Notions from rough set theory in a generalized dependency relation context

In this paper, we introduce a notion of generalized dependency relation between subsets of an arbitrary (not necessarily finite) set Omega starting with the classical Armstrong's rule. More specifically, we fix a given set system F on Omega and call any transitive binary relation -> on the power set P(Omega) such that B subset of A is an element of F implies B <- A; B <- A if and only if b <- A for all b is an element of B; a [F]-dependency relation on Omega. We use the generality of such a notion to investigate some common analogies between rough set theory on information tables, formal context analysis, Scott's information systems and possibility theory. More specifically, taking as inspirational models some classical notions derived by rough set theory on attribute set of an information table, we first generalize and study such notions for any [F]-dependency relation. Next, we interpret such general results relatively to natural dependency relations derived by rough set theory on objects of an information table, formal context analysis, Scott's information systems and possibility theory. Finally, we study the generation of [F]-dependency relations by starting from a fixed set D of subset ordered pairs of Omega. (C) 2018 Elsevier Inc. All rights reserved.