ECE 6720 FUZZY CONTROL SYSTEMS
Fall 2008
Homework Assignment #2
Total: 100 pts.
Due 6:30pm, Tuesday, September 23, 2008
1. Fuzzy sets A and B are given below:
A = .4/2 + .6/3 + .8/4 + 1/5 + .8/6 + .6/7 + .4/8
B = .1/1 + .2/2 + .6/4 + .7/5 + 1/7
1.1 Compute the fuzzy intersection of A and B using
a) standard intersection b) algebraic product
c) bounded difference d) drastic intersection
e) Dubois & Prade (α= .3, and .8, respectively)
You are to plot A∩B for each operation, respectively. Compare magnitudes of the
results and give your comments (i.e., give the order of the results). (40 pts.)
1.2 Compute the fuzzy union of A and B using
a) standard union b) algebraic sum
c) bounded union d) drastic sum
e) Dubois & Prade (α= .3, and .8, respectively)
You are to plot A∪B for each operation, respectively. Compare the results and give
your comments (i.e., give the order of the results). (40 pts.)
2. Perform the following operations on intervals:
a) = [9, 5] + [3, 4] b) [3, 5] ⋅ [2, 6]
c) = [8, 4] / [2, 4] d) [1, 7] - [10, 8] (6 pts.)
3. Calculate C = A ⋅ B using the extension principle and plot the results. Fuzzy sets A and
B are defined as:
A = .2/1 + 1/2 + .8/3 + .4/4
B= .1/2 + 1/4 + .7/6
(14 pts.)