Mental models analysis based on fuzzy rules for collaborative decision-making

Pedro I. Garcia-NunesSchool of Technology

University of CampinasLimeira, Brazil

Ana E. A. SilvaSchool of Technology

University of CampinasLimeira, Brazil

Antonio C. ZambonSchool of Technology

University of CampinasLimeira, Brazil

Gisele B. BaiocoSchool of Technology

University of CampinasLimeira, Brazil

The 26th International Conference on Software Engineering and Knowledge Engineering

SEKE 2014Hyatt Regency, Vancouver, Canada

July 1 - July 3, 2014

2

Summary

Introduction- Collaborative decision-making- Mental models (MMs)

Objective Methodology

- Distance ratio method- Fuzzy rule base- Mamdani’s method

Example of application- Algorithm running- Results

Conclusions References

3

Introduction

? KnowledgeKnowledge

Bounded rationality

Collaborative decision-making

Decision-makerA

Decision-makerB

4

Mental models (MMs)

Element 1 Element 2AElement 1 Element 2B

Element 3

0 1-1 0

0 1-1 0 0

0

010

(+)

(-)

(-)

(+)

(+)

5

Goals

This work proposes a method based on the development of a fuzzy rule base, whose variables are parameters of comparison and analysis of Mental Models. The result is a value associated with each mental model. This value indicates the degree of adequacy of the model to represent a certain problem domain. The higher the value the more adequate is the model to the problem representation.

6

Methodology

Distance ratio method Fuzzy Rule Knowledge Base

- Mamdani’s inference method- Center of gravity defuzzyfication method

7Distance ratio method (Schaffernich and Groesser, 2011)

0 1

-1 0

0 1

-1 0 0

0

010

a11 a12

a21 a22

b11 b12

b21 b22

b13

b33b32b31b23

diff(+)(+)

(+)(-) (-)

8

Distance ratio method(Schaffernicht and Groesser, 2011)

9

Base of Fuzzy Rules

Sixty fuzzy rules:

Twelve parameters Linguistic terms Mamdani’s inference method Center of gravity defuzzyfication method

10

Linguistic terms

11

Mamdani’s inference method

Adaptaded from JANG, SUM and MIZUTANI (1997)Center of Gravity:

Then

12

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 Mamdani’s method. 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 GeneralProximity considering AgentProximity and ProblemProximity, according to fuzzy rules; 2.2. Evaluate ElementRelevance considering GeneralProximity and 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 LoopRepresentativeness considering LoopRelevance and LDR, according to fuzzy rulesI; 4. For each pair of loops of mental model A, do: 4.1. Evaluate GeneralRepresentativeness considering Loop1Representativeness and Loop2Representativeness, according to fuzzy rules; 5. For all pairs of loops of mental model A, do: 5.1.Evaluate ConsolidatedRepresentativeness considering General1Representativeness and General2Representativeness, according to fuzzy rules; 6.Evaluate ModelRepresentativeness considering ConsolidatedRepresentativeness and MDR, according to fuzzy rules; 7. Apply G(C) in ModelRepresentativeness using Center of Gravity Equation; 8. Repeat steps 2-7 considering the mental model B.

13

Example of the algorithm execution

Element 1 Element 2AElement 1 Element 2B

Element 3

(+)

(-)

(-)

(+)

(+)

14

Example of the algorithm execution

Element 1 Element 2B

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 0.5PP 1.0

AP 0.2PP 0.2

AP 1.0PP 1.0

15

Example of the algorithm execution

diff = 1(+)(+)

(+)(-) (-)

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”.

16

Example of the algorithm execution

Element 1 Element 2B

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”.

17

Example of the Algorithm Execution

(+) R2(+) R2

(+)R3(-)

B1(-)B1

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

18

Example of the Algorithm execution

Element 1 Element 2B

Element 3

(-)B1

R1(+)

(+)R2

If LoopR1Representativeness is “High” and LoopB1Representativeness is “High” then General1Representativeness is “High”.

If General1Representativeness is “High” and General2Representativeness is “Medium” then ConsolidatedRepresentativeness is “Low”.

19

Example of the Algorithm execution

(+) R2(+) R2

(+)R3(-)

B1(-)B1

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

MDR(A, B) = 0.2

20

Example of the Algorithm execution

Element 1 Element 2B

Element 3

(-)B1

R1(+)

(+)R2

Average = G(C) / n

Average = 0.8

21

Example of the algorithm execution

Element 1 Element 2AElement 1 Element 2B

Element 3

(+)

(-)

(-)

(+)

(+)

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

22

Conclusion

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.

23

References

SCHAFFERNICHT, M.; GROESSER, S. A comprehensive method for comparing mental models of dynamic systems. European Journal of Operational Research 210, 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.

Thanks to

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

pedrogn@ft.unicamp.br aeasilva@ft.unicamp.br zambon@ft.unicamp.br gisele@ft.unicamp.br

www.ft.unicamp.brwww.unicamp.br

The 26th International Conference on Software Engineering and Knowledge Engineering

SEKE 2014Hyatt Regency, Vancouver, Canada

July 1 - July 3, 2014