L-fuzzy covering rough sets based on complete co-residuated lattice.

For L = (L , ⊙ , ⇝) a complete co-residuated lattice, the notions of ⊙ -subsethood degree and ⇝ -intersection degree between L-fuzzy sets are defined. It is shown that these notions reasonably extend the notions of subset and intersection between crisp sets. Then by using ⊙ -subsethood degree and ⇝ -intersection degree, a new model of L-fuzzy covering based L-fuzzy rough sets is investigated and studied. Firstly, a pair of L-fuzzy lower and upper approximation operators are constructed and their fundamental properties are discussed. Secondly, an axiom set or even a single axiom is presented to characterize the proposed approximate operators. Thirdly, the L-fuzzy topology and L-fuzzy co-topology induced by the L-fuzzy lower and upper approximation operators are researched, respectively. At last, the relationships between the new model and Qiao's L-fuzzy relation based rough sets are established. [ABSTRACT FROM AUTHOR]