Information Technology Reference
In-Depth Information
1
[
]
() ()
∫
n
min
μ
x
,
f
x
dx
l
n
l
λ
=
∫
0
,
l
=
1
m
,
n
=
1
N
.
1
[
]
() ()
max
μ
n
x
,
f
x
dx
l
0
or
1
()
()
n
l
∫
μ
n
σ
=
x
−
f
x
dx
,
l
=
1
m
,
n
=
1
N
.
l
0
()
μ
n
x
Let us denote a possibility that fuzzy number with membership function
is
~
()
equal to fuzzy number
with membership function
with
f
j
x
j
[
]
()
()
n
Pos
μ
x
=
f
x
. As known [153],
j
[
]
[
]
()
()
() ()
n
n
Pos
μ
x
=
f
x
=
max
min
μ
x
,
f
x
.
j
j
x
[
]
()
()
n
Pos , the evaluation of appearance of qualitative
characteristic of
n
-th object (with membership function
If
μ
x
=
f
x
=
γ
j
()
n
μ
x
,
n
=
1
N
) is
identified using linguistic value
X
with possibility γ
.
j
4.6 A Metho d of Determination of O pti mum Sets of C haracteristic
4.6 A Method of Determination of Optimum Sets of
Characteristic Linguistic Values
4.6 A Metho d of Determination of O pti mum Sets of C haracteristic
Experts can apply different sets of their linguistic values to estimate or describe
characteristics. Some sets bring difficulties to experts due to the insufficiency of
values, and other sets — due to redundancy of values. As a result of these
difficulties one should expect growth of fuzziness and mismatch of the
information provided by experts.
While estimating of attributes' appearances by an expert, a natural problem is:
“What are criteria to choose an optimum range of a linguistic scale applied to
estimate any characteristic?” In [28], the following criteria of an optimality of set
of characteristic linguistic values are defined:
1) set of values used by experts provides minimum uncertainty while
describing real objects;
2) set of values which ensure maximum consistency of the expert information.
In [28], problem of definition of optimum sets of characteristic linguistic values is
solved only if the first criterion is satisfied. In the present paragraph, while defining
the optimum sets of characteristic linguistic values the maximin problem is solved.
For the purpose of the characteristic
X
evaluation or description,
k
experts
are involved.
