Rough set model on strong L-fuzzy Alexandrov spaces

Abstract

For a commutative unital quantale L and a strong L-fuzzy topological space X, we define the open-hood $O_x$ for every point $x\in X$. Considering $\{O_x\mid x\in X\}$ as the family of basic granules, we define the upper and lower approximation operators $\varphi ,\psi$. It is shown that $\varphi ,\psi$ are a kind of a closure operator and an interior operator respectively, and they form an L-Galois adjunction on $L^X$. By introducing notions of one zooming-in operator and two zooming out operators, we study the composition and decomposition problems of $\varphi ,\psi$.