Information Technology Reference
In-Depth Information
In these situations a physician that is working with such computer-assisted sys-
tem should start to do monitoring of the supposed disease and look for a particu-
lar diagnosis (As was already told above, this search can be done in the specific
databases [5, 22, 23]).
If the available initial information contains
R
SD
and
R
SD
and the total degree of a
diagnosis is calculated as was defined in (25.7), then the following observation can
be done. If the total degree is not much different from meanings of
R
SD
, that can be
considered as an alarm of the RD.
25.4.2
A Comparison with Mamdani and TSK Methods of Fuzzy
Inference Process
Let us make several remarks concerning the proposed
mean
-absolutedifference in-
ference mechanism and well-known fuzzy inference methods such as Mamdani [19]
and Takagi-Sugeno-Kang (TSK)[29]. The main difference between the Mamdani
and TSK methods lies in the consequent of fuzzy rules. Mamdani fuzzy systems
use fuzzy sets as rule consequent whereas TSK fuzzy systems employ linear func-
tions of input variables as rule consequent. All the existing results on fuzzy systems
as universal approximators deal with Mamdani fuzzy systems only and no result
is available for TSK fuzzy systems with linear rule [28]. Let us consider the Ma-
madani inference process in a simplified form as it shown below, using denotations
introduced in this paper.
R
1
:
IF S
1
THEN D
1
also
R
2
:
IF S
2
THEN D
2
fact:
s
0
−−−−−−−−−−
consequence:
D
In Mamdani inference fuzzy implication is considered as min operator, also is in-
terpreted as max operator.
Moreover, the following operations are predefined:
•
The firing levels of the rules
α
1
=
S
1
(
s
0
)
,
α
2
=
S
2
(
s
0
)
•
the individual rule outputs are obtained by
D
1
(
D
2
(
d
)=(
α
1
∧
D
1
(
d
))
,
d
)=(
α
2
∧
D
2
(
d
))
