Visual Knowledge Representation for Decision Support

1
Visual Knowledge Representation for Decision
Support - from Cognitive Maps to Fuzzy
Knowledge Maps

• Shamim Khan School of Computer
  Sciencekhan_shamim_at_colstate.edu
• .

2

• A simplified view of knowledge
• Cognitive maps
• Fuzzy Cognitive Maps (FCM)
• Decision support using FCMs
• Limitations of FCMs
• Fuzzy Knowledge Maps
• Conclusion

3

• The goal of Artificial Intelligence (AI)
• Decision Support Systems and AI
• Knowledge representation and reasoning
• Schemes for knowledge representation
• Rules
• Semantic Networks

4
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.

5
Semantic Networks

• Knowledge as a pattern of nodes and arcs

• Visual nature helps with understanding

6
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)

7
Robert Axelrod , BA(Math), PhD(Political
Science) Professor for the Study of Human
Understanding University of Michigan
8
Variants of Cognitive Maps

• Also used in other fields eg, psychology,
  geography
• Axelrod's cognitive maps
• A mathematical model of a belief system
• Lays out important concepts and relationships on
  a 2D plane for predictions, decisions and
  explanations

9
Cognitive Maps- Structure and Analysis

• Directed edges represent causal relationships
  linking nodes
• Signs reflect promoting or inhibitory effects
• Rules to analyse cognitive maps
• Eg, effect of A on B positive if path A -gt -gt B
  has even number of negative edges

Accident
Speed
-
10
Cognitive Maps - an example (Axelrod 1976)
Amount of security in Persia
Ability of Persian govt. to maintain order
British utility


-
Policy of withdrawal

-
Strength of Persian govt.
Removal of better governors
-

Present policy of intervention in Persia
Allowing Persians to have continued small subsidy
Ability of Britain to put pressure on Persia


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Limitations of Axelrods cognitive maps

• Difficulty handling multiple paths between two
  nodes
• Conflicting inferences
• Static - do not evolve with time
• Real-life scenarios may also involve feedback
• Use of bivalent (true/false) logic
• Real-life causalities often expressed in inexact
  (fuzzy) terms
• Proposed solution
• Koskos Fuzzy Cognitive Maps (Kosko 1986)

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Cognitive Maps - an example (Axelrod 1976)
Amount of security in Persia
Ability of Persian govt. to maintain order
British utility


-
Policy of withdrawal

-
Strength of Persian govt.
Removal of better governors
-

Present policy of intervention in Persia
Allowing Persians to have continued small subsidy
Ability of Britain to put pressure on Persia


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Fuzzy Cognitive Maps (FCM)

• FCMs feature
• Inexact (fuzzy) linguistic expression of concepts
  and causal links
• Feedback enabling evolution with time

Accident
Moderately increases
Strongly increases
Speed
Traffic congestion
Very strongly decreases
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Fuzzy Cognitive Maps (FCM)

• FCMs feature
• Inexact (fuzzy) linguistic expression of concepts
  and causal links
• Feedback enabling evolution with time

Accident
Moderately increases
Strongly increases
0.5
Speed
0.7
0.9
Traffic congestion
Very strongly decreases
15
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

Fed with a stimulus state vector, the state of an
FCM is continuously updated until it converges
17
A fuzzy cognitive map concerning public health
C1 No. of ppl in the city
C1 No. of ppl in the city
C2 Migration into city
C2 Migration into city
0.9
0.9
0.6
C3 Modernization
0.7
C5 Sanitation facilities
0.9
0.9
C4 Garbage per area
-0.3
-0.3
C6 No. of diseases per 1000 residents
C6 No. of diseases per 1000 residents
-0.9
-0.9
0.8
C7 Bacteria per area
0.9
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Decision support using FCMs

• Given a stimulus vector, FCMs converge to one of
  three possibilities
• State vector remains unchanged
• A sequence of state vectors keep repeating
• The state vector keeps changing indefinitely
• The evolved state(s) of an FCM can provide useful
  decision support

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FCMs as decision support tools

• Problem domain analysis
• 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 non-monotonic

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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

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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

24
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
• Momentum,
• Relative strength index,
• Bollinger band,
• Moving averages.
• Two data sets
• Commonwealth Bank of Australia Ltd.
• Telstra Corporation Ltd.
• Study period
• 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

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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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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.