Membership functions

A membership function (MF) is any callable mapping a crisp value (scalar or NumPy array) to a degree in [0, 1]. The built-in shapes:

Factory	Shape	Parameters
fz.tri(a, b, c)	triangular	feet a/c, peak b
fz.trap(a, b, c, d)	trapezoidal	shoulders a/d, flat top b..c
fz.gauss(c, sigma)	gaussian	center c, spread sigma
fz.gbell(a, b, c)	generalized bell	width a, slope b, center c
fz.sigmoid(a, c)	sigmoidal	slope a, inflection c

import numpy as np, fuzzytool as fz

m = fz.gauss(5, 1.5)
m(5)                       # 1.0
m(np.array([3, 5, 7]))     # vectorized

Custom shapes

Any callable works — no registration needed:

def ramp(x):
    return np.clip(np.asarray(x, float) / 10, 0, 1)

var = fz.Variable("x", (0, 10))
var["high"] = ramp

This is the core extensibility idea: the inference engine only relies on the MembershipFunction Protocol (x -> degree), so a new shape is just a new callable.