Database Reference
In-Depth Information
Figure 1: Function “Approximately n” (n(+-)m, where m is a margin)
Fuzzy Quantifi ers
Fuzzy or linguistic quantifi ers (Galindo, 1999; Galindo et al., 2001a, Yager, 1983;
Zadeh, 1983) allow us to express fuzzy quantities or proportions in order to provide an ap-
proximate idea of the number of elements of a subset (or fulfi lling a certain condition) or of
the proportion of this number in relation to the total of possible elements. Fuzzy quantifi ers
can be absolute or relative:
•
Absolute quantifi ers
express quantities over the total number of elements of a par-
ticular set, stating whether this number is, for example, “large”, “small”, “many”,
“few”, “very many”.... Generalizing this concept, we can consider fuzzy numbers as
absolute fuzzy quantifi ers, in order to use expressions like “approximately between
5 and 10”, “approximately_8”.... Note that the expressed value may be positive or
negative.
In this case, we observe that the truth of the quantifi er depends on a single quantity.
For this reason, the defi nition of absolute fuzzy quantifi ers is, as we will see, very
similar to that of fuzzy numbers.
•
Relative quantifi ers
express measurements over the total number of elements which
fulfi l a certain condition depending on the total of possible elements, so that the truth
of the quantifi er depends on two quantities. This type of quantifi ers is used in expres-
sions like “the majority”, “the minority”, “approximately half”....
In this case, to evaluate the truth of the quantifi er we need to fi nd the total quantity of
elements which fulfi l the condition and consider this value with respect to the total
quantity of elements which could fulfi l it (including those which fulfi l it and those
which do not fulfi l it).
In Zadeh (1983), absolute fuzzy quantifi ers are defi ned as fuzzy sets in the interval [0, +∞)
and relative quantifi ers as fuzzy sets in the interval [0,1]. We have extended the defi nition
of absolute fuzzy quantifi ers to the interval (-∞,+∞). That is to say that a quantifi er Q is
represented as a function
Q
whose domain depends on whether it is absolute or relative:
