April 2016
Intermediate to advanced
386 pages
10h 3m
English
Content preview from Foundations of Fuzzy Logic and Semantic Web Languages
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126 Foundations of Fuzzy Logic and Semantic Web Languages
x ·
n
y via the matrix
M
·
n
=
0 0 0
0 0.25 0
0 0.5 0
0 0.75 0
0 1 0
0.25 0 0
0.25 0.25 0
0.25 0.5 0
0.25 0.75 0.25
0.25 1 0.25
0.5 0 0
0.5 0.25 0
0.5 0.5 0.25
0.5 0.75 0.25
0.5 1 0.5
0.75 0 0
0.75 0.25 0.25
0.75 0.5 0.25
0.75 0.75 0.5
0.75 1 0.75
1 0 0
1 0.25 0.25
1 0.5 0.5
1 0.75 0.75
1 1 1
Note that ·
n
is commutative, monotone, satisfies the boundary conditions, but
is not associative, thus, ·
n
is not a t-norm: e.g.,
0.25 ·
n
(0.75 ·
n
0.75) = 0 6= 0.25 = (0.25 ·
n
0.75) ·
n
0.75 .
Another, more direct, approach to deal with fuzzy combination functions is to ...
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