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Visual Knowledge
Representation for Decision
Support
- from Cognitive Maps to
Fuzzy Knowledge Maps
Shamim Khan
School of Computer Science
[email protected]
Introduction
 The
goal of Artificial Intelligence (AI)
 Decision Support Systems and AI
 Knowledge representation and reasoning
 Schemes for knowledge representation


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Rules
Semantic Networks
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Rule-based Knowledge
Representation
A
series of IF condition THEN action
statements
IF the stain of the organism is gramneg, and
the morphology of the organism is rod, and
the aerobicity of the organism is aerobic
THEN there is strongly suggestive evidence (.8) that
the class of organism is enterocabateriaceae
 An
inference engine searches for patterns
in the rules that match patterns in the data.
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Semantic Networks
 Knowledge
 Visual
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as a pattern of nodes and arcs
nature helps with understanding
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Cognitive Maps
- A causal view of knowledge
 Knowledge
as a network of concepts and
their causal relationships
 A visual representation scheme within a
computational framework
 First desribed as a decision support tool in
(Axelrod 1976)
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Robert Axelrod , BA(Math), PhD(Political Science)
Professor for the Study of Human Understanding
University of Michigan
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Variants of Cognitive Maps
 Also
used in other fields – eg, psychology,
geography
 Axelrod's


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cognitive maps
A mathematical model of a belief system
Lays out important concepts and
relationships on a 2D plane for
“predictions, decisions and explanations”
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Cognitive Maps
- Structure and Analysis
Directed edges represent causal relationships
linking nodes
 Signs reflect promoting or inhibitory effects

Speed
+
Accident
-

Rules to analyse cognitive maps
Eg, effect of A on B positive if path A -> … -> B has even
number of negative edges
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Cognitive Maps
- an example (Axelrod 1976)
Policy of
withdrawal
Amount of
security in
Persia
+
+
Ability of
Persian govt.
to maintain
order
Removal of better
governors
-
+
-
British
utility
Strength of
Persian govt.
+
Present
policy of
intervention
in Persia
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+
Allowing
Persians to
have
continued
small subsidy
+
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Ability of
Britain to put
pressure on
Persia
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Limitations of Axelrod’s
cognitive maps

Difficulty handling multiple paths between two
nodes


Static - do not evolve with time


Real-life scenarios may also involve feedback
Use of bivalent (true/false) logic


Conflicting inferences
Real-life causalities often expressed in inexact (fuzzy)
terms
Proposed solution:
Kosko’s Fuzzy Cognitive Maps (Kosko 1986)
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Cognitive Maps
- an example (Axelrod 1976)
Policy of
withdrawal
Amount of
security in
Persia
+
+
Ability of
Persian govt.
to maintain
order
Removal of better
governors
-
+
-
British
utility
Strength of
Persian govt.
+
Present
policy of
intervention
in Persia
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+
Allowing
Persians to
have
continued
small subsidy
+
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Ability of
Britain to put
pressure on
Persia
12
Fuzzy Cognitive Maps
(FCM)
FCMs feature
- Inexact (fuzzy) linguistic expression of
concepts and causal links
- Feedback enabling evolution with time
Moderately increases
Accident
Strongly increases
Speed
Very strongly
decreases
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Traffic congestion
13
Fuzzy Cognitive Maps
(FCM)
FCMs feature
- Inexact (fuzzy) linguistic expression of
concepts and causal links
- Feedback enabling evolution with time
Accident
Moderately increases
0.5
Speed
Strongly increases
0.7
0.9
Very strongly
decreases
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Traffic congestion
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FCM operation
The state of a node determined by
- sum of its inputs modified by causal
link weights, and
- a non-linear transfer function
Fed with a stimulus state vector, the state
of an FCM is continuously updated
until it converges
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FCM operation
The state of a node Ci determined by
- sum of its inputs modified by causal
link weights, and
- a non-linear transfer function S
n 1
ci (t  1)  S (  c j (t )  wij )
j 0
Fed with a stimulus state vector, the
state of an FCM is continuously
updated until it converges
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A fuzzy cognitive map concerning
public health
C1
No.
No. of
ofppl
ppl
in
in the
the city
city
+0.9
+0.6
+0.9
C4
Garbage
per area
C3
Modernization
-0.3
C6
No.
No. of
ofdiseases
diseases per
per1000
1000residents
residents
+0.9
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+0.7
+0.9
-0.9
C2
Migration
Migration
into
into city
city
C5
Sanitation
facilities
-0.9
+0.8
C7
Bacteria
per area
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Decision support using FCMs
Given a stimulus vector, FCMs
converge to one of three
possibilities
State vector remains unchanged
2. A sequence of state vectors keep
repeating
3. The state vector keeps changing
indefinitely
1.
The evolved state(s) of an FCM can
provide useful decision support
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FCMs as decision support tools

Problem domain analysis
-
-
-
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How significant is concept A?
What is the degree of influence of concept A
on concept B?
What will be the impact of a change in concept
A on other concepts?
Given a set of values for all concepts at a point
in time, how will the system evolve with time?
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FCMs as decision support tools
(cont.)

Goal oriented decision support (Khan et al
2004a)
– What state of affairs can lead to a given (goal)
state?

Group decision support (Khan et al 2004b)
– FCMs can be merged
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Limitations of FCMs
FCMS model only monotonic causal
relations
Influence on effect node increases
(decreases) with increasing (decreasing)
state value of cause node
Real world relationships can be nonmonotonic
Distance
run
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non-monotonic
relationship
Node A
Speed
Node B
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Fuzzy Knowledge Map (FKM)
A truly fuzzy system to overcome
limitations of the FCM (Khor et al
2004)
Relationship between nodes
represented using a set of fuzzy
rules
Distance
run
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Fuzzy rule set
Node A
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Speed
Node B
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Fuzzy Knowledge Map (FKM)
Relationship between nodes represented
using a set of fuzzy rules
Eg,
- If distance_run is very_short, then speed is low
- If distance_run is short, then speed is fast
- If distance_run is medium, then speed is vFast
- If distance_run is long, then speed is medium
- If distance_run is very_long, then speed is low
Distance
run
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Fuzzy rule set
Node A
Speed
Node B
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An FKM application experiment
A two-layer hierarchy of FKMs used for decision support
in share trading
 Inferences derived at the lower layer using market
indicators utilized at the higher layer to make
recommendations.

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Experiment

Indicators used:





Two data sets:



Commonwealth Bank of Australia Ltd.
Telstra Corporation Ltd.
Study period:

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Momentum,
Relative strength index,
Bollinger band,
Moving averages.
3 years ( Jan 2002 to Dec 2004).
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Results
Performance of the FKM model over the 3-year
study period
 FKM outperforms simple ‘Buy and hold’ strategy

Security
Commonwealth Bank Ltd.
Telstra Corp. Ltd.
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FKM model Buy & hold
Profit/Loss Profit/Loss
17%
11%
3%
11%
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Conclusion

Knowledge representation schemes can be more
useful if they



Help us visualize a problem domain for analysis and
inferencing
Allow incorporation of inexact/qualitative human
expert knowledge
Fuzzy knowledge maps overcome the limitations
of FCMs by allowing fuzzy expression of causal
knowledge and fuzzy reasoning
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References
•
•
•
•

•
•
Axelrod, R. (1976), “Structure of Decision”, Princeton University Press, US.
Kosko, B. (1986) "Fuzzy Cognitive Maps", Int. J. Man-Machine Studies,
Vol.24, pp.65-75.
Khan, M.S., Quaddus, M. A., and Intrapairot, A. (2001) "Application of a
Fuzzy Cognitive Map for Analysing Data Warehouse Diffusion", Proc.19th
IASTED Int. Conf. on Applied Informatics, Innsbruck 19-22 Feb., pp.32-37.
Khan, M.S., and Quaddus, M. (2004a)“Group Decision Support using Fuzzy
Cognitive Maps for Causal Reasoning”, Group Decision and Negotiation
Journal, Vol. 13, No. 5, pp.463-480.
Khan, M.S., Khor, S., and Chong, A. (2004b)"Fuzzy Cognitive Maps with
Genetic Algorithm for Goal-oriented Decision Support", International Journal
of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol.12, October
pp.31-42.
Khan, M.S., Khor, S. (2004c)"A Framework for Fuzzy Rule-based Cognitive
Maps", 8th Pacific Rim International Conf. on Artificial Intelligence,
Auckland, August 8-13, pp. 454-463.
Khor, S., Khan, M.S., and Payakpate, J. (2004d) “Fuzzy Knowledge
Representation for Decision Support”, KBCS-2004 Fifth International
Conference on Knowledge Based Computer Systems, Hyderabad, India,
December 19-22, 2004, pp.186-195.
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Questions?
Thank you!
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