3. CL3

A = {'x1': 0.2, 'x2': 0.4, 'x3': 0.6, 'x4': 0.8}

B = {'x1': 0.3, 'x2': 0.5, 'x3': 0.7, 'x4': 0.9}

R = {('x1', 'y1'): 0.2, ('x1', 'y2'): 0.4, ('x2', 'y1'): 0.6, ('x2', 'y2'): 0.8}

S = {('x1', 'y1'): 0.3, ('x1', 'y2'): 0.5, ('x2', 'y1'): 0.7, ('x2', 'y2'): 0.9}

def fuzzy_union(A, B):

    union = {}

    for key in A.keys():

        union[key] = max(A[key], B[key])

    return union

# Example usage

union_result = fuzzy_union(A, B)

print("Union:", union_result)

def fuzzy_intersection(A, B):

    intersection = {}

    for key in A.keys():

        intersection[key] = min(A[key], B[key])

    return intersection

# Example usage

intersection_result = fuzzy_intersection(A, B)

print("Intersection:", intersection_result)

def fuzzy_complement(A):

    complement = {}

    for key in A.keys():

        complement[key] = 1 - A[key]

    return complement

# Example usage

complement_result_A = fuzzy_complement(A)

complement_result_B = fuzzy_complement(B)

print("Complement A:", complement_result_A)

print("Complement B:", complement_result_B)

def fuzzy_difference(A, B):

    difference = {}

    for key in A.keys():

        difference[key] = min(A[key], 1 - B[key])

    return difference

# Example usage

difference_result = fuzzy_difference(A, B)

print("Difference:", difference_result)

def max_min_composition(R, S):

    composition = {}

    for (x, z) in R.keys():

        composition[(x, z)] = 0

        for y in [key[1] for key in R.keys() if key[0] == x]:

            composition[(x, z)] = max(composition[(x, z)], min(R[(x, y)], S[(y, z)]))

    return composition

# Example usage

composition_result = max_min_composition(R, S)

print("Max-Min Composition:", composition_result)