Characterizations of Fuzzy Closure Systems on L-ordered Sets
نویسندگان
چکیده
In this paper, we present equivalent characterizations of L-closure systems on lower bounded complete L-ordered sets and complete L-lattices, respectively. These results demonstrate the feasibility of notion of fuzzy closure system developed in our previous work (L.-K. Guo, G.-Q. Zhang, Q.-G. Li: Fuzzy closure systems on L-ordered sets. Math. Log. Quart. 57 (3) (2011), 281-291.). Also we develop the notions of L-closure systems closed for directed sups and L-closure operators preserving directed sups on L-ordered sets. The one-to-one correspondence between these two structures is derived when the underlying L-ordered set is directed complete.
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