Information Technology Reference
In-Depth Information
Where
()
()
()
()
()
()
μ
x
=
max
μ
x
;
μ
x
=
max
μ
x
;
f
0
=
1
f
1
=
0
.
l
l
l
l
1
2
1
≤
l
≤
m
1
≤
l
≤
m
l
≠
l
1
()
()
()
If
L
x
=
R
x
=
f
x
=
1
−
x
, then
U
1
{
[
]
}
()
()
=
∫
ζ
1
−
μ
x
−
μ
x
dx
=
,
l
l
U
U
2
U
1
2
∪
m
where
U
=
U
−
U
.
l
l
=
As COSS can serve as models of expert evaluation of characteristics, then degree
of COSS fuzziness is interpreted as mean degree of difficulties of description of
real objects and situations by an expert and, besides, as a quantity indicator of
quality of the fuzzy information provided by experts.
In [28] it is shown that linear transformation of universal set does not change
degree of fuzziness of the relevant COSS.
It is worth mentioning that researches of COSS properties and justification of
their employment for various practical problems are under development. The
history of these researches repeats history of researches of actually all sections of
the fuzzy set theory, where the theoretical component always noticeably lagged
behind the practical one.
1.6 Overview of Mo del-Buil di ng Metho ds for Membership Functions
1.6 Overview of Model-Building Methods for Membership
Functions of Fuzzy Sets and Semantic Spaces
1.6 Overview of Mo del-Buil di ng Metho ds for Membership Functions
Important phase of information processing is information formalization, i.e. its
representation in a form allowing application of means of known mathematical
theories at subsequent stages of its processing and analysis. For example, if the
obtained data are values of some chance quantity, the means of probability theory
and the mathematical statistics are applied; and if they are considered as values of
some fuzzy variable, means of the fuzzy set theory are applied.
Complexity of formalization of fuzzy information is that applied building
methods of membership functions of fuzzy sets and term-sets of semantic spaces
are beyond the fuzzy set theory, and therefore adequacy of formalization models
cannot be checked up within the scope of its means.
Let us consider known building methods of membership functions of fuzzy sets
and term-sets of semantic spaces which are directly set by a table, a formula, and
an example [56—59].
Example 1.5.
Various representations of a fuzzy set. The fuzzy set
~
= {business
success of various strategies of a financial structure development} is possible to
represent as:
x
..........
.......
1
2
3
4
1
()
μ
x
.........
0
2
0
0
0
~
1
A
