Information Technology Reference
In-Depth Information
Chapter 2
Intuitionistic Fuzzy IMs
Here, following [11, 16], we extend the concept of IM, introducing the concept of
an Intuitionistic Fuzzy IM (IFIM) and Extended IFIM (EIFIM).
2.1 Short Remarks on Intuitionistic Fuzziness
Initially, we give some remarks on Intuitionistic Fuzzy Sets (IFSs, see, e.g., [7, 13])
and especially, of their particular case, Intuitionistic Fuzzy Pairs (IFPs; see [26]).
The IFP is an object with the form
1, that
is used as an evaluation of some object or process. Its components (
a
and
b
)are
interpreted as degrees of membership and non-membership, or degrees of validity
and non-validity, or degree of correctness and non-correctness, etc.
Let us have two IFPs
x
a
,
b
, where
a
,
b
∈[
0
,
1
]
and
a
+
b
≤
.
The following relations have been defined in [26]:
=
a
,
b
and
y
=
c
,
d
x
<
y
iff
a
<
c
and
b
>
d
x
≤
y
iff
a
≤
c
and
b
≥
d
x
=
y
iff
a
=
c
and
b
=
d
x
≥
y
iff
a
≥
c
and
b
≤
d
x
>
y
iff
a
>
c
and
b
<
d
We define analogous of operations “conjunction” and “disjunction”:
x
&
y
=
min
(
a
,
c
),
max
(
b
,
d
)
x
∨
y
=
max
(
a
,
c
)),
min
(
b
,
d
)
x
+
y
=
a
+
c
−
a
.
c
,
b
.
d
x
.
y
=
a
.
c
,
b
+
d
−
b
.
d
a
+
c
2
b
+
d
2
x
@
y
=
,
.
Search WWH ::
Custom Search