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is referred to as analogue of a standard deviation for output observations.
(
)
n
~
∑
ˆ
2
f
Y
,
Y
i
2
i
HR
=
=
1
.
(
)
n
~
~
∑
2
f
Y
,
Y
i
is referred to as analogue of coefficient of determination.
i
=
1
1
n
(
~
)
∑
=
2
HS
=
f
Y
i
Y
,
.
i
n
−
m
−
1
is referred to as analogue of an evaluation of a standard error.
With definite input data and definite coefficients of regression model, the
developed hybrid fuzzy least-squares regression model is classical regression
model, and certain analogues of indexes are a standard deviation of output data,
determination coefficient and standard error evaluation, accordingly.
i
1
6.4 Linear Hybrid Fuzzy Least-Squares Regression Model on
the Basis of Nonnegative
T
-Numbers
6.4 Linear Hy bri d F uzzy Least-Squares Regression Mo del
The attention to nonnegative
T
-numbers is explained by the fact that while
constructing regression relations for qualitative characteristics, fuzzy numbers
which are formalizations of linguistic values of these characteristics based on
COSS can be considered as the initial information. As universal COSS set is the
segment [0, 1] rather often, the fuzzy numbers corresponding to its terms, are
nonnegative.
As known, the tolerance fuzzy number
~
with membership function
⎧
x
−
a
1
1
+
,
a
−
a
≤
x
<
a
,
a
>
0
⎪
1
L
1
L
a
⎪
⎪
L
x
−
a
()
1
−
2
,
a
<
x
≤
a
+
a
,
a
>
0
μ
x
=
⎨
~
2
2
R
R
a
A
⎪
R
1
a
≤
x
≤
a
;
⎪
1
2
⎪
0
x
<
a
−
a
or
x
>
a
+
a
.
⎩
1
L
2
R
is referred to as
T
-number (fuzzy number of
T
-type).
A
T
-number is symbolically recorded as
~
(
)
. The normal
A
≡
a
,
a
,
a
L
a
,
1
2
R
a
=
a
triangular number is the special case of
T
-number with
and is
1
2
~
(
)
A
≡
a
,
a
L
a
,
a
=
a
symbolically recorded as
. With
the triangular number is
L
R
1
R
referred to as symmetric, and with
a
≠
a
— asymmetric. A
T
-number is
L
R
referred to as nonnegative under the condition
a
−
a
≥
0
.
1
L
