Rough Sets and the Algebra of Conditional Logic

Stone algebras: 3-valued logic and rough sets

“…It is worth mention here that the C-algebras are the algebraic counterpart of McCarthy's three-valued logic (cf. [11]) and unlike our case where the set of truth values of proposed logic L S is a Stone algebra, a C-algebra may not form even a semi-lattice.…”

“…-In [11], Panicker and Banerjee adopted yet other definition of rough sets (first discussed by Pagliani [7]) to explore the C-algebraic structures of rough sets. As in [7], for an approximation space (U, R) and A ⊆ U , the pair (LA, (UA) c ) is called a rough set.…”

Formalizing rough sets using a new noncontingency axiomatic system

“…Then, corresponds to the lower approximation set of . But , , , and cannot describe the concepts of “” or “” of rough sets. If rough sets make a connection with three‐valued logic, 13–15 the positive, the negative, and the borderline regions 7 can be used to denote the logic values , , and , respectively 13–15 . Nevertheless, a formal system for rough sets is not established and rough sets are only mapped to three‐valued logic as logic values.…”

“…If rough sets make a connection with three‐valued logic, 13–15 the positive, the negative, and the borderline regions 7 can be used to denote the logic values , , and , respectively 13–15 . Nevertheless, a formal system for rough sets is not established and rough sets are only mapped to three‐valued logic as logic values.…”