A two-input single-output Sugeno fuzzy model with 4 rules is given by

R1: if X is small & Y is small then z = -x +3y +1

R2: if X is small & Y is large then z = -2y +3

R3: if X is large & Y is small then z = -6x +3

R4: if X is large & Y is large then z = x + 2y + 1

Assume that input membership functions are given as

Small(x) = triangle(x; -15, 5, 15)

Large(x) = triangle (x; 0, 20, 30)

Small(y) = triangle (y; -10, -5, 10)

Large(y) = triangle (y; 5, 10, 20)

a) Assume that this fuzzy system uses minimum as t-norm operator. What will be the output (z) of this fuzzy system for x=8 and y=6?

b) Assume that this fuzzy system uses product as t-norm operator. What will be the output (z) of this fuzzy system for x=8 and y=6?