transfer_functions_benchmark.py

#import skfuzzy
import numpy as np
from math import pi
from scipy.special import erf
import matplotlib.pylab as plt

#________________________V-shaped transfer functions______________________
def v1(x):
   v1=abs(erf((np.sqrt(pi)/2)*x))
   return v1

  
def v2(x):
   v2=abs(np.tanh(x))
   return v2
   
   
def v3(x):
   v3= abs(x/np.sqrt(1+np.square(x)))
   return v3  
   
   
def v4(x):
   v4= abs((2/pi)*np.arctan((pi/2)*x))
   return v4  
##______________________S-shaped transfer functions_______________________

def s1(x):
    
    s1=1 / (1 + np.exp(-2*x))
    
    return s1

def s2(x):
    s2 = 1 / (1 + np.exp(-x))  
    return s2
# s2 is called logistic function and can be imported using scipy.special.expit(x) library

def s3(x):
    s3=1 / (1 + np.exp(-x/3))
    return s3


def s4(x):
    s4=1 / (1 + np.exp(-x/2))
    return s4


##________________________the sigmoid functions_________________________

# A customized function for SIGMOID 

def sigmf1(x,b,c):
    b=10
    c=.5
    y = 1 / (1. + np.exp(- c * (x - b)))
   
    return y



## Built-in function for SIGMOID using skfuzzy.membership library

def sigmf2(x,b,c):
    b=10
    c=.5
    y=skfuzzy.membership.sigmf(x,b,c)

    return y


x = np.arange(-8, 8, 0.1) 
# x is used inside this script and will be replaced by a binary individual (1-d binary vector)
#when the transfer function is called or imported in the optimizers scripts