3. Suppose we have a universe of integers, Y = {1,2,3,4,5). We define the following linguistic terms as a mapping on to Y: "Small" = 1/1 + 0.8/2 + 0.6/3 +0.4/4 +0.2/5 "Large" = 0.2/1 + 0.4/2 + 0.6/3 + 0.8/4 + 1/5 (a) (b) Modify the above linguistic terms with hedges to obtain the linguistic terms "Very small", and "Very, very large". Construct a fuzzy set which describes the phrase "not very small and not very, very large". 4. Consider the following two discrete fuzzy sets, which are defined over the universe X = (-5,5): A = "zero" = {0/-2 + 0.5/-1 + 1.0/0 + 0.5/1 + 0/2) B = "positive medium" = {0/0+ 0.5/1 + 1.0/2 + 0.5/3 + 0/4} It is known that IF x is A THEN y is B (.e. IF x is "zero" THEN y is "positive medium") If we introduce a new antecedent A' = "positive small" = {0/-1+ 0.5/0+1/1 + 0.5/2 +0/3} find the new consequent B', using max-min composition rule of inference, i.e. B' = A'OR=A'o ( A B). 3. Suppose we have a universe of integers, Y = {1,2,3,4,5). We define the following linguistic terms as a mapping on to Y: "Small" = 1/1 + 0.8/2 + 0.6/3 +0.4/4 +0.2/5 "Large" = 0.2/1 + 0.4/2 + 0.6/3 + 0.8/4 + 1/5 (a) (b) Modify the above linguistic terms with hedges to obtain the linguistic terms "Very small", and "Very, very large". Construct a fuzzy set which describes the phrase "not very small and not very, very large". 4. Consider the following two discrete fuzzy sets, which are defined over the universe X = (-5,5): A = "zero" = {0/-2 + 0.5/-1 + 1.0/0 + 0.5/1 + 0/2) B = "positive medium" = {0/0+ 0.5/1 + 1.0/2 + 0.5/3 + 0/4} It is known that IF x is A THEN y is B (.e. IF x is "zero" THEN y is "positive medium") If we introduce a new antecedent A' = "positive small" = {0/-1+ 0.5/0+1/1 + 0.5/2 +0/3} find the new consequent B', using max-min composition rule of inference, i.e. B' = A'OR=A'o ( A B)