May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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3-24 Discrete Mathematical Structures
Intersection of Fuzzy Sets: The membership function of the intersection of two fuzzy sets A
and B is
µ
A∩B
= Min {µ
A
(x), µ
B
(x)} for all x ∈ U
Example: Let A = {(1, 0.1), (2, 0.2), (3, 0.4), (4, 0.6), (5, 0.8)}
and B = {(2, 0.1), (3, 0.3), (4, 0.2), (5, 0.4), (6, 0.7), (7, 1)}
Then A ∪B = {(1, 0.1), (2, 0.2), (3, 0.4), (4, 0.6), (5, 0.8), (6, 0.7), (7, 1)}
and
ABMinMin Min∩=
()
+
()
+
()
001
1
0102
2
0304
3
,. ., ..,.
+
()
+
()
+
()
Min
MinMin
0206
4
0408
5
007
6
., .
.,.,.
+
()
Min
01
7
,
AB∩=++++
++
0
1
01
2
03
3
02
4
04
5
0
6
0
7
....
= {(2, 0.1), (3, 0.3), (4, 0.2), (5, 0.4)}
Applications: The successful applications ...
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