Assignment #2

ECE449, Intelligent Systems Engineering

Points: 10

Due: Thursday, September 26, 2019, 3:30 PM,

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

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.

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