In this snippet, I made a function that calculates the max-min and min-max composition of two fuzzy relations. If you use it in a Jupyter Notebook, there's no need to import the numpy and Ipython libraries

fuzzyrelationscompositions.py

import numpy as np
from IPython.display import display, Markdown


def maxmincomposition(X,Y):
    C = np.zeros((X.shape[0],Y.shape[1]))
    # Iterar a traves de las filas de A
    for i in range(len(X)):
       # Iterar a traves de las columnas de B
       for j in range(len(Y[0])):
           # Iterar a traves de las filas de B
           for k in range(len(Y)):
                if(np.minimum(X[i][k], Y[k][j]) > C[i][j]):
                    C[i][j] =  np.minimum(X[i][k], Y[k][j])
    return C

# Ejemplo del libro de Syropoulos

A = np.array([[0.3,0.5,0.8], 
    [0,0.7,1],
    [0.4,0,0.5]])

B = np.array([[0.9,0,0.7,0.7], 
    [0.3,0.2,0,0.9],
    [1,0,0.5,0.5]])

# Ejemplo del libro de Bede

R = np.array([[0.3,0.7,0.2], 
    [1,0,0.9]])

S = np.array([[0.8,0.3], 
    [0.1,0],
    [0.5,0.6]])


display(Markdown('**Ejemplo del libro de Syropoulos**'))
display(Markdown('Dada una relacion difusa $A$'))

print(A)

display(Markdown('Y dada una relacion difusa $B$'))

print(B)

display(Markdown('$A\lhd B = $'))

print(maxmincomposition(A,B))

display(Markdown('**Ejemplo del libro de Bede**'))
display(Markdown('Dada una relacion difusa $R$'))

print(R)

display(Markdown('Y dada una relacion difusa $S$'))

print(S)

display(Markdown('$R\lhd S = $'))

print(maxmincomposition(R,S))

def minmaxcomposition(X,Y):
    C = np.ones((X.shape[0],Y.shape[1]))
    # Iterar a traves de las filas de A
    for i in range(len(X)):
       # Iterar a traves de las columnas de B
       for j in range(len(Y[0])):
           # Iterar a traves de las filas de B
           for k in range(len(Y)):
                if(np.maximum(X[i][k], Y[k][j]) < C[i][j]):
                    C[i][j] =  np.maximum(X[i][k], Y[k][j])
    return C



display(Markdown('**Ejemplo del libro de Syropoulos**'))
display(Markdown('Dada una relacion difusa $A$'))

print(A)

display(Markdown('Y dada una relacion difusa $B$'))

print(B)

display(Markdown('$A ⊳ B = $'))

print(minmaxcomposition(A,B))

display(Markdown('**Ejemplo del libro de Bede**'))
display(Markdown('Dada una relacion difusa $R$'))

print(R)

display(Markdown('Y dada una relacion difusa $S$'))

print(S)

display(Markdown('$R\lhd S = $'))

print(minmaxcomposition(R,S))