Fuzzy type theory; Mathematical fuzzy logic; Rough sets;Alternative Set Theory; Indiscernibility; Fuzzy equality

This paper is an overview paper extended by new results, that deals with the relation of the basic notions of rough set theory and the topological notions introduced in the Alternative Set Theory (AST). Using the formalism of higher-order fuzzy logic (FTT), we prove syntactically that the main properties and relations among all the considered concepts hold both in classical as well as rough fuzzy set theory, and show that the basic concepts of rough sets are among some of the topological concepts of AST.