ECE449, Intelligent Systems Engineering
in the assignment box in the ETLC atrium
Note: Show your work! Marks are allocated
for technique and not just the answer.
1. [6 marks] Show that drastic product and drastic sum (defined below) satisfy the law of contradiction
(𝐴 ∩ 𝐴̅= ∅) and the law of excluded middle (𝐴 ∪ 𝐴̅= 𝑋). [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
A = [1.0,0.8,0.5,0.1,0]
defined on universe
. Find all of
it’s unique -cuts. Show how A can be expressed in terms of the family of all of its -cuts.