The Relationship between Δ1 -completions and Formal L-contexts over an L-ordered Set

In this paper, the Δ1 -completions of an L-ordered set are introduced and characterized, which generalizes the Δ1 -completions of a crisp partial ordered set. Then the relationship between Δ1-completions and formal L-contexts over an L-ordered set is discussed. In particular, it is shown that Δ1 -completions of an L-ordered set are one-to-one correspondence with some formal L-contexts consisting of an L-closure system of upper L-subsets of the L-ordered set, an L-closure system of lower L-subsets of the L-ordered set, and an L-relation between these two systems.