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Fuzzy Signatures

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					Fuzzy Signatures in
SARS

      Student: Bai Qifeng
      Client: Prof. Tom Gedeon


                                 1
Problem of Fuzzy Theory
   A Major issue in fuzzy applications is how to create
    fuzzy rules

   the number of rules have an exponential increase
    with the number of inputs and terms.
    | R | O (T k )

   At least one activated rule for every input.
           e.g. 5 terms, 2 inputs => 25 rules
           5 terms, 5 inputs => 3,125 rules

                                                           2
Fuzzy Signature
 Fuzzy signatures structure data into vectors
  of fuzzy values, each of which can be a
  further vector.

 Fuzzy signatures can be regarded as Special
  multidimensional fuzzy data. Some of the
  dimensions are interrelated in the sense that
  they form sub-group of variables, which jointly
  determine some feature on a higher level.

                                                 3
Fuzzy Signature




                  4
Fuzzy Signatures
 The relationship between higher and lower
  levels is govern by fuzzy aggregations.

 Appropriate aggregations used in their child
  signatures are not necessary identical.

 They can be changed based on expert
  opinions and detailed circumstance.


                                                 5
Fuzzy Signatures in SARS
 The following scheme is of some daily symptom
  signatures of patients:

        
                                               8am   
                 8am            
               12 pm                       12 pm  
         f ever                      fever       
                4 pm                       4 pm   
                               main              
   AS          8 pm      AS              8 pm   
                12am                       12am  
        Cough                        Cough        
                 9 pm  
                                               9 pm   
            Nausea                           Nausea  
                                  Secondary          
              Sore                           Sore  
                                                           
                                                                6
Automatically Construct Fuzzy
Signature
 Searches the features of data structure,
  classify data based on their relevance and
  cluster the high relevant data.

 With clustering, the known situation can be
  used to build the model and then it can be
  used to another situation where it is not
  known.


                                                7
Fuzzy Clustering
    Hierarchical Method
       Creating a cluster tree.


   Objective Function Method
      Solving problems about fuzzy boundary in
      evaluating relevance of objects




                                                 8
Data Pretreatment
 Standardizing raw data


 Outlier
     Two-stage method
     Scatter Plot

 Missing data



                           9
Conclusion
 Choosing proper cluster algorithm and
  appropriate data pretreatment, try to find the
  appropriate fuzzy signatures

 After constructing the fuzzy signature, with
  aggregations, we can effectively reduce the
  number of rules in this fuzzy system.



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