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BISCDSS

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Multi-Criteria Decision Analysis with Uncertain and Incomplete Information. Application Areas ... Information (Can be uncertain) Granular (Scale and Precision) ... – PowerPoint PPT presentation

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Title: BISCDSS


1
Natural Language Computing and Reasoning
2
Symptoms X Diagnosis
Symptoms
Diagnosis
Test Attribute Set/ Question
3
Symptoms X Diagnosis
  • The use of Linguistic variables
  • Simple relations between variables by fuzzy
    conditional statement
  • Complex relations by fuzzy Algorithms
  • IF Symptom (A1 ) is a11 and Symptom (A2 ) is
    a12 and Symptom (An ) is a1n Then Diagnosis
    (F1) is a1
  • IF Symptom (A1 ) is a21 and Symptom (A2 ) is
    a22 and Symptom (An ) is a2n Then Diagnosis
    (F1) is a1
  • Question
  • IF Symptom (A1 ) is a1 and Symptom (A2 ) is a2
    and Symptom (An ) is an Then Diagnosis (F1) is
    b?

4
Other Applications
  • Application

Description
5
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6
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7
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8
University admissions
Different admission rates and Varying criteria
depending on the University strategy e.g.
UC-Berkeley and Stanford University
9
Outline
  • BISC Decision Support System
  • Neuro-Fuzzy-Evolutionary Computing NeF-ECom
  • Multi-Criteria Decision Analysis with Uncertain
    and Incomplete Information
  • Application Areas
  • ASIS

10
BISC- Decision Support System
BISC-DSS
Human Knowledge
HM
First Principle Models
Data Knowledge
11
  • OBJECTIVES
  • Develop soft-computing-based techniques for
    decision analysis
  • Tools to assist decision-makers in assessing
    the consequences of decision made in an
    environment of imprecision, uncertainty, and
    partial truth and providing a systematic risk
    analysis
  • Tools to assist decision-makers answer What if
    Questions, examine numerous alternatives very
    quickly and find the value of the inputs to
    achieve a desired level of output
  • Tools to be used with human interaction and
    feedback to achieve a capability to learn and
    adapt through time

12
DECISION ENVIRONMENT
  • Information (Can be uncertain)
  • Granular (Scale and Precision)
  • Query (Can be imprecise)
  • Measure (Similarity)
  • Aggregation (Can be fuzzy)
  • Ranking (Provide Alternatives)
  • Optimization (Multi-Objective Multi-Criteria)

13
BISC DSS Components and Structure
Model and Data Visualization
  • Model Management
  • Query
  • Aggregation
  • Ranking
  • Fitness Evaluation

Evolutionary Kernel Genetic Algorithm, Genetic
Programming, and DNA
  • Selection
  • Cross Over
  • Mutation

Input From Decision Makers
Experts Knowledge
Model Representation Including Linguistic
Formulation
Data Management
  • Functional Requirements
  • Constraints
  • Goals and Objectives
  • Linguistic Variables Requirement

14
Query (Request) Q
  • find if such query exists ? degree of match ?
    rank ? decision ( i.e. resource allocation)
  • compare queries ? rank ? decision (task
    allocation)
  • Use Fuzzy Min-Max with degree of preferences

15
Objective function Cost Function/ Fitness
Function
This may involve multi-objective, multi-criteria
optimization with conflict and fuzzy variables.
Therefore, use fuzzy-GA to solve the objective
function.
16
University admissions
Different admission rates and Varying criteria
depending on the University strategy e.g.
UC-Berkeley and Stanford University
17
Actual Model Given Student Rate of Success
Predicted Model Using Fuzzy-GA
Initial GA Population of Models
18
The BISC Decision Support System Conventional GA
Multi-Objective Multi-Criteria Optimization
Max
Preferences
Mean
Actual Prediction 0.5010 0.7961
0.5010 0.5176 0.5210 0.5686 0.4800
0.4588 0.5010 0.7176 0.5010
0.8588 0.5010 0.9490 0.5010 0.6980
0.5010 0.5922 0.5010 0.9373
0.5000 0.7412 0.5210 0.7608 0.5210
0.6353 0.5630 0.6784 0.5210
0.7490 0.5420 0.8667 0.5630 0.7843
Fitness
Min.
Std Dev.
Generation
19
The BISC Decision Support System Interactive-GA
Multi-Objective Multi-Criteria Optimization
Max
Preferences
Preferences
Actual Predicted 0.5010 0.4609
0.5010 0.4907 0.5210 0.5712 0.4800
0.4709 0.5010 0.5381 0.5010
0.5106 0.5010 0.5513 0.5010 0.5469
0.5010 0.5161 0.5010 0.5061
0.5000 0.5106 0.5210 0.5701 0.5210
0.5425 0.5630 0.5469 0.5210
0.5370 0.5420 0.4444 0.5630 0.5017
Mean
Fitness
Min.
Std Dev.
Generation
20
Neuro-Fuzzy-Evolutionary ComputingMulti-Criteria
Decision Analysis with Uncertain and Incomplete
Information
BISC-DSS Software
NeF-ECom
21
BISC DSS Software Architecture
  • Aggregation operators
  • Similarity measures
  • Norm-Pairs
  • Fuzzy sets

Application Template
Fuzzy Search Engine (FSE)
User Interface
Evolutionary Computing Kernel
DB
22
Basic concepts
Fuzzy sets/ Membership Functions (MFs)
Low Medium High
Triangular
Gaussian
Low diversity diverse High
diversity
Trapezoidal
23
Basic concepts
Fuzzy similarity measures
X and Y are fuzzy measures defined over the same
fuzzy sets with MFs µ1, µ2, , µm
Norm-Pair operators ? et ? (norm-conorm)
24
Basic concepts
Norm-Pairs
Fuzzy AND ?
Fuzzy OR ?
x and y are MF values in 0,1.
25
Basic concepts
Aggregation Operators
26
Basic concepts
Weighted Aggregation Operators
27
Advanced Multi-Aggregator Model
Basic concepts
  • Parameters
  • aggregators
  • weights
  • tree structure.

28
Compactification Algorithm InterpretationA
Simple Algorithm for Qualitative AnalysisRule
Extraction and Building Decision TreeNikravesh
and Zadeh (2005)(Zadeh, 1976)
29
Symptoms X Diagnosis
  • The use of Linguistic variables
  • Simple relations between variables by fuzzy
    conditional statement
  • Complex relations by fuzzy Algorithms
  • IF Symptom (A1 ) is a11 and Symptom (A2 ) is
    a12 and Symptom (An ) is a1n Then Diagnosis
    (F1) is a1
  • IF Symptom (A1 ) is a21 and Symptom (A2 ) is
    a22 and Symptom (An ) is a2n Then Diagnosis
    (F1) is a1
  • Question
  • IF Symptom (A1 ) is a1 and Symptom (A2 ) is a2
    and Symptom (An ) is an Then Diagnosis (F1) is
    b?

30
Symptoms X Diagnosis
Test Attribute Set
31
Table 1 (intermediate results)
Group 1(initial)
Pass (1)
Pass (2)
Pass (3)
32
MAXIMALLY COMPACT REPRESENTATION
33
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34
Chromosome Representation
Fuzzy Label, Set Value, Scalar Series Input
  • Composed of primitive statistical, fuzzy set,
    aggregator, similarity, arithmetic, and signal
    processing operators.
  • Each gene (or algorithm) is represented as a
    tree, accepts both scalar and series input, and
    outputs scalar features.
  • The chromosome produces a feature vector set.

Scalar Fuzzy Label Features
35
Multi Aggregator Tree
Advanced Multi-Aggregator Model
  • Parameters
  • aggregators
  • weights
  • tree structure.

36
H-DT3 Nikravesh Zadeh (2003)
Attrb.
BISC-DSS Nikravesh (2000)
Attrib./Feature Selection Nikravesh (2005)
C-Rules Zadeh (1976) Nikravesh (2003)
Transf.
RCR-PFRL Berenji (2003) Nikravesh (2003)
Compactification Zadeh (1976)
Signal
C-DT3 Zadeh (1976) Nikravesh (2003)
MA-DT3 Nikravesh (2003)
Cases
SVM, NN (RBF MLP), NF Nikravesh (2003)
37
BISC-DSS Software
38
BISC-DSS Software
39
EC Genetic Algorithms
  • Requirements
  • - Individual problem representation
  • - Fitness function for evaluation
  • - Termination criterion
  • Principle
  • Create randomly an initial population of
    individuals
  • Evolve the population
  • evaluate and select individuals
  • use them in genetic operators (crossover,
    mutation)
  • generate new generation
  • - Stop if termination criterion satisfied

40
EC Genetic Algorithms
Genetic Operators
41
EC Genetic Programming
  • Individual Computer program
  • Most common representation tree encoding
    (nodes functions, leaves terminals)
  • Fitness function returned value by the root
    node

Chosen node
Mutation
new individual
selected individual
resulting individual
42
EC Genetic Programming
Crossover
43
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44
BISC-DSS Interaction and Optimization
  • Comparison, Aggregation, Scoring
  • MODEL based on
  • Aggregation operators,
  • Similarity measures
  • Norm-Pairs
  • Fuzzy sets

DB
Fuzzy Search Engine (FSE)
QUERY
User Interface
ANSWERS
Evolutionary Computing Kernel
User preferences (re-ranking, selection)
OPTIMIZATION
45
Multi-Criteria Decision Model (1)
  • Multi-Attribute Query K attributes A1, A2,,AK

Scores
Database
Similarity calculation
Query
Query Answering Ranking based Selection
based (criteria number top answers) (criteria
threshold)
46
Multi-Criteria Decision Model (2)
Query
Data
Fuzzification
Fuzzy sets
For each attribute
Norm-pairs ?,?
Fuzzy similarity calculation
Fuzzy similarity measures
Aggregation model
aggregation
Scoring
Ranking or Selecting Answers
47
Multi-Criteria Decision Model (3)
  • Data Xi (xi1, xi2, , xiK), Query Q
    (y1, y2, , yk)
  • K attributes A1, A2,,AK
  • For each attribute Aj
  • rj fuzzy sets µ1(Aj,.), µ2(Aj,.),,µrj(Aj,.)
  • sj similarity(xij, yj), j 1, 2, , K
  • Score SIM(Q,Xi) Aggregation(s1, s2, , sk)

48
First Order Aggregation Model (1)
  • Norm-pair Min/Max
  • Fuzzy similarity measure Jaccard
  • Aggregation operator Weighted Mean

49
First Order Aggregation Model (2)
  • Aggregation model simple weighted aggregation
    operator
  • user preferences attribute weighting
  • (Degree of importance of each attribute)
  • Aggregation model parameters weighting vector

Optimization process find the optimal weights
Using GA.
50
First Order Aggregation Model (3)
  • Model parameters learning using GA
  • GA-based learning module
  • - Individuals weight vectors
  • - Genetic operators crossover, Mutation
  • Fitness function
  • Termination criterion

Specific fitness function
Problem specification
Optimal weights
51
Advanced Multi-Aggregator Model (1)
  • parameters
  • similarity measures
  • norm-pairs
  • aggregation operators
  • weights
  • aggregation model structure

Representation of user/expert preferences
52
Advanced Multi-Aggregator Model (2)
  • Model description
  • Parameters
  • aggregators
  • weights
  • tree structure.

53
Advanced Multi-Aggregator Model (3)
  • Model parameters learning using GP

Aggregators set, Attributes set, Model constraints
Specific DNA encoding
GP-based learning module
Problem specification
Specific fitness function
Optimal multi-aggregation model
54
Basic concepts
Neural Network Aggregator
55
Basic concepts
NeuroFuzzy Aggregator
56
Committee Machine
Committee Machines
57
Model evaluation
rejected
accepted
D
Similarity calculation
Score Ranking
  • Fitness function combining
  • accuracy rates to maximize
  • distance D to maximize
  • model structure size to minimize

58
Other Applications
  • Application

Description
59
Issues with Missing Data and Uncertainties
UCI Repository
Nikravesh, 2004
60
Automated Sensory Inspection System
BISC-DSS-ASIS Software
ASIS
61
Applications
62
Chromosome Representation
Genes
Chromosome
It is not part of current ASIS-BISC-DSS
y
Feature Vector, Automated
x1
xi
xn
Feature Vector, Expert Knowledge
x1E
xiE
xnE
63
Primitive Operators
  • Minimum
  • Maximum
  • Ratio of Means
  • Add, Subtract, Multiply, Divide
  • Subseries
  • Subsampling
  • Derivative Approximation
  • Convolution Filtering
  • Mean
  • Standard Deviation
  • Variance
  • Skewness
  • Kurtosis
  • Integral
  • Sum
  • Linear Combination

It is not part of current ASIS-BISC-DSS
64
Signal Attribute/ Character Analysis
  • 1. Conventional Hilbert Attributes
  • 2. FFT-based frequency-domain attributes/TFA
  • 3. Empirical Correlation of Attributes
  • 4. Clustering of Attributes
  • 6. Multi-trace correlation/coherence attributes
  • 7. Wavelet Character Analysis
  • 7. Use Neural Networks for Integration

65
Conventional Attributes
  • Amplitude Envelope
  • Ampl. Weighted Cosine Phase
  • Ampl. Weighted Freq.
  • Amplitude Weighted Phase
  • Apparent Polarity
  • Average Frequency
  • Cosine Instantaneous Phase
  • Derivative Inst. Amplitude
  • Derivative
  • Instantaneous Frequency
  • Dominant Frequency
  • Instantaneous Phase
  • Integrated Abs. Amplitude
  • Trace Integration
  • Raw Acoustic Wave Trace
  • 2nd Derivative Inst. Ampl.
  • 2nd Derivative

66
Chromosome Representation
Fuzzy Label, Set Value, Scalar Series Input
  • Composed of primitive statistical, fuzzy set,
    aggregator, similarity, arithmetic, and signal
    processing operators.
  • Each gene (or algorithm) is represented as a
    tree, accepts both scalar and series input, and
    outputs scalar features.
  • The chromosome produces a feature vector set.

Scalar Fuzzy Label Features
67
Front/Back-end Architecture (BISC-Zeus)
Time Series
Classifier Generator
Genetic Algorithm Feature Selection Based on ASIS
Feature Extraction
Front-end Stochastic Search
Classification
Support Vector Machine BISC-DSS
Back-end Classification
Time Series Classifier
68
Classifier Architecture (BISC-Zeus)
Classifier Generator
Time Series
TIME SERIES CLASSIFIER
FEATUREEXTRACTOR
FEATURE SET
MODEL
Prediction Result
BISC-DSS
Feature Selection Based On ASIS
69
Fitness In-sample Rate (BISC-Zeus)
N Features
K Features
Chromosome
Training Set
Processed Set
A
B
Feature Extractor Feature Selection Based On
ASIS
Model
C
E
  • Steps
  • Run Feature Extractor
  • Produce Training Set
  • Train SVM/BISC-DSS
  • Produce Model
  • Run Classifier
  • Produce Result Set
  • Calculate Score

Classifier
BISC-DSS
F
D
Score
Result Set
70
Fitness N-Fold Cross Valid (BISC-Zeus)
N Features
K Features
Chromosome
Training Set
Processed Set
A
B
Feature Extractor Feature Selection Based On
ASIS
E
Model
D
  • Steps
  • Run Feature Extractor
  • Produce Training Set
  • Produce Testing Partitions
  • Train on Complement

C
Testing Partitions
Classifier
F
E. Produce Model F. Predict Labels of
Test Set G. Score if finished, otherwise,
goto step D.
BISC-DSS
Result Set
Finished? No
Yes
Score
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BISC-DSS Clustering-Based ANSIS
Sets of Ranked Attributes AS1, AS2, AS3, AS4
Input All the Attributes
Final Set of Attributes selected using
Unsupervised Clustering
AS1
Att1, Att2, Att3, Att4,
Unsupervised Clustering K-Mean, PCA, SOM,
AS2
Att11, Att12, Att13, Att14
Modeling Techniques Principal Component Analysis
(PCA) Singular Value decomposition (SVD) Mahalanob
is Distance (MD) One Class Suppoer vector
Machine (1CSVM)
AS3
Att21, Att22, Att23, Att24, ..
Selected Attributes
AS4
Att31, Att32, Att33, Att34,
Cluster, Classification, Anomaly, Rules, Decision
Tree,
Final Set of Attributes selected using Modeling
Technique
Marked Data as Clusters, Anomaly,
In Progress
BISC-DSS Software
74
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78
One-Class ClassificationAnalysis of new data
79
One-Class SVM - Experiments
80
One-Class SVM Experiment 1
81
One-Class SVM Experiment 2
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