|Title:||Non-standard cut classification of fuzzy sets||Journal:||Information Sciences||Volume:||177||Issue:||1||First page:||161||Last page:||169||Issue Date:||1-Jan-2007||Rank:||M21||ISSN:||0020-0255||DOI:||10.1016/j.ins.2006.05.001||Abstract:||
Several important non-standard cut sets of lattice-valued fuzzy sets are investigated. These are strong cuts, "not less" and "neither less nor equal" cuts. In each case it is proved that collection of all cuts of any lattice-valued fuzzy set form a complete lattice under inclusion. Decomposition theorem (representation by cuts) is proved for "neither less nor equal" cuts. Necessary and sufficient conditions under which two lattice-valued fuzzy sets with the same domain have equal families of corresponding cut sets are given.
|Keywords:||Closure | Cut | Equivalent fuzzy sets | Lattice-valued fuzzy set||Publisher:||Elsevier||Project:||Slovak Grant Agency VEGA, Grant No. 1/2002/05
Algebarske strukture i metode za procesiranje informacija, 144011
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