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ference example. In fuzzy theory, the membership function (x) for a fuzzy
variable x specifies the degree of an element belonging to a fuzzy set. It maps x
into the range [0, 1], where 1 is full membership and 0 is no membership. Fig-
ure 6.6(a) shows a high membership function for modeling the local score (Γ),
and Figure 6.6(b) shows the five levels of membership function. Figure 6.6(c)
illustrates the inference process. Consider two fuzzy variables: one is the prod-
uct quality (Q) and another is the delivery time (T ), with initial values Q =
0.84 and T = 0.26. To illustrate, we apply the following two simple fuzzy
inference rules in Figure 6.6:
1. If Q is very good AND T is moderate, then Gamma is high.
2. If Q is ordinary AND T is fast, then Gamma is medium.
high
= Γ
(
)
Γ
(
)
Very Low
Low
Medium
High
Very High
(0.75)
=
1
High
1.0
1.0
0.5
0.5
(0.6)
=
0.26
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
(a) high local score
(b) five levels of local scores
Rule 1:
Q is very good
AND
T is moderate
IMPLY
Γ
is high
Aggregate
Γ
Rule 2:
Q is ordinary
AND
T is fast
IMPLY
is medium
Q = 0.84
T = 0.26
Γ
= 0.6
(c) trust aggregation
FIGURE 6.6: Illustration of fuzzy inference [Song et al., 2005].
All rules are processed in parallel. The resulting membership is determined
by assessing all terms in the premise. The fuzzy operator AND is then applied
to determine the support degree of the rules. The AGGREGATE operator
superimposes two resulting membership curves. The final local score Γ = 0.6
is generated by defuzzifying from the aggregation result. This is done by taking
the centroid of the superimposed membership curve in Figure 6.6(c). In a real-
life P2P reputation system, this fuzzy logic inference process could demand
tens to hundreds of rules.
In FuzzyTrust, three system design criteria are developed below to match
with the eBay characteristics.
1. The network bandwidth consumption required to exchange local trust
scores for hot spots can be extremely high. Thus, a reputation system
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