Transcript Affinity Set and Its Applications

Affinity Set and Its
Applications
Moussa Larbani and Yuh-Wen Chen
Outline




Research Background
Comparison of Other Sets
Definitions
Potential Applications
Research Background




Inspiration from the ancient social system and
human behavior
Affinity: a luck to bring people together
Simple idea: classification of objects based on
the dynamic relationship between them
Description of the dynamic relationship
between two objects: affinity
Some Observations of Affinity




Political Party
Business Contract
Marriage
Traffic Accident
Comparison of Other Sets


Fuzzy Sets
Rough Sets
Fuzzy Sets and Uncertainty

Information
Meaningful data
 Knowledge get from experience


Uncertainty


The condition in which the possibility of error
exist
Complexity
The emergence of fuzzy set
theory

To deal with uncertainty
Avoid
 Statistical mechanics
 Fuzzy set (Zadeh in 1965)


Crisp set
A collection of things
 Boundary is require to be precise

Fuzzy sets

Definition


The pair of member and the degree of
membership of the member
Membership function
Applications of Fuzzy Sets


Pattern recognition and clustering
Fuzzy control


Fuzzy decision


Stock market, finance, investment
Expert system


Automobiles, air-condition, robotics
Database, information retrieval, image processing
Combined with other field

Neural network, genetic algorithms
Rough Sets and Inconsistent
Information Table
Attributes
Headache
e1
e2
e3
e4
e5
e6
e7
e8
yes
yes
yes
no
no
no
no
no
Decision
Temperature
Flu
normal
high
very_high
normal
high
very_high
high
very_high
no
yes
yes
no
no
yes
yes
no
Certain rules for examples are:
(Temperature, normal)  (Flu, no),
(Headache, yes) and (Temperature, high)  (Flu, yes),
(Headache, yes) and (Temperature, very_high)  (Flu,
yes).
Uncertain (or possible) rules are (This example
is a correction of one presented in Pawlak (1995):
(Headache, no)  (Flu, no)*,
(Temperature, high)  (Flu, yes)*,
(Temperature, very_high)  (Flu, yes).
How do we measure the strength of a rule?
Consider the following possible measure:
# of positive examples covered by the rule
# of examples covered by the rule (including both positive and negative)
By this definition of probability or strength of a possible rule,
3
the first rule (Headache, no)  (Flu, no) has a probability of 5 .
Examples e4, e5,and e8 from the table are positive examples
covered by the rule. Examples e6 and e7 are negative examples
covered by the rule.
In applying the rules to a new patient, suppose that the
patient does not have a headache but his temperature is
high. We want to decide whether this patient has the
flu. Both the first and second rules above apply (the
two labeled *) so we use the higher probability rule.
Suppose that we do not have information on the
temperature of a new patient but we have information
about his headache. In this case, we would use the
lower probability.
e5
e8
e4
Lower and upper
approximations
of set X
upper approximation of X
e7
e6
Set X
e1
e2
e3
lower approximation of X
Inconsistent Information Table
Attributes
Headache Temperature
e1
e2
e3
e4
e5
e6
e7
e8
yes
yes
yes
yes
no
no
no
no
high
high
very_high
very_high
high
very_high
high
very_high
Decision
Pain
Flu
yes
yes
yes
yes
yes
no
yes
no
yes
yes
yes
yes
no
yes
yes
no
Inconsistent Information Table
Attributes
Headache Temperature
e9
e10
e11
e12
e13
e14
e15
e16
no
no
no
no
no
no
no
no
high
high
very_high
high
high
very_high
high
high
Decision
Pain
Flu
no
yes
no
no
yes
no
no
no
yes
no
no
no
no
no
no
no
Set X
Definitions of Affinity Sets
緣份的科學???

Indirect Affinity


As mentioned earlier, a close relationship between
people or things that have similar qualities, structures,
properties or features etc. we call this type off
affinity indirect affinity.
Direct Affinity

Direct affinity is natural liking for or attraction to a
person or a thing or an idea, etc. In direct affinity
two elements are involved: the subjects of affinity
and the affinity that takes place between them.
Potential Application 1

Prediction
Prediction
Financial State Forecasting
More Definitions
Potential Application 2

Data Mining
Data Mining
Direct Affinity
Potential Application 3

Network Control
Network Control
B
0.1
A
0.6
C
0.5
0.1
0.3
0.2
0.4
0.2
D
E
0.3
References



Julia A. Johnson and Mengchi Liu
, Rough Sets for Informative
Question Answering, University of Regina
Bart Kosko, Fuzzy thinking: The new science of
fuzzy logic
Moussa Larbani and Yuh-Wen Chen,
Developing the Affinity Set Theory and Its
Applications