- 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
- Assume a fuzzy set A=[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.
