Abstract
For probing into further the relations of the general algebraic theories and fuzzy rough sets theories, this paper presents several new theories and definitions on fuzzy rough sets including half-group, group, subgroup, ring, subring, ideal, field. These new algebraic theories studied on fuzzy rough sets will break through the boundary of deterministic attribute space in general algebraic theories so that we may discuss and solve some fuzzy or uncertain problems on approximate space of fuzzy rough sets. Thus, the new theories development in this paper leads to advancements in general algebra and in turn can form the theoretic base for further applications of fuzzy rough sets. Advancements in general algebra through the study of algebraic theories on fuzzy rough sets are not only applicable to fuzzy rough sets fields, but also are of important theoretical value to modern algebra.
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