Affiliations: Department of Mathematics, Gangneung-Wonju National University, Gangneung, Gangwondo, Korea
Correspondence:
[*]
Corresponding author. Yong Chan Kim, Department of Mathematics, Gangneung-Wonju National University, Gangneung, Gangwondo 25457, Korea. E-mail: [email protected].
Note: [1] This work was supported by Research Fund of Gangneung-Wonju National University.
Abstract: In this paper, as an extension of variable precision (θ, σ)-fuzzy rough sets, we introduce the notion of the generalized granular variable precision
(R_β,R¯β)
-fuzzy rough sets determined by fuzzy granules with R ∈ LX×Y on a residuated and co-residuated lattice with an involution N. We investigate the properties of
R_β
and
R¯β
with eLY and dLY are (L, ⊙)-fuzzy preorder and (L, ⊕)-fuzzy co-preorder, respectively. Moreover, we investigate Alexander topologies and Alexander co-topologies induced by
R_⊤
and
R¯⊥
, respectively. For an L-fuzzy relation R ∈ LX×X and
R_β,R¯β
for each β ∈ L, we obtain Alexandrov L-fuzzy pretopologies and Alexandrov L-fuzzy precotopologies on X, respectively. We give their examples.
