Shamim Khan School of Computer Science k han_shamim@colstate

Visual Knowledge Visual Knowledge Representation for Representation for Decision Support Decision Support

- from Cognitive Maps to - from Cognitive Maps to Fuzzy Knowledge MapsFuzzy Knowledge Maps

Shamim Khan Shamim Khan School of Computer ScienceSchool of Computer [email protected] [email protected]

..

IntroductionIntroduction

The goal of Artificial Intelligence (AI)The goal of Artificial Intelligence (AI) Decision Support Systems and AIDecision Support Systems and AI Knowledge representation and Knowledge representation and

reasoningreasoning Schemes for knowledge Schemes for knowledge

representationrepresentation RulesRules Semantic NetworksSemantic Networks

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Rule-based Knowledge Rule-based Knowledge RepresentationRepresentation

A series of IF A series of IF condition condition THEN THEN actionaction statementsstatements

IF the stain of the organism is gramneg, andIF the stain of the organism is gramneg, and

the morphology of the organism is rod, andthe morphology of the organism is rod, and

the aerobicity of the organism is aerobicthe aerobicity of the organism is aerobic

THEN there is strongly suggestive evidence (.8) thatTHEN there is strongly suggestive evidence (.8) that

the class of organism is enterocabateriaceaethe class of organism is enterocabateriaceae

An inference engine searches for An inference engine searches for patterns in the rules that match patterns in the rules that match patterns in the data.patterns in the data.


Semantic NetworksSemantic Networks Knowledge as a pattern of nodes and Knowledge as a pattern of nodes and

arcsarcs


VVisual nature helps with isual nature helps with understandingunderstanding


Cognitive Maps Cognitive Maps - A causal view of - A causal view of

knowledgeknowledge Knowledge as a network of concepts Knowledge as a network of concepts

and their causal relationshipsand their causal relationships A visual representation scheme A visual representation scheme

within a computational frameworkwithin a computational framework First desribed as a decision support First desribed as a decision support

tool in tool in (Axelrod 1976) (Axelrod 1976)


Robert Axelrod , BA(Math), PhD(Political Robert Axelrod , BA(Math), PhD(Political Science)Science)Professor for the Study of Human Professor for the Study of Human UnderstandingUnderstandingUniversity of MichiganUniversity of Michigan


Variants of Cognitive Maps Variants of Cognitive Maps

Also used in other fields – eg, Also used in other fields – eg, psychology, geography psychology, geography

Axelrod's cognitive maps Axelrod's cognitive maps A mathematical model of a belief A mathematical model of a belief

systemsystem Lays out important concepts and Lays out important concepts and

relationships on a 2D plane for relationships on a 2D plane for “predictions, decisions and “predictions, decisions and explanations”explanations”


Cognitive MapsCognitive Maps- Structure and Analysis- Structure and Analysis

Directed edges represent causal Directed edges represent causal relationships linking nodesrelationships linking nodes

Signs reflect promoting or inhibitory effectsSigns reflect promoting or inhibitory effects

Rules to analyse cognitive mapsRules to analyse cognitive mapsEg, effect of A on B positive if path A -> … -> B Eg, effect of A on B positive if path A -> … -> B

has even number of negative edgeshas even number of negative edges

Speed Accident+

-


Cognitive Maps Cognitive Maps - an example (Axelrod 1976)- an example (Axelrod 1976)

Policy of withdrawal

Amount of security in Persia

Ability of Persian govt. to maintain order

British utility

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

-

+ +

+

-

+ +

+-


Limitations of Axelrod’s Limitations of Axelrod’s cognitive mapscognitive maps

Difficulty handling multiple paths between Difficulty handling multiple paths between two nodestwo nodes Conflicting inferencesConflicting inferences

Static - do not evolve with time Static - do not evolve with time Real-life scenarios may also involve feedbackReal-life scenarios may also involve feedback

Use of bivalent (true/false) logicUse of bivalent (true/false) logic Real-life causalities often expressed in inexact Real-life causalities often expressed in inexact

(fuzzy) terms(fuzzy) terms Proposed solution:Proposed solution:

Kosko’s Fuzzy Cognitive Maps (Kosko Kosko’s Fuzzy Cognitive Maps (Kosko 1986)1986)


Cognitive Maps Cognitive Maps - an example (Axelrod 1976)- an example (Axelrod 1976)

Policy of withdrawal

Amount of security in Persia

Ability of Persian govt. to maintain order

British utility

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

-

+ +

+

-

+ +

+-

Fuzzy Cognitive Maps Fuzzy Cognitive Maps (FCM)(FCM)

FCMs feature FCMs feature - Inexact (fuzzy) linguistic expression of concepts and Inexact (fuzzy) linguistic expression of concepts and

causal linkscausal links- Feedback enabling evolution with timeFeedback enabling evolution with time

Speed

Accident

Traffic congestion

Strongly increases

Moderately increases

Very strongly decreases

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Fuzzy Cognitive Maps Fuzzy Cognitive Maps (FCM)(FCM)

FCMs feature FCMs feature - Inexact (fuzzy) linguistic expression of concepts and Inexact (fuzzy) linguistic expression of concepts and

causal linkscausal links- Feedback enabling evolution with timFeedback enabling evolution with timee

Speed

Accident

Traffic congestion

Strongly increases

Moderately increases

Very strongly decreases

0.5

0.70.9


FCM operationFCM operationThe state of a node determined The state of a node determined

byby- sum of its inputs modified by sum of its inputs modified by

causal link weights, andcausal link weights, and- a non-linear transfer functiona non-linear transfer function

Fed with a stimulus state vector, Fed with a stimulus state vector, the state of an FCM is the state of an FCM is continuously updated until it continuously updated until it convergesconverges


FCM operationFCM operation

))(()1(1

0ij

n

jji wtcStc

The state of a node The state of a node CCii determined bydetermined by

- sum of its inputs modified by sum of its inputs modified by causal link weights, andcausal link weights, and

- a non-linear transfer function a non-linear transfer function SS

Fed with a stimulus state vector, Fed with a stimulus state vector, the state of an FCM is the state of an FCM is continuously updated until it continuously updated until it convergesconverges

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A fuzzy cognitive map A fuzzy cognitive map concerning public healthconcerning public health

C1No. of ppl in the city


C2Migration into city


C3Modernization

C3Modernization

C4Garbage per area

C4Garbage per area C6

No. of diseases per 1000 residents

C6No. of diseases per 1000 residents

C5Sanitation facilities

C5Sanitation facilities

C7Bacteria per area

C7Bacteria per area

+0.9

+0.7

+0.9

+0.8

+0.9

+0.9

+0.6

-0.9

-0.3

-0.9



C6No. of diseases

per 1000 residents

+0.9

-0.3

Decision support using Decision support using FCMsFCMs

Given a stimulus vector, FCMs Given a stimulus vector, FCMs converge to one of three converge to one of three possibilitiespossibilities

1.1. State vector remains unchangedState vector remains unchanged2.2. A sequence of state vectors keep A sequence of state vectors keep

repeatingrepeating3.3. The state vector keeps changing The state vector keeps changing

indefinitelyindefinitely

The evolved state(s) of an FCM The evolved state(s) of an FCM can provide useful decision can provide useful decision supportsupport

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FCMs as decision support FCMs as decision support toolstools

Problem domain analysisProblem domain analysis- How significant is conceptHow significant is concept A? A?- What is the degree of influence of What is the degree of influence of

concept concept A A on concept on concept BB??- What will be the impact of a change in What will be the impact of a change in

concept concept A A on other concepts?on other concepts?- Given a set of values for all concepts at Given a set of values for all concepts at

a point in time, how will the system a point in time, how will the system evolve with time?evolve with time?


FCMs as decision support FCMs as decision support tools (cont.)tools (cont.)

Goal oriented decision support Goal oriented decision support (Khan et al 2004a) (Khan et al 2004a) – What state of affairs can lead to a given – What state of affairs can lead to a given (goal) state?(goal) state?

Group decision support (Khan et al Group decision support (Khan et al 2004b) – 2004b) – FCMs can be mergedFCMs can be merged


Limitations of FCMsLimitations of FCMs

FCMS model only monotonic causal FCMS model only monotonic causal relations relations

- Influence on effect node increases Influence on effect node increases (decreases) with increasing (decreases) with increasing (decreasing) state value of cause (decreasing) state value of cause nodenode

Real world relationships can be non-Real world relationships can be non-monotonicmonotonic

Node B

non-monotonic relationship

Node A

Distance run

Speed


Fuzzy Knowledge Map Fuzzy Knowledge Map (FKM)(FKM)

A truly fuzzy system to A truly fuzzy system to overcome limitations of the overcome limitations of the FCM FCM (Khor et al 2004) (Khor et al 2004)

Relationship between nodes Relationship between nodes represented using a set of represented using a set of fuzzy rules fuzzy rules

Fuzzy rule set

Node A

Distance run

Speed

Node B


Fuzzy Knowledge Map Fuzzy Knowledge Map (FKM)(FKM)

Relationship between nodes represented Relationship between nodes represented using a set of fuzzy rules using a set of fuzzy rules

Eg,Eg,- If distance_run is very_short, then speed is low- If distance_run is very_short, then speed is low- If distance_run is short, then speed is fast- If distance_run is short, then speed is fast- If distance_run is medium, then speed is vFast- If distance_run is medium, then speed is vFast- If distance_run is long, then speed is medium- If distance_run is long, then speed is medium- If distance_run is very_long, then speed is low- If distance_run is very_long, then speed is low

Fuzzy rule set

Node A

Distance run

Speed

Node B

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An FKM application An FKM application experimentexperiment

A two-layer hierarchy of FKMs used for decision A two-layer hierarchy of FKMs used for decision support in share tradingsupport in share trading

Inferences derived at the lower layer using market Inferences derived at the lower layer using market indicators utilized at the higher layer to make indicators utilized at the higher layer to make recommendations.recommendations.

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ExperimentExperiment

Indicators used: Indicators used: Momentum, Momentum, Relative strength index,Relative strength index, Bollinger band, Bollinger band, Moving averages.Moving averages.

Two data sets:Two data sets: Commonwealth Bank of Australia Ltd.Commonwealth Bank of Australia Ltd. Telstra Corporation Ltd. Telstra Corporation Ltd.

Study period: Study period: 3 years ( Jan 2002 to Dec 2004).3 years ( Jan 2002 to Dec 2004).


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ResultsResults

Performance of the FKM model over the 3-year Performance of the FKM model over the 3-year study period study period

FKM outperforms simple ‘Buy and hold’ strategyFKM outperforms simple ‘Buy and hold’ strategy

FKM model Buy & holdProfit/Loss Profit/Loss

Commonwealth Bank Ltd. 17% 11%Telstra Corp. Ltd. 3% 11%

Security


ConclusionConclusion

Knowledge representation schemes can Knowledge representation schemes can be more useful if theybe more useful if they Help us visualize a problem domain for Help us visualize a problem domain for

analysis and inferencinganalysis and inferencing Allow incorporation of inexact/qualitative Allow incorporation of inexact/qualitative

human expert knowledgehuman expert knowledge

Fuzzy knowledge maps overcome the Fuzzy knowledge maps overcome the limitations of FCMs by allowing fuzzy limitations of FCMs by allowing fuzzy expression of causal knowledge and fuzzy expression of causal knowledge and fuzzy reasoningreasoning


ReferencesReferences

• Axelrod, R. (1976), “Structure of Decision”, Princeton University Press, US.Axelrod, R. (1976), “Structure of Decision”, Princeton University Press, US. • Kosko, B. (1986) "Fuzzy Cognitive Maps", Int. J. Man-Machine Studies, Kosko, B. (1986) "Fuzzy Cognitive Maps", Int. J. Man-Machine Studies,

Vol.24, pp.65-75. Vol.24, pp.65-75. • Khan, M.S., Quaddus, M. A., and Intrapairot, A. (2001) "Application of a Fuzzy Khan, M.S., Quaddus, M. A., and Intrapairot, A. (2001) "Application of a Fuzzy

Cognitive Map for Analysing Data Warehouse Diffusion", Proc.19th IASTED Cognitive Map for Analysing Data Warehouse Diffusion", Proc.19th IASTED Int. Conf. on Applied Informatics, Innsbruck 19-22 Feb., pp.32-37.Int. Conf. on Applied Informatics, Innsbruck 19-22 Feb., pp.32-37.

• Khan, M.S., and Quaddus, M. (2004a)“Group Decision Support using Fuzzy Khan, M.S., and Quaddus, M. (2004a)“Group Decision Support using Fuzzy Cognitive Maps for Causal Reasoning”, Group Decision and Negotiation Cognitive Maps for Causal Reasoning”, Group Decision and Negotiation Journal, Vol. 13, No. 5, pp.463-480.Journal, Vol. 13, No. 5, pp.463-480.

Khan, M.S., Khor, S., and Chong, A. (2004b)"Fuzzy Cognitive Maps with Khan, M.S., Khor, S., and Chong, A. (2004b)"Fuzzy Cognitive Maps with Genetic Algorithm for Goal-oriented Decision Support", International Journal of Genetic Algorithm for Goal-oriented Decision Support", International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol.12, October Uncertainty, Fuzziness and Knowledge-Based Systems, Vol.12, October pp.31-42.pp.31-42.

• Khan, M.S., Khor, S. (2004c)"A Framework for Fuzzy Rule-based Cognitive Khan, M.S., Khor, S. (2004c)"A Framework for Fuzzy Rule-based Cognitive Maps", 8th Pacific Rim International Conf. on Artificial Intelligence, Auckland, Maps", 8th Pacific Rim International Conf. on Artificial Intelligence, Auckland, August 8-13, pp. 454-463.August 8-13, pp. 454-463.

• Khor, S., Khan, M.S., and Payakpate, J. (2004d) “Khor, S., Khan, M.S., and Payakpate, J. (2004d) “Fuzzy Knowledge Fuzzy Knowledge Representation for Decision SupportRepresentation for Decision Support”, KBCS-2004 Fifth International ”, KBCS-2004 Fifth International Conference on Knowledge Based Computer Systems, Hyderabad, India, Conference on Knowledge Based Computer Systems, Hyderabad, India, December 19-22, 2004, pp.186-195.December 19-22, 2004, pp.186-195.


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Shamim Khan School of Computer Science k han_shamim@colstate