On mathematical structures of fuzzy rough set algebras

In rough set theory, the lower and upper approximation operators are important notions defined by a binary rela-tion. In this paper, we introduce a general type of relation-based fuzzy rough model determined by a triangular norm. Prop-erties of fuzzy rough approximation operators are examined. The fuzzy rough approximation operators are also characterized by axioms. A comparative study of the fuzzy rough set algebra with other mathematical structures such as fuzzy topological spaces, fuzzy measurable spaces, and fuzzy belief structures is investigated.