Compositions in Fuzzy Relations - MATLAB/Python

Question

I want to calculate Fuzzy Relation Compositions on MATLAB/Python and was wondering if there are any built-in functions in MATLAB or Python for doing this...

here's an example :

R1 = [{ 3, 4, .7}, {3, 5, 0}, { 4, 4, 1}, { 4, 5, .1}]

R2 = [{ 3,3, 0}, { 3, 5, .1}, { 4, 4, 0}, { 4, 5, .6}]

I'm trying to calculate :

R1oR2

I'm looking for 'Max-Min' and 'Max-Product' approaches...

Answer 1

Ok... since no one gave an answer, I ended up writing it by myself... here's the Python Code:

import numpy as np

# Max-Min Composition given by Zadeh
def maxMin(x, y):
    z = []
    for x1 in x:
        for y1 in y.T:
            z.append(max(np.minimum(x1, y1)))
    return np.array(z).reshape((x.shape[0], y.shape[1]))

# Max-Product Composition given by Rosenfeld
def maxProduct(x, y):
    z = []
    for x1 in x:
        for y1 in y.T:
            z.append(max(np.multiply(x1, y1)))
    return np.array(z).reshape((x.shape[0], y.shape[1]))

# 3 arrays for the example
r1 = np.array([[1, 0, .7], [.3, .2, 0], [0, .5, 1]])
r2 = np.array([[.6, .6, 0], [0, .6, .1], [0, .1, 0]])
r3 = np.array([[1, 0, .7], [0, 1, 0], [.7, 0, 1]])

print "R1oR2 => Max-Min :\n" + str(maxMin(r1, r2)) + "\n"
print "R1oR2 => Max-Product :\n" + str(maxProduct(r1, r2)) + "\n\n"

print "R1oR3 => Max-Min :\n" + str(maxMin(r1, r3)) + "\n"
print "R1oR3 => Max-Product :\n" + str(maxProduct(r1, r3)) + "\n\n"

print "R1oR2oR3 => Max-Min :\n" + str(maxMin(r1, maxMin(r2, r3))) + "\n"
print "R1oR2oR3 => Max-Product :\n" + str(maxProduct(r1, maxProduct(r2, r3))) + "\n\n"

and here's the answer it gives:

R1oR2 => Max-Min :
[[ 0.6  0.6  0. ]
 [ 0.3  0.3  0.1]
 [ 0.   0.5  0.1]]

R1oR2 => Max-Product :
[[ 0.6   0.6   0.  ]
 [ 0.18  0.18  0.02]
 [ 0.    0.3   0.05]]


R1oR3 => Max-Min :
[[ 1.   0.   0.7]
 [ 0.3  0.2  0.3]
 [ 0.7  0.5  1. ]]

R1oR3 => Max-Product :
[[ 1.    0.    0.7 ]
 [ 0.3   0.2   0.21]
 [ 0.7   0.5   1.  ]]


R1oR2oR3 => Max-Min :
[[ 0.6  0.6  0.6]
 [ 0.3  0.3  0.3]
 [ 0.1  0.5  0.1]]

R1oR2oR3 => Max-Product :
[[ 0.6    0.6    0.42 ]
 [ 0.18   0.18   0.126]
 [ 0.035  0.3    0.05 ]]