Assignment 2 Solution

[6 marks] Show that drastic product and drastic sum (defined below) satisfy the law of contradiction ( ̅ ) and the law of excluded middle ( ̅ ). [Hint: substitute the t-norm and s-norm

∩ =∅ ∪ =

operation for intersection and union in the two laws, respectively]




Drastic product x t y = x if y = 1 Drastic sum x s y = y if x = 0




y if x = 1 x if y = 0

0 otherwise 1 otherwise













2. [4 marks] Assume a fuzzy set













= [1.0,0.8,0.5,0.1,0]












defined on universe










X= 1,2













,3,4










,5 . Find all of



it’s unique -cuts. Show how A can be expressed in terms of the family of all of its -cuts.