A Fuzzy Approach to Reasoning with Trust, Distrust and
Insufficient Trust
Nathan Griffiths
University of Warwick, UK
A Fuzzy Approach to Reasoning with Trust, Distrust and Insufficient Trust – p.1
Introduction
Multiagent systems rely on the interactions of many
autonomous (often self-interested) agents
Agents have specific individual capabilities, knowledge
and resources, and vary in reliability, quality and
honesty
A Fuzzy Approach to Reasoning with Trust, Distrust and Insufficient Trust – p.2
Introduction
Multiagent systems rely on the interactions of many
autonomous (often self-interested) agents
Agents have specific individual capabilities, knowledge
and resources, and vary in reliability, quality and
honesty
When an agent cooperates it is entering into an
uncertain interaction, that has an associated risk of
failure or reduced performance
A Fuzzy Approach to Reasoning with Trust, Distrust and Insufficient Trust – p.2
Introduction
Multiagent systems rely on the interactions of many
autonomous (often self-interested) agents
Agents have specific individual capabilities, knowledge
and resources, and vary in reliability, quality and
honesty
When an agent cooperates it is entering into an
uncertain interaction, that has an associated risk of
failure or reduced performance
Agents can use trust to manage this risk
This research uses fuzzy logic to allow agents to
represent and reason with uncertain and imprecise
information regarding others’ trustworthiness.
A Fuzzy Approach to Reasoning with Trust, Distrust and Insufficient Trust – p.2
Trust and Reputation
Trust and reputation are related, but distinct, concepts
Trust represents an agent’s individual assessment of
the reliability, honesty etc. of another
Reputation is built from a combination of individual
trust assessments (or opinions)
A Fuzzy Approach to Reasoning with Trust, Distrust and Insufficient Trust – p.3
Trust and Reputation
Trust and reputation are related, but distinct, concepts
Trust represents an agent’s individual assessment of
the reliability, honesty etc. of another
Reputation is built from a combination of individual
trust assessments (or opinions)
Many of the existing applications of trust combine trust
and reputation, using a global aggregation of individual
trust into a reputation assessment (e.g. Sabater and
Sierra; Song et al.; Xiong and Liu, etc.)
Existing approaches often do not consider the issues
of distrust and lack of trust.
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Trust and Reputation
To use reputation, we must address issues of:
motivating the sharing of private information
subjectivity and context of information
In some domains it is not clear how to address
these. . .
Therefore, although both trust and reputation are
important, it is useful to treat them as distinct (but
related) notions
We focus on trust alone — enable agents to make use
of what (little?) information they have.
(NB: we see trust and reputation as complimentary; ideally we would
have both, but sometimes reputation is not practicable.)
A Fuzzy Approach to Reasoning with Trust, Distrust and Insufficient Trust – p.4
Fuzzy Logic for Trust
Although trust is based on previous experience, there
is inherent uncertainty and imprecision: assessments
are subjective and agents may change unpredictably
over time
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Fuzzy Logic for Trust
Although trust is based on previous experience, there
is inherent uncertainty and imprecision: assessments
are subjective and agents may change unpredictably
over time
Fuzzy logic enables representation of this uncertainty
and imprecision
Existing models (Manchala; Ramchurn et al.; Song et
al.) have successfully used fuzzy logic to represent
trust in multiagent systems
However, these approaches use trust as a means of
establishing reputation, rather than as means to
directly support decision making.
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Basic Fuzzy Concepts
Sets have fuzzy boundaries: objects have a degree of
membership µ(x) ∈ [0 : 1]
Fuzzy sets are used to define terms with respect to a
variable, e.g. the term young
^ on the variable age
Can use linguistic hedges to modify terms, e.g.
very young
^
Relations between variables can be defined using
fuzzy inference rules, e.g. if age is young
^ and income is
g
g then customerPotential is high
very high
Rules are applied in parallel and the conclusion
membership degrees aggregated, and a crisp value
extracted.
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Trust
Trust is generally taken to be the belief that an agent
will act in the best interests of another (i.e. will
cooperate), even if given the opportunity to do
otherwise (i.e. to defect)
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Trust
Trust is generally taken to be the belief that an agent
will act in the best interests of another (i.e. will
cooperate), even if given the opportunity to do
otherwise (i.e. to defect)
Distrust is not simply the negation of trust, but rather it
is a belief that an agent will act against the best
interests of another [Marsh]
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Trust
Trust is generally taken to be the belief that an agent
will act in the best interests of another (i.e. will
cooperate), even if given the opportunity to do
otherwise (i.e. to defect)
Distrust is not simply the negation of trust, but rather it
is a belief that an agent will act against the best
interests of another [Marsh]
Untrust corresponds to the space between distrust and
trust, in which an agent is positively trusted, but not
sufficiently to cooperate with [Marsh]
Undistrust is a negative trust, but insufficient to make
definite conclusions in the reasoning process.
A Fuzzy Approach to Reasoning with Trust, Distrust and Insufficient Trust – p.7
Trust
Marsh’s model:
D
UT
−1
T
0
1
The addition of undistrust:
D
−1
UT
UD
0
T
1
A Fuzzy Approach to Reasoning with Trust, Distrust and Insufficient Trust – p.8
Dimensions of Trust
Trust is based on an agent’s experiences, and so
agents must track their interaction histories, and
record whether their expectations have been met
Trust comprises the combination of the different
characteristics of an interaction
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Dimensions of Trust
Trust is based on an agent’s experiences, and so
agents must track their interaction histories, and
record whether their expectations have been met
Trust comprises the combination of the different
characteristics of an interaction
Agents can model such characteristics as dimensions
of trust, which taken together give an assessment of
an agent’s trustworthiness
For example, we use the dimensions of success, cost,
quality and timeliness.
A Fuzzy Approach to Reasoning with Trust, Distrust and Insufficient Trust – p.9
Interaction Histories
Agents maintain a history of the interactions that they
have had with an agent α, and track the number of
successful (Iαd+ ) and unsuccessful (Iαd− ) interactions for
each dimension d, in terms of whether their
expectations were met
The experience, edα , in each dimension d is:
d+
d−
I
−
I
α
edα = αd+
Iα + Iαd−
This crisp value is fuzzified as Eαd = fuzzySingleton(edα ).
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Interaction Histories
Agents track of the outcomes of their interactions by
using a window of experience that is maintained for
each agent
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Interaction Histories
Agents track of the outcomes of their interactions by
using a window of experience that is maintained for
each agent
Over time, stored information may become outdated
Outdated experiences are purged: the record of an
interaction is removed after a purge lag
Small purge lag: records do not persist, quick
response to changes, may give keep insufficient
information; Long purge lag copes with perturbations,
slow to respond
A Fuzzy Approach to Reasoning with Trust, Distrust and Insufficient Trust – p.11
Interaction Histories
Agents track of the outcomes of their interactions by
using a window of experience that is maintained for
each agent
Over time, stored information may become outdated
Outdated experiences are purged: the record of an
interaction is removed after a purge lag
Small purge lag: records do not persist, quick
response to changes, may give keep insufficient
information; Long purge lag copes with perturbations,
slow to respond
Confidence level given by confidence dα = Iαd+ + Iαd−
Low confidence implies untrust or undistrust.
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Fuzzy Trust
Define fuzzy terms for experience:
NB
NM
NS
Z
PS
PM
PB
1
−1
−0.5
0
0.5
1
0
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Fuzzy Trust
Define fuzzy terms for experience:
NB
NM
NS
Z
PS
PM
PB
1
−1
−0.5
0
0.5
1
0
and for trust:
HD
D
UT
UD
T
HT
1
−1
−0.5
0
0.5
1
0
A Fuzzy Approach to Reasoning with Trust, Distrust and Insufficient Trust – p.12
Fuzzy Trust
For each dimension we define a set of fuzzy inference
rules that take the fuzzified experiences as antecedents
and make conclusions regarding trust, e.g.
(RU T 1) if confidence dα < minConfidence and Eαd is positive
^
then Tα is untrust
(RU T 2) if confidence dα < minConfidence and Eαd is negative
^
then Tα is undistrust
(etc . . . )
(RT 3)
^
^
Eαd is negativeBig
then Tα is highDistrust
d
^
^ or undistrust
^
if Eα
is negativeMedium
then Tα is very distrust
d is negativeSmall
^
^
if Eα
then Tα is undistrust
(RT 4)
if
(RT 1)
(RT 2)
if
(RT 5)
^ or untrust
^
Eαd is zero
g then Tα is undistrust
d
^
^
if Eα
is positiveSmall
then Tα is untrust
(RT 6)
if
^
] or untrust
^ (etc . . . )
Eαd is positiveMedium
then Tα is very trust
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Determining Trust
Check whether there have been sufficient interactions;
if not assign untrust or undistrust (rules RU T n)
Otherwise, apply fuzzy inference rules (RT n), e.g.
1
1
PS
RT 5
PM
RT 6
0
0
0
0.25
0
0.5
0.5
T
UT
0
0.25
0.5
0
0
0.22
0.5
0.5
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Agent Selection
Distrusted agents filtered out: reject if
^ ) > maxDistrust
similarity(Tα , highDistrust
A Fuzzy Approach to Reasoning with Trust, Distrust and Insufficient Trust – p.15
Agent Selection
Distrusted agents filtered out: reject if
^ ) > maxDistrust
similarity(Tα , highDistrust
Untrusted and undistrusted agents: if no trusted
agents then with some probability (rebootstrap rate)
the agent with the highest trust level from the set of
untrusted and undistrusted agents will be selected
A Fuzzy Approach to Reasoning with Trust, Distrust and Insufficient Trust – p.15
Agent Selection
Distrusted agents filtered out: reject if
^ ) > maxDistrust
similarity(Tα , highDistrust
Untrusted and undistrusted agents: if no trusted
agents then with some probability (rebootstrap rate)
the agent with the highest trust level from the set of
untrusted and undistrusted agents will be selected
Otherwise, combine trust with other factors (advertised
cost, quality, etc.) to determine agent rating using rules
of the form:
g
^ and Fαc is medium
^ and Fαq is very high
(RR n) if Tα is highTrust
g
then Rα is high
g
^ and Fαc is medium
^ and Fαq is high
(RR m)if Tα is low distrust
g (etc. . . )
then Rα is low
A Fuzzy Approach to Reasoning with Trust, Distrust and Insufficient Trust – p.15
Bootstrapping
Initially agents have insufficient experience for
reasoning
Each agent goes through a bootstrapping phase in
which partners are chosen randomly by way of
exploration
During bootstrapping undistrusted, untrusted, and
trusted agents have an equal chance of being
selected.
A Fuzzy Approach to Reasoning with Trust, Distrust and Insufficient Trust – p.16
Experimental Results
Implemented using the NRC FuzzyJ Toolkit
Evaluate different configurations of the fuzzy decision
mechanism for exactly the same set of possible
interactions (i.e. use a fixed generated “environment
history”)
Simulated an agent selecting a partner from 50 others
for 2000 interactions (bootstrapping phase = 100
interactions)
Reliability of agents reduced after 1000 interactions.
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Experimental Results
Success rate
1
fuzzy
fuzzy - no distrust
fuzzy - no untrust
fuzzy - no untrust or distrust
random
0.8
0.6
0.4
0.2
0
0
500
1000
1500
2000
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Experimental Results
Results averaged across 20 “environments”:
Selection mechanism
Success rate
Cost rate
Quality rate
Fuzzy trust
0.64
0.73
0.84
No distrust
0.63
0.68
0.81
No untrust, undistrust
0.63
0.58
0.79
No distrust, untrust, undistrust
0.61
0.56
0.78
Random (control)
0.42
0.39
0.64
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Summary
We have shown how fuzzy logic can be used to
represent trust
We have proposed a new notion of undistrust and
incorporated this into the reasoning process
Initial experimental results indicate that the approach
provides a significant reduction in failure rate, and
improvement in cost and quality rates
We have shown how distrust, untrust and undistrust
improve performance
There are many areas of ongoing work, including
additional experimentation, and integration with
existing models of reputation.
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