September 2014
Intermediate to advanced
632 pages
21h 5m
English
Content preview from Soft Computing and Its Applications, Volume One
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204 Soft Computing and Its Applications
FIGURE 86 Compatibility covering tree.
FUZZY PRE-ORDER RELATION
Denition 2.92 Given fuzzy relation R in set A, if the followings are well kept for
all , this relation is called pre-order relation.
Reexive relation
Transitve relation
.
If certain relation is transitive but not reexive, this relation is called “semi-pre-
order’’ or “nonreexive fuzzy pre-order’’.
Example 2.95 We consider a semi-pre-order relation.
a b c
a
b
c
0.2
0.0
0.0
1.0
0.6
1.0
0.4
0.3
0.3
Fuzzy Sets, Fuzzy Operators, and Fuzzy Relations 205
If the ...
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