Abstract
By learning function S-rough sets, we find that transfer functions play the roles in practice are that define which elements into the set Q and which elements left the set Q. But the changed elements have been mapped into what kinds of elements that are not very important, so it is not necessary to intensive study the transfer functions. Thus we can defines a dynamic fuzzy sets in the set D to reconsider the fates of the elements of Q. By using function S-rough sets and dynamic fuzzy sets, the new definition of dynamic fuzzy (λ,η)–function rough sets are given, then the mathematical structure and characteristics of dynamic fuzzy (λ,η)–function rough sets are discussed. The structural relations of dynamic fuzzy (λ,η)–function rough sets and function S-rough sets are deeply deliberated. Dynamic fuzzy (λ,η)–function rough sets are the general form of function S-rough sets, then function S-rough sets are the special cases of dynamic fuzzy (λ,η)–function rough sets. Dynamic fuzzy (λ,η)–function rough sets are the new direction in the study of rough sets. In terms of practical application, dynamic fuzzy (λ,η)–function rough sets can achieve some better results than the other methods.
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