Topological characterizations of generalized fuzzy rough sets

In this paper, topological characterizations of generalized fuzzy rough sets are investigated in the context of basic rough equalities. Various fuzzy topologies induced by different fuzzy relations are studied with respect to the lower fuzzy rough approximation operator determined by a fuzzy implicator, which is left-continuous in the first argument and right-continuous in the second argument. The relationships among fuzzy topologies induced by fuzzy relations are discussed. The algebraic structures of T-similarity set of fuzzy relations are investigated with respect to different fuzzy implicators, where T is a left-continuous t-norm. Moreover, the T-transitive subset of T-similarity set is proven to be a complete distributive lattice.