|Title:||On lattice valued up-sets and down-sets||Journal:||Fuzzy Sets and Systems||Volume:||161||Issue:||12||First page:||1699||Last page:||1710||Issue Date:||16-Jun-2010||Rank:||M21a||ISSN:||0165-0114||DOI:||10.1016/j.fss.2009.11.012||Abstract:||
Isotone and anti-isotone mappings from a poset into a complete lattice are investigated as lattice-valued up-sets and down-sets, respectively. Cuts of these are shown to be analogue crisp sub-posets of the domain: up-set or semi-filters and down-sets or semi-ideals. The collection of all lattice-valued up-sets (down-sets) of a poset is a complete lattice under the order inherited from the lattice. Among other results, for a collection of crisp up-sets (down-sets) of a poset, necessary and sufficient conditions are given under which this collection consists of cuts of a lattice valued up-set (down-sets). A generalization in the sense of closed fuzzy sets with respect to fuzzy relations is also carried out.
|Keywords:||Closedness | L-valued down-sets | L-valued sets | L-valued up-sets||Publisher:||Elsevier||Project:||Serbian Ministry of Science and Environment, Grant no. 144011
Provincial Secretariat for Science and Technological Development, Autonomous Province of Vojvodina, grant “Lattice methods and applications”
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