ON (L;M)-FUZZY CLOSURE SPACES

Document Type : Research Paper

Authors

1 Department of Mathematics, Kocaeli University, 41380, Kocaeli, Turkey.

2 Department of Mathematics, Faculty of Science, Sohag 82524, Egypt.

Abstract

The aim of this paper is to introduce $(L,M)$-fuzzy closure
structure where $L$ and $M$ are strictly two-sided, commutative
quantales. Firstly, we define $(L,M)$-fuzzy closure spaces and get
some relations between $(L,M)$-double fuzzy topological spaces and
$(L,M)$-fuzzy closure spaces. Then, we introduce initial
$(L,M)$-fuzzy closure structures and we prove that the category
$(L,M)$-{bf FC} of $(L,M)$-fuzzy closure spaces and
$(L,M)$-$mathcal{C}$-maps is a topological category over the
category {bf SET}. From this fact, we define products of
$(L,M)$-fuzzy closure spaces. Finally, we show that an initial
structure of $(L,M)$-double fuzzy topological spaces can be obtained
by the initial structure of $(L,M)$-fuzzy closure spaces induced by
them.

Keywords


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