Information Technology Reference
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maximum degree of compatibility; however, the membership degree decreases
while the response time increases. It also shows that response time has the mini-
mum degree of incompatibility between 0 to 5 seconds; however, the membership
degree increases while the response time increases. Note that the response time is
set to be 2 to 5 seconds in the contract; however, the range between 0 to 2 is also
acceptable with the same membership value as the initial range in the contract
has [3]. With the same reasoning, the availability of 80 to 100 has the maximum
degree of compatibility illustrated in Figure 2. However, the membership degree
of compatibility decreases while the availability decreases.
Fig. 2.
Membership functions for ResponseTime and Availability
Having defined the membership functions, the mapping between the input and
output space will be done by defining a list of
if-then statements
called
rules
.We
have already defined what do we mean being compatible and incompatible for
the quality parameters and specified their ranges using membership functions.
Since we are relaxing the antecedent using a fuzzy statement, it is also required
to represent the membership degree of the output (i.e. here satisfaction). There-
fore, the satisfaction degree is also represented as fuzzy sets: satisfaction is low,
satisfaction is average and satisfaction is high.
We define three if-then rules as below. it represents the
antecedent
and
con-
sequent
of the rule. All the rules are applied in parallel and their order in unim-
portant. We define the fuzzy union/disjunction (
OR
) and the fuzzy conjunction/
intersection (
AND
)using
max
and
min
functions respectively. Therefore
AANDB
is represented as
min
(
A, B
)and
AORB
is represented as
max
(
A, B
).
1
.If
(
ResponseT ime is compatible
)
and
(
AvailabilityisCompatible
)
then
(
Satisfaction is high
).
2
.If
(
ResponseT ime is incompatible
)
or
(
Availability is incompatible
)
then
(
Satisfaction is average
).
3
.If
(
ResponseT ime is incompatible
)
and
(
Availability is incompatible
)
then
(
Satisfaction is low
).
