Shamim Khan School of Computer Science k han_shamim@colstate .

1. Visual Knowledge Representation for Decision Support - from Cognitive Maps to Fuzzy Knowledge Maps Shamim Khan School of Computer Sciencekhan_shamim@colstate.edu .

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

3. 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. Faculty Research Forum

4. Semantic Networks • Knowledge as a pattern of nodes and arcs • Visual nature helps with understanding Faculty Research Forum

5. 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) Faculty Research Forum

6. Robert Axelrod , BA(Math), PhD(Political Science) Professor for the Study of Human Understanding University of Michigan Faculty Research Forum

7. 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” Faculty Research Forum

8. 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 -> … -> B has even number of negative edges + Accident Speed - Faculty Research Forum

9. Cognitive Maps - an example (Axelrod 1976) Amount of security in Persia + Ability of Persian govt. to maintain order + British utility - Policy of withdrawal + - Removal of better governors Strength of Persian govt. - + Present policy of intervention in Persia Allowing Persians to have continued small subsidy Ability of Britain to put pressure on Persia + + Faculty Research Forum

10. Limitations of Axelrod’s 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: Kosko’s Fuzzy Cognitive Maps (Kosko 1986) Faculty Research Forum

11. Cognitive Maps - an example (Axelrod 1976) Amount of security in Persia + Ability of Persian govt. to maintain order + British utility - Policy of withdrawal + - Removal of better governors Strength of Persian govt. - + Present policy of intervention in Persia Allowing Persians to have continued small subsidy Ability of Britain to put pressure on Persia + + Faculty Research Forum

12. 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 Faculty Research Forum

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 Strongly increases Speed 0.7 0.9 Traffic congestion Very strongly decreases Faculty Research Forum

14. 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 Faculty Research Forum

15. 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 Faculty Research Forum

16. 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? Faculty Research Forum

17. 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 Faculty Research Forum

18. non-monotonic relationship Distance run Speed Node A Node B 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 Faculty Research Forum

19. Distance run Fuzzy rule set Speed Node A Node B 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 Faculty Research Forum

20. Distance run Fuzzy rule set Speed Node A Node B 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 Faculty Research Forum

21. 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. Faculty Research Forum

22. 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). Faculty Research Forum

23. Results • Performance of the FKM model over the 3-year study period • FKM outperforms simple ‘Buy and hold’ strategy Faculty Research Forum

24. 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 Faculty Research Forum

25. 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. Faculty Research Forum

26. Questions? Thank you! Faculty Research Forum