The 26th International Conference on Software Engineering and Knowledge Engineering
SEKE 2014
Hyatt Regency, Vancouver, Canada
July 1 - July 3, 2014
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

 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
2

Bounded rationality
Knowledge
?
Knowledge
Decision-maker
A
Decision-maker
B
Collaborative decision-making
3

(+)
Element 1
A
Element 2
(-)
0 1
-1 0
Element 1
(-)
B
(+)
Element 2
(+)
Element 3
0 1 0
-1 0 0
0 1 0
4

 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.
5

 Distance ratio method
 Fuzzy Rule Knowledge Base
Mamdani’s inference method
Center of gravity defuzzyfication method
6

(-)
0 1
-1 0 a11 a12 a21 a22
Distance ratio method
(Schaffernich and Groesser, 2011)
(+)
(-)
(+)
(+)
0 1 0
-1 0 0
0 1 0 b11 b12 b21 b22 b31 b32 b13 b23 b33
7

Distance ratio method
(Schaffernicht and Groesser, 2011)
8

Sixty fuzzy rules:
 Twelve parameters
 Linguistic terms
 Mamdani’s inference method
 Center of gravity defuzzyfication method
9

10

Then
11
Adaptaded from JANG, SUM and MIZUTANI (1997)
Center of Gravity:

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 General
Proximity
2.2. Evaluate Element
Relevance considering Agent
Proximity considering General and Problem
Proximity
Proximity
, according to fuzzy rules; and EDR, according to fuzzy rules;
3. For each relationship between two elements of the mental model A, do:
3.1. Evaluate Loop rules;
Relevance considering Elemento1
Relevance and Element2
Relevance
, according to fuzzy
3.2. Evaluate Loop
Representativeness considering LoopRelevance and LDR, according to fuzzy rulesI;
4. For each pair of loops of mental model A, do:
4.1. Evaluate General
Representativeness according to fuzzy rules; considering Loop1
5. For all pairs of loops of mental model A, do:
Representativeness and Loop2
Representativeness
,
5.1.Evaluate Consolidated
Representativeness
General2
Representativeness considering General1
, according to fuzzy rules;
Representativeness
6.Evaluate Model rules;
Representativeness considering Consolidated
Representativeness and and MDR, according to fuzzy
7. Apply G(C) in Model
Representativeness using Center of Gravity Equation;
8. Repeat steps 2-7 considering the mental model B.
12

13
(+)
Element 1
A
Element 2
(-)
Element 1
(-)
B
(+)
Element 2
(+)
Element 3

AP 0.5
PP 1.0
Element 1
(-)
B
(+)
AP 1.0
PP 1.0
Element 2
(+)
AP 0.2
PP 0.2
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”.
14

(-)
(+)
(-)
(+)
(+)
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”.
15

Element 1
(-)
B1
B
R1(+)
Element 2
(+)
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”.
16

(-)
B1
(+) R2
(-)
B1
(+) R2
(+)
R3
LDR(m,n) = 0.029
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”.
17

Element 1
(-)
B1
B
R1(+)
Element 2
(+)
R2
Element 3
18
If LoopR1Representativeness is “High” and LoopB1Representativeness is “High” then General1Representativeness is “High”.
If General1Representativeness is “High” and General2Representativeness is “Medium” then ConsolidatedRepresentativeness is “Low”.

(-)
B1
(+) R2
(-)
B1
(+) R2
(+)
R3
MDR(A , B) = 0.2
19
If ConsolidatedRepresentativeness is “Medium” and MDR is “Low” then ModelRepresentativeness is “High”.

20
Element 1
(-)
B1
B
R1(+)
Element 2
(+)
R2
Element 3
Average = G(C) / n
Average = 0.8

21
(+)
Element 1
A
Element 2
(-)
Element 1
(-)
B
(+)
Element 2
(+)
Element 3
The representativeness of mental model B is 0.8 in this sample.

 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.
22

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.
23

The 26th International Conference on Software Engineering and Knowledge Engineering
SEKE 2014
Hyatt Regency, Vancouver, Canada
July 1 - July 3, 2014 zambon@ft.unicamp.br
gisele@ft.unicamp.br
pedrogn@ft.unicamp.br
aeasilva@ft.unicamp.br
www.ft.unicamp.br
www.unicamp.br
The authors would like to thank CAPES (Coordination for Brazilian Higher Education Staff Development) for the scholarship financial support.