Source code for pyFTS.common.Membership

"""
Membership functions for Fuzzy Sets
"""

import numpy as np
import math
from pyFTS import *


[docs]def trimf(x, parameters): """ Triangular fuzzy membership function :param x: data point :param parameters: a list with 3 real values :return: the membership value of x given the parameters """ xx = np.round(x, 3) if xx < parameters[0]: return 0 elif parameters[0] <= xx < parameters[1]: return (x - parameters[0]) / (parameters[1] - parameters[0]) elif parameters[1] <= xx <= parameters[2]: return (parameters[2] - xx) / (parameters[2] - parameters[1]) else: return 0
[docs]def trapmf(x, parameters): """ Trapezoidal fuzzy membership function :param x: data point :param parameters: a list with 4 real values :return: the membership value of x given the parameters """ if x < parameters[0]: return 0 elif parameters[0] <= x < parameters[1]: return (x - parameters[0]) / (parameters[1] - parameters[0]) elif parameters[1] <= x <= parameters[2]: return 1 elif parameters[2] <= x <= parameters[3]: return (parameters[3] - x) / (parameters[3] - parameters[2]) else: return 0
[docs]def gaussmf(x, parameters): """ Gaussian fuzzy membership function :param x: data point :param parameters: a list with 2 real values (mean and variance) :return: the membership value of x given the parameters """ return math.exp((-(x - parameters[0])**2)/(2 * parameters[1]**2))
[docs]def bellmf(x, parameters): """ Bell shaped membership function :param x: :param parameters: :return: """ return 1 / (1 + abs((x - parameters[2]) / parameters[0]) ** (2 * parameters[1]))
[docs]def sigmf(x, parameters): """ Sigmoid / Logistic membership function :param x: :param parameters: an list with 2 real values (smoothness and midpoint) :return: """ return 1 / (1 + math.exp(-parameters[0] * (x - parameters[1])))