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I'm learning fuzzy logic and i don't find many examples explaining Zadeh extension principle i found this one but i dob't how to solve it. Can you help me ?

Let us consider two fuzzy subsets A and B defined by their membership functions μA and μB. μA and μB are defined from {1,2,3,4,5} to {0, α, β, 1} (where 0 < α < β < 1 ) as :

μA = {(0 | 1) + (α | 2) + (1 | 3) + (1 | 4) + (α | 5)}

μB = {(0 | 1) + (0 | 2) + (β | 3) + (1 | 4) + (β | 5)}

using the principle extension of Zadeh : suppose f is a function with n arguments that maps a point in omega to point in V, determine the membership of A + B and min(A,B) ?

Thanks.

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