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

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 2

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

Mental models (MMs) Element 1 Element 2 A Element 1 Element 2 B Element (+) (-) (+) 4

Goals 5  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.

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

Distance ratio method (Schaffernich and Groesser, 2011) a11 a12 a21 a22 b11 b12 b21 b22 b13 b33b32b31 b23 diff (+) (-) 7

Distance ratio method (Schaffernicht and Groesser, 2011) 8

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

Linguistic terms 10

Mamdani’s inference method Adaptaded from JANG, SUM and MIZUTANI (1997) Center of Gravity: Then 11

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

Example of the algorithm execution Element 1 Element 2 A Element 1 Element 2 B Element 3 (+) (-) (+) 13

Example of the algorithm execution Element 1 Element 2 B 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

Example of the algorithm execution diff = 1 (+) (-) 15 EDR (A, B) = 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”.

Example of the algorithm execution Element 1 Element 2 B 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”. 16

Example of the Algorithm Execution (+) R2 (+) R3 (-) B1 (-) B1 17 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) = LDR(m,n) = 1

Example of the Algorithm execution Element 1 Element 2 B 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”. 18

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

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

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

Conclusion 22  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.

References 23 SCHAFFERNICHT, M.; GROESSER, S. A comprehensive method for comparing mental models of dynamic systems. European Journal of Operational Research 210, 57-67, 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. The 26th International Conference on Software Engineering and Knowledge Engineering SEKE 2014 Hyatt Regency, Vancouver, Canada July 1 - July 3, 2014