Information Technology Reference
In-Depth Information
3
5
7
9
9, 9
7, 9
5, 9
7, 7
5, 7
3, 9
Inclusion order relation
5, 5
3, 7
Product order relation
3, 5
3, 3
≤
The diagram represents two lattice structures with respect to
I
(product order re-
lation) and
be the set of experts
who assign interval-value from
I
D
to every formula. Assuming the ordinary t-norm
ↆ
e
(inclusion order relation) over
I
D
.Let
{
T
1
,
T
2
,
T
3
}
∧
on
D
, one can immediately obtain the corresponding residuum
→
on
D
, and hence
∧
I
D
,
→
I
D
on
I
D
can be constructed. Given a set of formulae
X
and a formula
ʱ
,tocompute
ʣ
), first for each
T
i
(
i
=1,2,3),thevalue
gr
(
X
|≈
ʱ
) in the sense of both (
ʣ
) and (
x
∈
X
T
i
(
x
)
) needs to be computed. Let the respective values corresponding
to
T
1
,
T
2
,
T
3
be [3
,
5], [5
,
7], [7
,
7]. Then, for (
→
I
D
T
i
(
ʱ
), the least interval [3
,
5] will be selected
and the left-hand end point 3 would be counted as the grade of
X
ʣ
ʣ
),
|≈
ʱ
. Following (
[5
,
5] will be chosen as the interval included in all the intervals in the sense of
ↆ
e
,and
its right-hand end point 5 would be counted as the grade of
X
. The first method
pulls down one of the experts high opinion, which is here 7, drastically to 3; whereas the
second admits some room for adjustment between different opinions, and pulls down
the valueto5.Thus, (
|≈
ʱ
ʣ
) provides a good sense of respecting individual's opinion.
ʣ
)
3.4
Graded Consequence: Form (
Among the above two forms of graded consequence, (
) is based on a
conservative
attitude as it choses the left-hand end point of the interval lying below each expert's
(
T
i
) opinion for computing the valueof
ʣ
∧
x
∈
X
T
i
(
x
)
→
I
T
i
(
ʱ
). On the other hand, form
ʣ
) admits very
liberal
attitude as it takes the right-hand end point of the interval-value
which lies at the common consensus zone of the values for
(
) taking
care of every expert's opinion. Both of these reflect two extremities of decision making
attitude. Below we would look for an approach where considering each expert's opin-
ionfirstanintervalfor
∧
x
∈
X
T
i
(
x
)
→
I
T
i
(
ʱ
) is assigned. Then, a number of times the
assigned interval can be revised; the number being stipulated by different constraints.
Finally among these iterations for the values of
∧
x
∈
X
T
i
(
x
)
→
I
T
i
(
ʱ
∧
→
) one would be cho-
sen, and from all such revised interval-values the common zone will be selected. This
idea of iterative revision of an interval-value assignment is taken care of in the follow-
ing series of definitions. Finally Theorem 3.8 of this section throws light on the fact that
the forms generated from iterative-revisions (
X
T
i
(
x
)
I
T
i
(
ʱ
x
∈
ʣ
1
,
ʣ
2
) retain a place between the two
extreme attitudes of decision making.
Definition 3.4.
I
[
a
,
b
]
is a collection of iterated revisions [
x
i
,
y
i
]'sof[
a
,
b
], given by:
I
[
a
,
b
]
=
[
x
i
,
y
i
] :
x
0
=
a
,
y
0
=
b
,
[
x
i
,
y
i
]
ↆ
e
[
x
i
−
1
,
y
i
−
1
] and [
x
i
−
1
,
y
i
−
1
] is non-degenerate
{
}
.
