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language which are referred to as linguistic values. Linguistic values can be
defined also for quantitative characteristics; however, for the qualitative
characteristics physical values cannot be defined.
Two model-building methods of qualitative characteristics COSS are described
above. Formalization of the information based on the expert evaluations of
appearances of different qualitative characteristics allows operating not with
values of the characteristics measured in different scales, but with membership
functions of the concepts applied to an evaluation of characteristics of real objects.
These methods are inapplicable to construct quantitative characteristic COSS.
So, we offer to construct membership functions of COSS terms on the basis of
direct inquiry of a single expert, these COSS's can be applied to formalize both
quantitative and qualitative characteristics pari passu.
It is worth mentioning that a COSS based on inquiry of experts will always
possess some property of uniqueness, i.e. it reflects judgments of the experts who
often use the information known to few people who are “in gathering”.
Actually, if one wants to build COSS "height" = {low, average, high, very
high} from point of view of Moscow and Tokyo experts, then, obviously, there
will be two spaces with a different collection of membership functions. If one
wants to build COSS "profit" = {very low, low, average, high, very high}, the
money equivalent which is considered as high profit, will dramatically differ for
different firms. It is just the case when defining similar categories experts use the
information known to few people only, on the one hand, and unique for a certain
firm, on the other hand.
Model-building techniques of COSS term-sets membership functions for
quantitative and qualitative characteristics have in essence identical approaches
and differ only in universal sets.
Let us construct COSS with a title
X
and term-set
(){
}
,
T
X
=
X
,
X
,...,
X
1
2
m
where
X
,
1
are terms corresponding to the minimum and maximum intensity
degree of characteristic appearance within a universal set
X
m
[
]
.
U
=
a
,
b
(
)
x
1
,
x
2
Let us assume that an expert defines typical intervals
for terms
X
;
l
l
, and these intervals are equal to unity for all points of membership
function of corresponding terms. For some terms, points (one for each term) can
be typical rather than intervals. Without loss of generality, typical intervals for
qualitative characteristics can be defined by the following procedure. Let there be
a test for demonstration of studied qualitative characteristic for the object (0 is a
minimum quantity of points which an object can obtain as testing results, i.e.
complete absence of characteristic appearance;
n
is maximum quantity of points,
i.e. its total availability of the characteristic appearance). Let us normalize all
possible test points with a maximum point
n
and let us give the chance to the
expert to answer regarding typical intervals for terms
X
belonging to [0, 1].
The questions asked to the expert can be formulated as follows: “What interval
of normalized test points you consider typical for a term?”. In case of quantitative
characteristic the expert defines subsets of universal set which are typical for each
of terms from his/her point of view.
l
=
1
m
