Some results on $L$-complete lattices

Document Type: Research Paper


1 Mathematical Institute, Slovak Academy of Sciences, Stefanikova 49, SK-814 73 Bratislava, Slovakia and Depart. Algebra Geom, Palacky Univer., 17. listopadu 12, CZ-771 46 Olomouc, Czech Republic

2 University of Applied Science and Technology, Tehran, Iran


The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.
First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a special element of $L^P$. A relation between $L$-fuzzy complete lattices and fixpoints is found and fuzzy versions of monotonicity, rolling, fusion  and exchange rules on $L$-complete lattices are stated.
Finally, we investigate the set of all monotone maps on a fuzzy directed complete posets, $DCPO$s, and
find a condition which under the set of all fixpoints of a monotone map on a fuzzy $DCPO$ is a fuzzy $DCPO$.


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