Geodesic
A note on cut properties of semilattices valued fuzzy sets
Novi Sad Journal of Mathematics, Tome 45 (2015) no. 2.

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Semilattice valued fuzzy sets are investigated in the framework of cuts. A theorem of synthesis for such fuzzy sets is proved. Families of cuts for meet(join)-fuzzy sets are proved to be special semi-closure systems. Conversely, for every such semi-closure system, we prove existence of a semilattice and a semilattice-valued fuzzy set whose collection of cuts is the given semi-closure system. We also show that for an arbitrary collection of subsets of a nonempty set, there is a semilattice valued fuzzy set whose collection of cuts contains these subsets. Using meet-irreducible elements in a finite meet-semilattice, we give conditions under which all the cuts of a meet-semilattice-valued fuzzy set are different and we describe a representation of the semilattice by the collection of cuts ordered dually by inclusion.
Publié le :
DOI : 10.30755/NSJOM.2014.099
Classification : 03E72, 06A12
Keywords: meet (join)-fuzzy sets, cuts, semi-closure systems, dual semi-closure systems 
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     title = {A note on cut properties of semilattices valued fuzzy sets},
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     pages = {27 - 37},
     publisher = {mathdoc},
     volume = {45},
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     year = {2015},
     doi = {10.30755/NSJOM.2014.099},
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Harina Monim; Sri Wahyuni; Indah E. Wijayanti. A note on cut properties of semilattices valued fuzzy sets. Novi Sad Journal of Mathematics, Tome 45 (2015) no. 2. doi : 10.30755/NSJOM.2014.099. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.2014.099/

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