September 2014
Intermediate to advanced
632 pages
21h 5m
English
Content preview from Soft Computing and Its Applications, Volume One
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480 Soft Computing and Its Applications
SIMILARITY AS DEGREE OF EQUALITY
Fuzzy sets are considered similar if they are defined by overlapping membership func-
tions that assign approximately the same values of membership to the elements in
their universe of discourse. Their similarity is the degree to which they can be con-
sidered as equal. The classical definition of equality is crisp. Let and be the
membership functions of fuzzy sets A and B, respectively. Then A and B are equal,
if
ab
(x) (x), x X.µ =µ ∀ ∈
If we apply this concept of equality to the fuzzy sets in
Figure 53 we get and since their membership functions are different.
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