Rough Set Pair Research Articles

Defining rough sets using tolerances compatible with an equivalence

We consider tolerances $T$ compatible with an equivalence $E$ on $U$, meaning that the relational product $E \circ T$ is included in $T$. We present the essential properties of $E$-compatible tolerances and study rough approximations defined by such $E$ and $T$. We consider rough set pairs $(X_E,X^T)$, where the lower approximation $X_E$ is defined as is customary in rough set theory, but $X^T$ allows more elements to be possibly in $X$ than $X^E$. Motivating examples of $E$-compatible tolerances are given, and the essential lattice-theoretical properties of the ordered set of rough sets $\{ (X_E,X^T) \mid X \subseteq U\}$ are established.

Analysis of Tourist Site Level of Tangshan City based on Rough Set Pair

Analysis of Tourist Site Level of Tangshan City based on Rough Set Pair

Generalized Rough Logics with Rough Algebraic Semantics

The collection of the rough set pairs <lower approximation, upper approximation> of an approximation (U, R) can be made into a Stone algebra by defining two binary operators and one unary operator on the pairs. By introducing a more unary operator, one can get a regular double Stone algebra to describe the rough set pairs of an approximation space. Sequent calculi corresponding to the rough algebras, including rough Stone algebras, Stone algebras, rough double Stone algebras, and regular double Stone algebras are proposed in this paper. The sequent calculi are called rough Stone logic (RSL), Stone logic (SL), rough double Stone logic (RDSL), and double Stone Logic (DSL). The languages, axioms and rules are presented. The soundness and completeness of the logics are proved.