Solved–Assignment 2 –Solution

Description

[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

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.