Modelling weapon assignment as a multiobjective decision problem
Cognitive Modelling Assignment
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![Page 1: Cognitive Modelling Assignment](https://reader035.fdocuments.in/reader035/viewer/2022062721/5681384e550346895d9ffa55/html5/thumbnails/1.jpg)
Cognitive Modelling Assignment
Create Model
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Examining the data for single classification
• Step 1: Examine the training data and establish the patterns within.– I took notes on two patterns: 1.How often a symptom occurred in one disease as a
percentage of how often that symptom occurred overall.
2.What proportion one symptom was of all the examples of one disease.
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Patterns of Dimensions
• A clear pattern emerged throughout, for each of the 3 disease categories it could be said that one dimension was more reliable than the others.
• However, I noticed that this differed for each disease – unlike in the exemplar model
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How the question was asked
• The importance of how the question was asked:Had it been presented differently it would have favoured the method applied by the exemplar model
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Part 1 of my model
• I built this theory into my model by applying a “reliability parameter” βi.
• Each dimension has a different reliability parameter β1 β2 β3
• These reliability parameters vary from disease to disease- the model has to be applied independently for each category
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Reliability parameters
• Disease A: D1 (.9) most reliable to the point of outweighing D2(.1) or D3(.5) (especially if D1=A)
• Disease B: D3(.7) seems most reliable, followed by D2(.5), then D1(.3)
• Disease C: Again D1 (.9) most reliable, followed closely by D3(.8), D2 inconsistent (.3)
• (These were worked out from combining the two patterns mentioned earlier)
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Part 2 of my model
• The second part of my model was to define a membership score for each symptom for each disease.
• To do this I took how often the symptom occurred in the disease as a proportion of how often it occurred overall and I then subtracted how often it occurred elsewhere
• M= S-S’
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M=S-S’
• M=S-S’, S’=1-S
• WHY?
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M=S-S’
• This formula provides a negative value if a symptoms membership in a different disease outweighs its membership in the tested disease
• If it has even distribution between two then a value of zero is given
• IF it is most common in this disease then it has a positive value
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Model
• The model is created by combining part 1 and part two in a product.
• The reliability parameter for a dimension is multiplied by the membership score for the given symptom
• The products are then summed to give the overall similarity score for the test item
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Model for single classification
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Example: Model Applied to Disease A
M M M
1 1 -1 0.333332 -0.6 -0.5 -13 0 0.2 -0.64 -1 -1 -0.65 -1 -0.5 -1
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βiMi
β 0.9 0.1 0.5
1 0.9 -0.1 0.166665
2 -0.54 -0.05 -0.5
3 0 0.02 -0.3
4 -0.9 -0.1 -0.3
5 -0.9 -0.05 -0.5
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Similarity ScoresTEST ITEM SIMILARITY SCORE1 0.9666652 -1.093 -0.284 -1.35 -1.45
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Rescaled Data/People ScoresModel A
People A
Model B
People B
Model C
People C
3.22222 6.78 -1.66667 -2.00 -4.88897 -9.06
-3.63333 -9.33 -0.27787 -3.22 1.22224 6.11
-0.93333 -3.11 -4 -5.28 -1.6 -3.78
-4.33333 -3.06 -0.33334 -0.56 -0.399 0.22
-4.83333 -1.39 1.05544 7.00 -2.77767 -7.00
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Correlation to data
Disease Correlation
A 0.74399B 0.798195C 0.967607Average 0.836597
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Disease A
1 2 3 4 5
-12
-10
-8
-6
-4
-2
0
2
4
6
8
MODELACTUAL
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Disease B
1 2 3 4 5
-6
-4
-2
0
2
4
6
8
MODELACTUAL
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Disease C
1 2 3 4 5
-10
-8
-6
-4
-2
0
2
4
6
8
MODELACTUAL
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Conjunction Classification
• I took an integrative approach to my conjunctive classification.
• The reason for this is that I don’t think people would combine their answers from earlier questions to answer a new question.
• Instead I think people would recall the examples they had seen and combine these in some way
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Conjunction Classification
• As such, I combined the data at the symptom membership score stage (i.e. When determining M)
• I believe people would use A&B given as a sample of how to create conjunctions.
• These examples include prominent members of both categories and I feel this would be a rule to go by.
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Max
• One way I thought about incorporating the “most prominent members of both categories” idea into my model way by using the MAX of the two M values, however this results in obvious problems. (High values of A will be high values of AB and AC ignoring the other disease)
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Reliability parameter
When choosing my reliability parameters for the conjunction categories I chose the max of the two included categories as I feel that this would be prioritised in the conjunction also
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Conjunction model
• After trying Max I looked at the other functions and “SUM” and “ NORMALISED SUM” made the most intuitive sense as I think people would probably say “it could be in A or B then it might be in A&B” (The SUM models were rescaled from -6to6)
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β=MAX, M=SUMMODEL AB ACTUAL
MODEL AC ACTUAL
MODEL BC ACTUAL
-0.77778 1.17 -1 -5.39 -4.77781 -7.83
-3.62265 -8.56 -1.87213 -4.06 -0.41667 4.33
-2.53333 -3.72 -1.5 -1.06 -3.03333 -4.72
-2.86672 -2.72 -2.9995 -5.06 -0.53333 -1.67
-2.22235 -3.33 -4.47163 -7.28 -0.41667 -0.89
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CORRELATIONCATEGORY CORRELATION
A&B0.926166
A&C0.646386
B&C0.868461
AVERAGE0.813671
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A&B
1 2 3 4 5
-10
-8
-6
-4
-2
0
2
MODEL ABACTUAL
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A&C
1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
MODEL ACACTUAL
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B&C
1 2 3 4 5
-10
-8
-6
-4
-2
0
2
4
6
MODEL BCACTUAL
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Varying the Model
• Using the Sum model didn’t always provide high values for the most prominent characteristics. As such, I retested the model inputting a value of 1 where any symptom had a value of 1 for either category
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Varied ModelMODEL AB ACTUAL
MODEL AC ACTUAL
MODEL BC ACTUAL
1.55552 1.17 0.5 -5.39 -3.94448 -7.83
-3.62265 -8.56 -1.87213 -4.06 1.08333 4.33
-2.53333 -3.72 -1.5 -1.06 -3.03333 -4.72
-2.86672 -2.72 -2.9995 -5.06 0.3 -1.67
-2.22235 -3.33 -4.47163 -7.28 -0.41667 -0.89
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CorrelationsCATEGORY CORRELATION
A&B0.863503
B&C0.929426
A&C0.412961
AVERAGE0.735297
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A&B
1 2 3 4 5
-10
-8
-6
-4
-2
0
2
4
MODEL ABACTUAL
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B&C
1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
MODEL ACACTUAL
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A&C
1 2 3 4 5
-10
-8
-6
-4
-2
0
2
4
6
MODEL BCACTUAL
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NORMALISED SUM
• Finally, I decided that using Normalised sum might be a better measure of the parameters I want to include. As such I applied the model with NORMALISED SUM and MAX reliability parameter
• This data had to be rescaled from -9to9 to -10to10
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Β=MAX, M=NSUMMODEL AB ACTUAL
MODEL AC ACTUAL
MODEL BC ACTUAL
1.29603 1.17 0.09875 -5.39 -3.92597 -7.83
-2.63524 -8.56 -1.24062 -4.06 1.11723 4.33
-2.04444 -3.72 -0.66667 -1.06 -1.6 -4.72
-1.48896 -2.72 -2.3463 -5.06 0.84462 -1.67
-0.76859 -3.33 -3.90728 -7.28 0.22832 -0.89
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CORRELATIONCATEGORY CORRELATION
A&B0.897844
B&C0.895839
A&C0.608521
AVERAGE0.800735
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A&B
1 2 3 4 5
-10
-8
-6
-4
-2
0
2
MODEL ABACTUAL
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A&C
1 2 3 4 5
-8
-7
-6
-5
-4
-3
-2
-1
0
1
MODEL ACACTUAL
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B&C
1 2 3 4 5
-10
-8
-6
-4
-2
0
2
4
6
MODEL BCACTUAL