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Mental models analysis based on fuzzy

rules for collaborative decision-making

Pedro I. Garcia-Nunes

School of Technology

University of Campinas

Limeira, Brazil

Ana E. A. Silva



Limeira, Brazil

Antonio C. Zambon



Limeira, Brazil

Gisele B. Baioco



Limeira, Brazil

The 26th International Conference on Software Engineering and Knowledge Engineering

SEKE 2014Hyatt Regency, Vancouver, CanadaJuly 1 - July 3, 2014


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Summary

Introduction

- Collaborative decision-making

- Mental models (MMs)

Objective

Methodology- Distance ratio method

- Fuzzy rule base

- Mamdanismethod

Example of application

- Algorithm running- Results

Conclusions

References

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Introduction

? KnowledgeKnowledgeBounded rationality

Collaborative decision-making

Decision-maker

ADecision-maker

B

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Mental models (MMs)

Element 1 Element 2A

Element 1 Element 2B

Element 3

0 1

-1 0

0 1

-1 0 0

0

010

(+)

(-)

(-)

(+)

(+)

4


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Goals

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This work proposes a method based on the development of a

rule base, whose variables are parameters of comparison and

analysis of MMs. The base execution result is a value associated

with each mental model. This value indicates the degree ofadequacy of the model to represent a problem domain.


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Methodology

Distance ratio method

Fuzzy rule base- Mamdanismethod

- Center of gravity

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(Schaffernich and Groesser, 2011)

0 1

-1 0

0 1

-1 0 0

0

010

a11 a12

a21 a22

b11 b12

b21 b22

b13

b33b32b31

b23

diff(+)(+)

(+)(-) (-)

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(Schaffernicht and Groesser, 2011)

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Fuzzy rule base

Sixty fuzzy rules:

Twelve parameters Linguistic terms

Mamdanismethod

Center of gravity method

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Linguistic terms

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Mamdanismethod

Adaptaded from JANG, SUM and MIZUTANI (1997)

Center of Gravity:

Then

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Algorithm

Input:two mental models (A and B); a knowledge base consisting of 60 rules of inference, whose

linguistic values of the variables are obtained through Mamdanismethod.Output:values corresponding to representativeness degree of each model.

1. Calculate EDR, LDR and MDR about the models A and B, using Distance Ratio Equations;

2. For each element of the mental model A, do:

2.1. Evaluate GeneralProximityconsidering AgentProximityand ProblemProximity, according to fuzzy rules;

2.2. Evaluate ElementRelevanceconsidering GeneralProximityand EDR, according to fuzzy rules;

3. For each relationship between two elements of the mental model A, do:

3.1. Evaluate LoopRelevance

considering Elemento1Relevance

and Element2Relevance

, according to fuzzy

rules;

3.2. Evaluate LoopRepresentativenessconsidering LoopRelevance and LDR, according to fuzzy rulesI;

4. For each pair of loops of mental model A, do:

4.1. Evaluate GeneralRepresentativenessconsidering Loop1Representativenessand Loop2Representativeness,

according to fuzzy rules;

5. For all pairs of loops of mental model A, do:

5.1.Evaluate ConsolidatedRepresentativenessconsidering General1Representativenessand

General2Representativeness, according to fuzzy rules;6.Evaluate ModelRepresentativenessconsidering ConsolidatedRepresentativenessand MDR, according to fuzzy

rules;

7. Apply G(C) in ModelRepresentativenessusing Center of Gravity Equation;

8. Repeat steps 2-7 considering the mental model B.

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Example of application: Algorithm running



Element 3

(+)

(-)

(-)

(+)

(+)

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Element 3

(-)

(+)

(+)

If AgentProximity (AP) is Medium and ProblemProximity (PP) is High then GeneralProximity is High.

If AgentProximity (AP) is High and ProblemProximity (PP) is High then GeneralProximity is High.

If AgentProximity (AP) is Low and ProblemProximity (PP) is Low then GeneralProximity is Low.

AP 0.5

PP 1.0

AP 0.2

PP 0.2

AP 1.0

PP 1.0

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diff = 1(+)(+)

(+)(-) (-)

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EDR (A, B)= 0.059

vuA = 0

vuB = 1

vC = 2

If GeneralProximity is High and EDR is Low then Element1Relevance is High.

If GeneralProximity is High and EDR is Low then Element2Relevance is High.

If GeneralProximity is Low and EDR is Low then Element3Relevance is Medium.

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Element 3

(-)B1

R1(+)

(+)

R2

If Element1Relevance is High and Element2Relevance is High then LoopR1Relevance is High.

If Element2Relevance is High and Element1Relevance is High then LoopB1Relevance is High.

If Element3Relevance is High and Element2Relevance is Medium then LoopR2Relevance is Low.

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(+) R2(+) R2

(+)

R3(-)

B1

(-)

B1

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If LoopR1Relevance is High and LDR is Low then LoopR1Representativeness is High.

If LoopR2Relevance is High and LDR is Low then LoopR2Representativeness is High.

If LoopR3Relevance is High and LDR is High then LoopR3Representativeness is Medium.

LDR(m,n) = 0.029

LDR(m,n) = 0.029

LDR(m,n) = 1


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(+) R2(+) R2

(+)

R3(-)

B1

(-)

B1

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If ConsolidatedRepresentativeness is Medium and MDR is Low then ModelRepresentativeness is High.

MDR(A, B) = 0.2

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Element 1 Element 2

B

Element 3

(-)

B1

R1(+)

(+)

R2

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Average= G(C) / n

Average = 0.8

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Example of application: Results



Element 3

(+)

(-)

(-)

(+)

(+)

21

The representativeness of mental model B is 0.8 in this sample.

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Conclusion

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The collaborative decision process presents challenges associated with

the consensus among many decision makers through common

knowledge identification. Thus, the shared decision making depends on

the comparison of MMs from several decision-makers. Results showed that it is possible to use the methodology to compare

MMs and that it is possible to identify more adequate MMs through

the analysis of the mental model representativeness value.

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References

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SCHAFFERNICHT, M.; GROESSER, S. A comprehensive method for comparing mental models

of dynamic systems. European Journal of Operational Research210, 57-67, 2011.

JANG, J. R.; SUM, C.; MIZUTANI, E. Neuro-Fuzzy and Soft Computing A Computational

Approach to Learning and Machine Intelligence. Prentice Hall Inc., 1997.


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Thanks to

The authors would like to thank CAPES (Coordination for Brazilian Higher Education Staff Development) for the scholarship financial

support.

[email protected] [email protected] [email protected] [email protected]

www.ft.unicamp.br

www.unicamp.br

The 26th International Conference on Software Engineering and Knowledge Engineering

SEKE 2014Hyatt Regency, Vancouver, Canada

July 1 - July 3, 2014
http://www.ft.unicamp.br/http://www.unicamp.br/http://www.unicamp.br/http://www.ft.unicamp.br/

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