Logics of time and computation
Logics of time and computation
Relational interpretations of neighborhood operators and rough set approximation operators
Information Sciences—Informatics and Computer Science: An International Journal
On the structure of rough approximations
Fundamenta Informaticae
Modal-Like Operators in Boolean Lattices, Galois Connections and Fixed Points
Fundamenta Informaticae
On the structure of generalized rough sets
Information Sciences: an International Journal
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In this paper we consider the problem whether for a map ϕ : A(B) → B there is a relation R on A(B) such that properties of a map ϕ: B → B are reflected to R. This is a converse problem that J. Järvinen proved in [5]. We give an affirmative answer to the problem. Moreover we give equational bases which characterize properties of the map ϕ. This means that the classes of some types of algebras form varieties. Hence, there are full correspondence between properties of relations and varieties of modal algebras. This work was partially supported by Grant-Aid for Scientific Research (No.15500016), Japan Society for the Promotion of Science.