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

1. The 26th InternationalConferenceon Software EngineeringandKnowledgeEngineering SEKE 2014 Mental modelsanalysisbasedonfuzzyrules for collaborativedecision-making Pedro I. Garcia-Nunes Schoolof Technology Universityof Campinas Limeira, Brazil Antonio C. Zambon Schoolof Technology Universityof Campinas Limeira, Brazil Ana E. A. Silva Schoolof Technology Universityof Campinas Limeira, Brazil Gisele B. Baioco Schoolof Technology Universityof Campinas Limeira, Brazil

2. Summary • Introduction • - Collaborativedecision-making • - Mental models (MMs) • Objective • Methodology • - Distanceratiomethod • - Fuzzyrule base • - Mamdani’smethod • Exampleofapplication • Algorithmrunning • Results • Conclusions • References

3. Introduction ? Knowledge Knowledge Boundedrationality Decision-maker A Decision-maker B Collaborativedecision-making

4. Mental models (MMs) (+) B (+) Element 1 Element 2 (+) A Element 1 (-) Element 2 (-) Element 3 1 1 0 0 0 -1 -1 0 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 • Distanceratiomethod • FuzzyRuleKnowledge Base • - Mamdani’sinferencemethod • - Center ofgravitydefuzzyficationmethod

7. Distanceratiomethod(SchaffernichandGroesser, 2011) diff (+) (+) (+) (-) (-) b13 b12 1 1 a12 b11 a11 0 0 0 b23 b22 b21 a22 b33 b31 b32 a21 -1 -1 0 0 0 0 1 0

8. Distanceratiomethod(SchaffernichtandGroesser, 2011)

9. Base ofFuzzyRules • Sixtyfuzzyrules: • Twelveparameters • Linguisticterms • Mamdani’sinferencemethod • Center ofgravitydefuzzyficationmethod

10. Linguisticterms

11. Mamdani’sinferencemethod Then Center ofGravity: Adaptadedfrom JANG, SUM and MIZUTANI (1997)

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. Exampleofthealgorithmexecution (+) B Element 1 Element 2 (+) (+) (-) A Element 1 Element 2 (-) Element 3

14. Exampleofthealgorithmexecution AP 1.0 (+) PP 1.0 AP 0.5 B Element 1 Element 2 PP 1.0 (+) (-) AP 0.2 Element 3 PP 0.2 IfAgentProximity (AP) is “Medium” andProblemProximity (PP) is “High” thenGeneralProximityis “High”. IfAgentProximity (AP) is “High” andProblemProximity (PP) is “High” thenGeneralProximityis “High”. IfAgentProximity (AP) is “Low” andProblemProximity (PP) is “Low” thenGeneralProximityis “Low”.

15. Exampleofthealgorithmexecution diff = 1 (+) (+) (+) (-) (-) vuA = 0 vuB = 1 EDR (A, B) = 0.059 vC = 2 IfGeneralProximityis “High” andEDR is “Low” then Element1Relevance is “High”. IfGeneralProximityis “High” andEDR is “Low” then Element2Relevance is “High”. IfGeneralProximityis “Low” andEDR is “Low” then Element3Relevance is “Medium”.

16. Exampleofthealgorithmexecution R1(+) B Element 1 Element 2 (+) R2 (-) B1 Element 3 If Element1Relevance is “High” andElement2Relevance is “High” then LoopR1Relevance is “High”. If Element2Relevance is “High” andElement1Relevance is “High” then LoopB1Relevance is “High”. If Element3Relevance is “High” andElement2Relevance is “Medium” then LoopR2Relevance is “Low”.

17. ExampleoftheAlgorithmExecution (+) R2 (+) R2 LDR(m,n) = 0.029 (+) R3 (-) B1 (-) B1 LDR(m,n) = 0.029 LDR(m,n) = 1 If LoopR1Relevance is “High” andLDR 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. ExampleoftheAlgorithmexecution R1(+) B Element 1 Element 2 (+) R2 (-) B1 Element 3 If LoopR1Representativeness is “High” andLoopB1Representativeness is “High” then General1Representativeness is “High”. If General1Representativeness is “High” andGeneral2Representativeness is “Medium” thenConsolidatedRepresentativenessis “Low”.

19. ExampleoftheAlgorithmexecution (+) R2 (+) R2 (+) R3 (-) B1 (-) B1 MDR(A, B) = 0.2 IfConsolidatedRepresentativenessis “Medium” andMDR is “Low” thenModelRepresentativenessis “High”.

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

21. Exampleofthealgorithmexecution (+) B Element 1 Element 2 (+) (+) (-) A Element 1 Element 2 (-) Element 3 The representativenessof mental model B is 0.8 in thissample.

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 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 Research210, 57-67, 2011.

24. Thanksto The 26th InternationalConferenceon Software EngineeringandKnowledgeEngineering SEKE 2014 pedrogn@ft.unicamp.br aeasilva@ft.unicamp.br zambon@ft.unicamp.br gisele@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.