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

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

• Shamim Khan School of Information Technology,
• Murdoch University, Perth, Western
  Australias.khan_at_murdoch.edu.au
• .

2

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

3
A simple view of knowledge

• Domain knowledge can be viewed as a collection of
  important concepts or events and their
  relationships.
• Visual representation of knowledge can help us
  understand complex relationships.
• A visual representation scheme within a
  computational framework can help us make
  decisions.

4
Cognitive Maps

• Axelrod's cognitive maps
• Developed as a mathematical model of a belief
  system
• Lays out important concepts and relationships on
  a 2D plane
• "If a cognitive map can accurately represent a
  decision maker's belief system, then that person
  should make predictions, decisions and
  explanations that correspond to those made by the
  cognitive map .. " (Axelrod 1976)

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Cognitive Maps

• A collection of points or nodes representing
  concepts/issues/facts
• Directed edges represent causal relationships
  linking nodes
• Signed edges reflect promoting or inhibitory
  effects
• Rules developed to analyse cognitive maps
• Eg, the effect of A on B is positive if the path
  A -gt -gt B has even number of negative edges

6
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 involve feedback
• Use of bivalent (crisp) logic
• Real-life causalities often expressed in inexact
  (fuzzy) terms
• 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


9
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
11
FCM operation

• FCMs operate like recurrent neural networks
• 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
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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 Modernisation
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
• FCM 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 all other concepts?
• Given a set of values for all concepts at point
  in time, how will the system evolve with time?
• Goal oriented decision support (Khan et al 2004a)
  What state of affairs can lead to a given
  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 and not necessarily causal
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Fuzzy Knowledge Map (FKM)

• A truly fuzzy system to overcome limitations of
  the FCM (Khor et al 2004)
• Relationship between an antecedent node and a
  consequent node represented using a set of fuzzy
  rules
• Eg,
• - If distance_run is vShort, 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 vLong, then speed is low

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Derivation of consequent node state

• Given,
• ai state of an antecedent node Ni,
• Sij set of n fuzzy rules representing influence
  dj of node Ni on node Nj,
• dj is calculated through fuzzification, fuzzy
  rule application and defuzzification

18
Membership functions of four crop yield factors
and crop yield
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Conclusion

• Knowledge representation schemes can be more
  useful if they
• Help us visualise a problem domain for analysis
  and inferencing
• Allow incorporation of human expert knowledge
  that are often expressed in inexact qualitative
  fashion
• Fuzzy knowledge maps overcome the limitations of
  FCMs by allowing fuzzy expression of knowledge
  and fuzzy reasoning.
• Encouraging initial results need further
  validation.

20
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.