Affinity Set and Its Applications Moussa Larbani and Yuh-Wen Chen

Outline Research Background Research Background Comparison of Other Sets Comparison of Other Sets Definitions Definitions Potential Applications Potential Applications

Research Background Inspiration from the ancient social system and human behavior Inspiration from the ancient social system and human behavior Affinity: a luck to bring people together Affinity: a luck to bring people together Simple idea: classification of objects based on the dynamic relationship between them Simple idea: classification of objects based on the dynamic relationship between them Description of the dynamic relationship between two objects: affinity Description of the dynamic relationship between two objects: affinity

Some Observations of Affinity Political Party Political Party Business Contract Business Contract Marriage Marriage Traffic Accident Traffic Accident

Comparison of Other Sets Fuzzy Sets Fuzzy Sets Rough Sets Rough Sets

Fuzzy Sets and Uncertainty Information Information Meaningful data Meaningful data Knowledge get from experience Knowledge get from experience Uncertainty Uncertainty The condition in which the possibility of error exist The condition in which the possibility of error exist Complexity Complexity

The emergence of fuzzy set theory To deal with uncertainty To deal with uncertainty Avoid Avoid Statistical mechanics Statistical mechanics Fuzzy set (Zadeh in 1965) Fuzzy set (Zadeh in 1965) Crisp set Crisp set A collection of things A collection of things Boundary is require to be precise Boundary is require to be precise

Fuzzy sets Definition Definition The pair of member and the degree of membership of the member The pair of member and the degree of membership of the member Membership function Membership function

Applications of Fuzzy Sets Pattern recognition and clustering Pattern recognition and clustering Fuzzy control Fuzzy control Automobiles, air-condition, robotics Automobiles, air-condition, robotics Fuzzy decision Fuzzy decision Stock market, finance, investment Stock market, finance, investment Expert system Expert system Database, information retrieval, image processing Database, information retrieval, image processing Combined with other field Combined with other field Neural network, genetic algorithms Neural network, genetic algorithms

Rough Sets and Inconsistent Information Table Attributes Headache Temperature Headache TemperatureDecisionFlu e1 yes normal yes normalno e2 yes high yes highyes e3 yes very_high yes very_highyes e4 no normal no normalno e5 no high no highno e6 no very_high no very_highyes e7 no high no highyes e8 no very_high no very_highno

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: By this definition of probability or strength of a possible rule, the first rule (Headache, no)  (Flu, no) has a probability of. Examples e 4, e 5,and e 8 from the table are positive examples covered by the rule. Examples e 6 and e 7 are negative examples covered by the rule. # of positive examples covered by the rule # of examples covered by the rule (including both positive and negative) 5 3

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.

Lower and upper Lower and upper approximations approximations of set X of set X upper approximation of X upper approximation of X Set X Set X lower approximation of X lower approximation of X e2e3 e7e6 e5e8 e1 e4

Inconsistent Information Table Attributes Headache Temperature Pain DecisionFlu e1 yes high yes yes high yesyes e2 yes e3 yes very_high yes yes very_high yesyes e4 yes e5 no high yes no high yesno e6 no very_high no no very_high noyes e7 no high yes no high yesyes e8 no very_high no no very_high nono

Inconsistent Information Table Attributes Headache Temperature Pain DecisionFlu e9 no high no no high noyes e10 no high yes no high yesno e11 no very_high no no very_high nono e12 no high no no high nono e13 no high yes no high yesno e14 no very_high no no very_high nono e15 no high no no high nono e16 no

Set X

Definitions of Affinity Sets 緣份的科學 ???

Indirect Affinity 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. 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 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. 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

Prediction

Financial State Forecasting

More Definitions

Potential Application 2 Data Mining Data Mining

Data Mining

Direct Affinity

Potential Application 3 Network Control Network Control

Network Control A C DE B

References Julia A. Johnson and Mengchi Liu, Rough Sets for Informative Question Answering, University of Regina 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 Bart Kosko, Fuzzy thinking: The new science of fuzzy logic Moussa Larbani and Yuh-Wen Chen, Developing the Affinity Set Theory and Its Applications Moussa Larbani and Yuh-Wen Chen, Developing the Affinity Set Theory and Its Applications