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Some results on $L$-complete lattices | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 8، دوره 13، شماره 6، زمستان 2016، صفحه 135-152 اصل مقاله (442.34 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2016.2825 | ||
| نویسندگان | ||
| Anatolij Dvurecenskij1؛ Omid Zahiri* 2 | ||
| 1Mathematical 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 | ||
| 2University of Applied Science and Technology, Tehran, Iran | ||
| چکیده | ||
| 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 $DCPO$. | ||
| کلیدواژه‌ها | ||
| Fuzzy complete lattice؛ Fixpoint؛ Fuzzy DCPO؛ Fuzzy directed poset؛ Monotone map | ||
| مراجع | ||
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