaussian up to mean1, flat 1.0 in [mean1, mean2], right Gaussian after mean2.

Parameters

mean1

number

Left Gaussian center.

stdDev1

number

Left Gaussian standard deviation.

mean2

number

Right Gaussian center.

stdDev2

number

Right Gaussian standard deviation.

Returns

GaussianProductShape

A GaussianProductShape.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

FuzzyShape.gaussianProduct(36.5, 0.3, 37.5, 0.2)
// {"kind": "GaussianProduct", "mean1": 36.5, "stdDev1": 0.3, "mean2": 37.5, "stdDev2": 0.2}

piecewiseLinear()

readonly piecewiseLinear(points): PiecewiseLinearShape

Create a piecewise linear fuzzy membership function.

Membership is linearly interpolated between the provided (x, mu) data points.

Parameters

points

[number, number][]

Array of [x, mu] tuples defining the membership function.

Returns

PiecewiseLinearShape

A PiecewiseLinearShape.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

FuzzyShape.piecewiseLinear([[0, 0], [0.5, 1], [1, 0]])
// {"kind": "PiecewiseLinear", "points": [[0, 0], [0.5, 1], [1, 0]]}

piShape()

readonly piShape(a, b, c, d): PiShapeShape

Create a Pi-shaped (pimf) fuzzy membership function.

Smooth flat-top bump: μ(x) = SShape(x, a, b) * ZShape(x, c, d). Like a smooth trapezoidal.

Parameters

a

number

Left foot (SShape start).

b

number

Left shoulder (SShape end).

c

number

Right shoulder (ZShape start).

d

number

Right foot (ZShape end).

Returns

PiShapeShape

A PiShapeShape.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

FuzzyShape.piShape(10, 20, 60, 80)
// {"kind": "PiShape", "a": 10, "b": 20, "c": 60, "d": 80}

sigmoid()

readonly sigmoid(midpoint, steepness): SigmoidShape

Create a sigmoid (logistic) fuzzy membership function.

Monotonic S-curve transition: μ(x) = 1 / (1 + exp(-steepness * (x - midpoint))). Positive steepness = increasing, negative = decreasing.

Parameters

midpoint

number

The x-value where membership = 0.5 (inflection point).

steepness

number

Controls transition sharpness. Positive = left-to-right rise.

Returns

SigmoidShape

A SigmoidShape.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

// DNA match confidence: sharp transition around 95%
FuzzyShape.sigmoid(0.95, 20)
// {"kind": "Sigmoid", "midpoint": 0.95, "steepness": 20}

sigmoidDifference()

readonly sigmoidDifference(midpoint1, steepness1, midpoint2, steepness2): SigmoidDifferenceShape

Create a sigmoid difference fuzzy membership function.

Difference of two sigmoids: creates a smooth bounded region (like a smooth trapezoidal). μ(x) = sigmoid(x, midpoint1, steepness1) - sigmoid(x, midpoint2, steepness2).

Parameters

midpoint1

number

Left transition inflection point.

steepness1

number

Left transition sharpness (positive = rising).

midpoint2

number

Right transition inflection point.

steepness2

number

Right transition sharpness (positive = falling).

Returns

SigmoidDifferenceShape

A SigmoidDifferenceShape.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

// Smooth region between pH 6.5 and 7.5
FuzzyShape.sigmoidDifference(6.5, 10, 7.5, 10)
// {"kind": "SigmoidDifference", "midpoint1": 6.5, "steepness1": 10, "midpoint2": 7.5, "steepness2": 10}

sigmoidProduct()

readonly sigmoidProduct(midpoint1, steepness1, midpoint2, steepness2): SigmoidProductShape

Create a sigmoid product fuzzy membership function.

Product of two sigmoids: μ(x) = sigmoid(x, midpoint1, steepness1) * sigmoid(x, midpoint2, steepness2). Always non-negative (unlike sigmoidDifference).

Parameters

midpoint1

number

First sigmoid inflection point.

steepness1

number

First sigmoid sharpness.

midpoint2

number

Second sigmoid inflection point.

steepness2

number

Second sigmoid sharpness.

Returns

SigmoidProductShape

A SigmoidProductShape.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

FuzzyShape.sigmoidProduct(6.5, 10, 7.5, -10)
// {"kind": "SigmoidProduct", "midpoint1": 6.5, "steepness1": 10, "midpoint2": 7.5, "steepness2": -10}

spike()

readonly spike(center, width): SpikeShape

Create a spike (Laplacian/double-exponential) fuzzy membership function.

μ(x) = exp(-|x - center| / width). Sharp cusp at center with exponential tails.

Parameters

center

number

Peak of the spike (membership = 1).

width

number

Controls the rate of exponential decay.

Returns

SpikeShape

A SpikeShape.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

FuzzyShape.spike(100, 5)
// {"kind": "Spike", "center": 100, "width": 5}

sShape()

readonly sShape(a, b): SShapeShape

Create an S-shaped (smf) fuzzy membership function.

Smooth monotonic spline from 0 to 1 using piecewise quadratic. Reaches exact 0 and 1 (unlike sigmoid).

Parameters

a

number

Foot: x-value where membership starts rising from 0.

b

number

Shoulder: x-value where membership reaches 1.

Returns

SShapeShape

An SShapeShape.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

FuzzyShape.sShape(20, 80)
// {"kind": "SShape", "a": 20, "b": 80}

trapezoidal()

readonly trapezoidal(a, b, c, d): TrapezoidalShape

Create a trapezoidal fuzzy membership function.

Parameters

a

number

Left foot (membership starts rising from 0).

b

number

Left shoulder (membership reaches 1).

c

number

Right shoulder (membership starts falling from 1).

d

number

Right foot (membership returns to 0).

Returns

TrapezoidalShape

A TrapezoidalShape.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

FuzzyShape.trapezoidal(18, 20, 24, 26)

triangular()

readonly triangular(a, b, c): TriangularShape

Create a triangular fuzzy membership function.

Parameters

a

number

Left foot (membership = 0).

b

number

Peak (membership = 1).

c

number

Right foot (membership = 0).

Returns

TriangularShape

A TriangularShape: {"kind": "Triangular", "a": 20, "b": 22, "c": 24}.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

FuzzyShape.triangular(20, 22, 24)

zShape()

readonly zShape(a, b): ZShapeShape

Create a Z-shaped (zmf) fuzzy membership function.

Mirror of sShape. Smooth monotonic spline from 1 to 0 using piecewise quadratic.

Parameters

a

number

Shoulder: x-value where membership starts falling from 1.

b

number

Foot: x-value where membership reaches 0.

Returns

ZShapeShape

A ZShapeShape.

Remarks

Serialization format: Tagged by "kind" (FuzzyShapeDto).

Example

FuzzyShape.zShape(20, 80)
// {"kind": "ZShape", "a": 20, "b": 80}

Remarks

Discriminator field is "kind", NOT "type". This differs from most other tagged unions in the API which use "type".

Example

import { FuzzyShape, Value } from '@kortexya/reasoninglayer';

const shape = FuzzyShape.triangular(20, 22, 24);
const fuzzyAge = Value.fuzzyNumber(shape);