Module type2fuzzy.membership.generate_it2fs
generation of interval type 2 fuzzy sets
Expand source code
'''
generation of interval type 2 fuzzy sets
'''
import math
import numpy as np
from type2fuzzy.membership.intervaltype2fuzzyset import IntervalType2FuzzySet
from type2fuzzy.membership.crispset import CrispSet
def create_gaussian_fixed_sigma(primary_domain, m1, m2, sigma=1.0):
'''
Creates an interval type-2 fuzzy set with fixed standard deviation and uncertain mean
Arguments:
----------
primary_domain -- list, elements of primary domain
m1 -- lowest value of mean
m2 -- highest value of mean
sigma -- standard deviation , default 1
Returns:
--------
interval_set -- created interval type-2 fuzzy set
References:
-----------
Karnik, Nilesh N., and Jerry M. Mendel.
"Introduction to type-2 fuzzy logic systems."
1998 IEEE International Conference on Fuzzy Systems Proceedings.
IEEE World Congress on Computational Intelligence (
Cat. No. 98CH36228). Vol. 2. IEEE, 1998.
'''
# check that m1 is smaller than m2
if m1 > m2:
raise Exception('ERROR: m1 vaue must be smaller or equal to m2')
interval_set = IntervalType2FuzzySet()
toggle_peak = False
element = None
for x in primary_domain:
u1 = math.exp(-0.5*((x-float(m1))/sigma)**2)
u2 = math.exp(-0.5*((x-float(m2))/sigma)**2)
# once m1 has a value of 1 the plateu starts and ands when m2 reaches a value of 1
if u1 == 1:
toggle_peak = True
if u2 == 1:
toggle_peak = False
if toggle_peak:
element = CrispSet(min(u1, u2), 1)
else:
element = CrispSet(min(u1, u2), max(u1, u2))
# add the element to the it2fs
interval_set.add_element(x, element)
return interval_set
def create_gaussian_fixed_mean(primary_domain, sigma1, sigma2, mean=1.0):
'''
Creates an interval type-2 fuzzy set with fixed standard deviation and uncertain mean
Arguments:
----------
primary_domain -- list, elements of primary domain
sigma1 -- lowest value of standard deviation
sigma2 -- highest value of standard deviation
mean -- mean , default 1
Returns:
--------
interval_set -- created interval type-2 fuzzy set
References:
-----------
Karnik, Nilesh N., and Jerry M. Mendel.
"Introduction to type-2 fuzzy logic systems."
1998 IEEE International Conference on Fuzzy Systems Proceedings.
IEEE World Congress on Computational Intelligence (
Cat. No. 98CH36228). Vol. 2. IEEE, 1998.
'''
# check that m1 is smaller than m2
if sigma1 > sigma2:
raise Exception('ERROR: m1 vaue must be smaller or equal to m2')
interval_set = IntervalType2FuzzySet()
u1 = 0
u2 = 0
for x in primary_domain:
u1 = math.exp(-0.5*((x-float(mean))/sigma1)**2)
u2 = math.exp(-0.5*((x-float(mean))/sigma2)**2)
# add the element to the it2fs
interval_set.add_element(x, CrispSet(min(u1, u2), max(u1, u2)))
return interval_setFunctions
def create_gaussian_fixed_mean(primary_domain, sigma1, sigma2, mean=1.0)-
Creates an interval type-2 fuzzy set with fixed standard deviation and uncertain mean
Arguments:
primary_domain – list, elements of primary domain
sigma1 – lowest value of standard deviation
sigma2 – highest value of standard deviation
mean – mean , default 1
Returns:
interval_set – created interval type-2 fuzzy set
References:
Karnik, Nilesh N., and Jerry M. Mendel. "Introduction to type-2 fuzzy logic systems." 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence ( Cat. No. 98CH36228). Vol. 2. IEEE, 1998.
Expand source code
def create_gaussian_fixed_mean(primary_domain, sigma1, sigma2, mean=1.0): ''' Creates an interval type-2 fuzzy set with fixed standard deviation and uncertain mean Arguments: ---------- primary_domain -- list, elements of primary domain sigma1 -- lowest value of standard deviation sigma2 -- highest value of standard deviation mean -- mean , default 1 Returns: -------- interval_set -- created interval type-2 fuzzy set References: ----------- Karnik, Nilesh N., and Jerry M. Mendel. "Introduction to type-2 fuzzy logic systems." 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence ( Cat. No. 98CH36228). Vol. 2. IEEE, 1998. ''' # check that m1 is smaller than m2 if sigma1 > sigma2: raise Exception('ERROR: m1 vaue must be smaller or equal to m2') interval_set = IntervalType2FuzzySet() u1 = 0 u2 = 0 for x in primary_domain: u1 = math.exp(-0.5*((x-float(mean))/sigma1)**2) u2 = math.exp(-0.5*((x-float(mean))/sigma2)**2) # add the element to the it2fs interval_set.add_element(x, CrispSet(min(u1, u2), max(u1, u2))) return interval_set def create_gaussian_fixed_sigma(primary_domain, m1, m2, sigma=1.0)-
Creates an interval type-2 fuzzy set with fixed standard deviation and uncertain mean
Arguments:
primary_domain – list, elements of primary domain
m1 – lowest value of mean
m2 – highest value of mean
sigma – standard deviation , default 1
Returns:
interval_set – created interval type-2 fuzzy set
References:
Karnik, Nilesh N., and Jerry M. Mendel. "Introduction to type-2 fuzzy logic systems." 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence ( Cat. No. 98CH36228). Vol. 2. IEEE, 1998.
Expand source code
def create_gaussian_fixed_sigma(primary_domain, m1, m2, sigma=1.0): ''' Creates an interval type-2 fuzzy set with fixed standard deviation and uncertain mean Arguments: ---------- primary_domain -- list, elements of primary domain m1 -- lowest value of mean m2 -- highest value of mean sigma -- standard deviation , default 1 Returns: -------- interval_set -- created interval type-2 fuzzy set References: ----------- Karnik, Nilesh N., and Jerry M. Mendel. "Introduction to type-2 fuzzy logic systems." 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence ( Cat. No. 98CH36228). Vol. 2. IEEE, 1998. ''' # check that m1 is smaller than m2 if m1 > m2: raise Exception('ERROR: m1 vaue must be smaller or equal to m2') interval_set = IntervalType2FuzzySet() toggle_peak = False element = None for x in primary_domain: u1 = math.exp(-0.5*((x-float(m1))/sigma)**2) u2 = math.exp(-0.5*((x-float(m2))/sigma)**2) # once m1 has a value of 1 the plateu starts and ands when m2 reaches a value of 1 if u1 == 1: toggle_peak = True if u2 == 1: toggle_peak = False if toggle_peak: element = CrispSet(min(u1, u2), 1) else: element = CrispSet(min(u1, u2), max(u1, u2)) # add the element to the it2fs interval_set.add_element(x, element) return interval_set