MultiAggregator Fuzzy Decision Model: Evolutionary Computingbased Optimization

1
MultiAggregator Fuzzy Decision Model
Evolutionary Computingbased Optimization

• Souad Souafi-Bensafi, Masoud Nikravesh

BISC The Berkeley Initiative in Soft Computing
Electrical Engineering and Computer Sciences
Department
2
Outline

• Decision Support System (BISCDSS)
• Objectives, Architecture, application example
  University Admissions
• Basic concepts fuzzy sets, fuzzy similarity
  measures, aggregation operators
• Evolutionary Computing (EC)
• Multi-criteria decisional model ECbased
  optimization

3
BISC-DSS Objectives

• Develop Soft Computing techniques for
  multi-criteria decision analysis
• Handle imprecise, uncertain and incomplete
  information or data
• human-machine interaction, learning and
  adaptation through time

• conceptual level
• Resemble human behavior by allowing
  approximation
• objects do not need to match exactly the decision
  criteria
• implementation level
• Designed in a generic form to
• accommodate more diverse applications

4
BISC DSS Architecture
Application Template

• Aggregation operators
• Similarity measures
• Norm-Pairs
• Fuzzy sets

Fuzzy Search Engine (FSE)
User Interface
Evolutionary Computing Kernel
DB
5
University admissions
Different admission rates and Varying criteria
depending on the University strategy e.g.
UC-Berkeley and Stanford University
6
University admissions

• Attributes
• AP Advanced Placement
• IBHL International Baccalaureat Higher Level
  (IBHL)
• HW Honors and Awards
• GPA 12th grade courses GPA
• CP Course pattern
• GPAP Pattern of Grades through time
• CAoSI Creative Achievement or Sustained
  Intellectual
• AAaO Academic Achievement and Outreach
• CIaCV Contribution to the intellectual and
  cultural vitality
• DPBaE Diversity in the Personal Background and
  Experience
• Concern Concern for Community and others
• AAA Achievements, Art or Athletics
• Leadership, Motivation, Employment

7
University admissions
Labels/Granulation EthnicName American,
Chinese, French, Greek, , Not
Care Residency California Resident, US
Resident, International, Not Care Sex
Male, Female, Not Care AP Very Low,
Low, Medium, High, Very High IBHL
Very Low, Low, Medium, High, Very
High HW Few, Some, Lot, Not
Care GPA Very Low, Low, Medium,
High, Very High DPBaE low diversity,
kind low diversity, diverse, high
diversity, kind high diversity, exceptional
8
Basic concepts
Fuzzy sets/ Membership Functions (MFs)

• Triangular
• Gaussian
• Trapezoidal

9
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)
10
Basic concepts
Norm-Pairs
Fuzzy AND ?
Fuzzy OR ?
x and y are MF values in 0,1.
11
Basic concepts
Aggregation Operators
12
Basic concepts
Weighted Aggregation Operators
13
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

14
EC Genetic Algorithms
Genetic Operators
15
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
16
EC Genetic Programming
Crossover
17
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
18
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)
19
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
20
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)

21
1st order aggregation model (1)

• Norm-pair Min/Max
• Fuzzy similarity measure Jaccard
• Aggregation operator Weighted Mean

22
1st 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.
23
1st 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
24
Advanced Multi-Aggregator Model (1)

• parameters
• similarity measures
• norm-pairs
• aggregation operators
• weights
• aggregation model structure

Representation of user/expert preferences
25
Advanced Multi-Aggregator Model (2)

• Model description

• Parameters
• aggregators
• weights
• tree structure.

26
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
27
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

28
Other applications
Finance credit scoring Medicine diagnosis Mark
eting electronic shopping Education
university admissions Banking fraud detection