Authors: Lazarević, Vera
Šešelja, Branimir
Tepavčević, Andreja 
Title: Bisemilattice-valued fuzzy sets
Journal: Novi Sad Journal of Mathematics - NSJOM
Volume: 28
Issue: 3
First page: 105
Last page: 114
Issue Date: 1-Jan-1998
Rank: M51
ISSN: 1450-5444
URL: https://www.dmi.uns.ac.rs/nsjom/Papers/28_3/NSJOM_28_3_105_114.pdf
Abstract: 
Bisemilattice-valued fuzzy set (B-fuzzy set) is defined to be a mapping from a nonempty set to bisemilattice (an algebraic structure with two binary operations, both commutative, associative and idempotent).
To each B-fuzzy set corresponds two collections of subsets, levels (cuts) of that fuzzy set. These two families are determined by two ordering relations on a bisemilattice. Theorems of decomposition of B-fuzzy sets into levels are formulated and proved in the paper. Starting from two families of subsets of a set X, we give conditions for synthesis of a B-buzzy set. Some other properties of B-fuzzy sets are also formulated.
Keywords: fuzzy sets | bisemilattice
Publisher: Faculty of Science, University of Novi Sad

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