2. Answer the following questions (20 marks) (a) For a fuzzy rule: IF (x is A) AND (y is B) THEN (z is C), given the fact of: (x is A') AND (y is B'), derive Mcy, using max-product operator. (b) Consider two fuzzy sets A and B as shown in Figure 1. If min is used as the T-norm operator. 1) Specify the grade of inclusion B C A in MF representation Upcx in terms of /(x) and up(x); 2) Make a graphical representation of urca; 3) Which one of these two fuzzy sets is fuzzier? 1-- - - - - - Figure 1 - -- 0 1 2 3 4 5 6 7 8 9 10 x 2. Answer the following questions (20 marks) (a) For a fuzzy rule: IF (x is A) AND (y is B) THEN (z is C), given the fact of: (x is A') AND (y is B'), derive Mcy, using max-product operator. (b) Consider two fuzzy sets A and B as shown in Figure 1. If min is used as the T-norm operator. 1) Specify the grade of inclusion B C A in MF representation Upcx in terms of /(x) and up(x); 2) Make a graphical representation of urca; 3) Which one of these two fuzzy sets is fuzzier? 1-- - - - - - Figure 1 - -- 0 1 2 3 4 5 6 7 8 9 10 x