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These fuzzy quantifiers are of two main types
•
Absolute quantifiers
, when are fuzzy numbers in
R
(independent of the cardinality
of the universe of discourse)
•
Relative quantifiers
, when are fuzzy numbers in
[
0
,
1
]
(dependent of the cardinality
of the universe of discourse)
Of course, the “interval” arithmetical quantifiers belong to the class of absolute
(fuzzy) quantifiers as a (crisp) particular case, and the “percentage” arithmetical
quantifiers belong to the class of relative (fuzzy) quantifiers as a (crisp) particular
case.
The important problem is to compute the degree of validity, or truth, of statements
with fuzzy quantifiers, like for example:
•
In a given class, there are about three students whose fluency in English is low,
that firstly should be represented in fuzzy terms. To do that, call
μ
A
3
the fuzzy quan-
tifiers, and
μ
LF
the degree of low English-fluency, and rewrite the above statement
as
•
There are
μ
LF
's.
Then, the degree of validity can be taken as
μ
A
3
,
=
μ
A
3
(
|
μ
LF
|
),
|
μ
LF
|
μ
F
.
t
with
the cardinality of
For example, with
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