Abstract
We give in this paper the definitions of
(
L
,
M
)
-double fuzzy filter base and
(
L
,
M
)
-double fuzzy filter structures where
L
and
M
are strictly two-sided commutative quantales, and we also investigate the relations between them. Moreover, we propose second-order image and preimage operators of
(
L
,
M
)
-double fuzzy filter base and study some of its fundamental properties. Finally, we handle the given structures in the categorical aspect. For instance, we show that the category
(
L
,
M
)
-
DFIL
of
(
L
,
M
)
-double fuzzy filter spaces and filter maps between these spaces is a topological category over the category
SET
.