Mental models analysis based on fuzzy rule for

```The 26th International Conference on Software Engineering and Knowledge Engineering
SEKE 2014
July 1 - July 3, 2014
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
School of Technology
University of Campinas
Limeira, Brazil
Antonio C. Zambon
School of Technology
University of Campinas
Limeira, Brazil
Gisele B. Baioco
School of Technology
University of Campinas
Limeira, Brazil
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
Knowledge
?
Knowledge
Bounded rationality
Decision-maker
A
Decision-maker
B
Collaborative decision-making
4
Mental models (MMs)
(+)
(+)
Element 1
A
Element 2
Element 1
B
Element 2
(-)
(-)
Element 3
0 1
-1 0
0 1 0
-1 0 0
0 1 0
(+)
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
Distance ratio method
(Schaffernich and Groesser, 2011)
(+)
(-)
(+)
(+)
(-)
0
1
-1
0
0
1
0
-1
0
0
0
1
0
a11
a12
b11
b12
b13
a21
a22
b21
b22
b31
b32
b23
b33
diff
7
8
Distance ratio method
(Schaffernicht and Groesser, 2011)
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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
Then
Center of Gravity:
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.
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Example of the algorithm execution
(+)
(+)
Element 1
(-)
A
Element 2
Element 1
B
Element 2
(-)
Element 3
(+)
14
Example of the algorithm execution
AP 1.0
(+)
AP 0.5
PP 1.0
Element 1
B
Element 2
PP 1.0
(+)
(-)
AP 0.2
Element 3
PP 0.2
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”.
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Example of the algorithm execution
(+)
(-)
(+)
(-)
(+)
diff = 1
vuA = 0
vuB = 1
vC = 2
EDR (A, B) = 0.059
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
R1(+)
Element 1
B
Element 2
(-)
B1
(+)
R2
Element 3
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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Example of the Algorithm Execution
(+) R2
(-)
B1
(+) R2
(-)
B1
LDR(m,n) = 0.029
(+)
R3
LDR(m,n) = 0.029
LDR(m,n) = 1
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”.
18
Example of the Algorithm execution
R1(+)
Element 1
B
Element 2
(+)
R2
(-)
B1
Element 3
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
(-)
B1
(+) R2
(-)
B1
(+)
R3
MDR(A, B) = 0.2
If ConsolidatedRepresentativeness is “Medium” and MDR is “Low” then ModelRepresentativeness is “High”.
20
Example of the Algorithm execution
R1(+)
Element 1
B
Average = G(C) / n
Element 2
(+)
R2
(-)
B1
Element 3
Average = 0.8
21
Example of the algorithm execution
(+)
(+)
Element 1
(-)
A
Element 2
Element 1
B
Element 2
(-)
Element 3
The representativeness of mental model B is 0.8 in this sample.
(+)
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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
JANG, J. R.; SUM, C.; MIZUTANI, E. Neuro-Fuzzy and Soft Computing – A Computational
Approach to Learning and Machine Intelligence. Prentice Hall Inc., 1997.
SCHAFFERNICHT, M.; GROESSER, S. A comprehensive method for comparing mental models
of dynamic systems. European Journal of Operational Research 210, 57-67, 2011.
Thanks to
The 26th International Conference on Software Engineering and Knowledge Engineering
SEKE 2014