2.4. Fuzzy Equivalence Relation and Hierarchy
In Chapter 1, we use the concept of quotient set in mathematics for establishing a multi-granular space. Our discussions have so far been limited to the partition of a domain so that each element belongs definitely to one and only one equivalence class. In reality, this is not always the case. Sometimes, the boundaries between two equivalence classes are not clear-cut. Two classes may have overlapped elements or their boundaries are fuzzy, i.e. the classification is fuzzy (Cheeseman, 1986; Nutter, 1987).
In clear-cut classification, we use equivalence relation R for establishing our model. A natural question is whether fuzzy equivalence relation can be used for constructing fuzzy classification model. ...
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