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Positive and Negative Classes

            The classes  are called positive classes because they contain all positive attributes; the classes  are called negative classes because they have negative attributes. The classes  and  contain both positive and negative attributes, they are called mixed or contrary classes.
            If we have three attributes A,B,C with their opponents or complements as  and, then we can write the different class frequencies as below in table as shown.


 

 

 

Total

 

 

Total



In this table the positive classes are  and ABC whereas the negative classes are. All other classes are mixed.


Order of Classes:
            The order of the class depends upon the number of attributes going into that class. If a certain class can give us information about only one attribute, it is called class of order one.
            The classes  and  are classes of the order one and the frequencies,  and  are the frequencies of order one. The classes,  and  are the classes of order two and the frequencies and  are the frequencies of order two. The classes,,  and  are the classes of order three and (ABC),  ...  are the frequencies of order three. The sample size n does not contain any attribute and is therefore called frequency of order zero.




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