|Title:||L-E-Fuzzy Lattices||Journal:||International Journal of Fuzzy Systems||Volume:||17||Issue:||3||First page:||366||Last page:||374||Issue Date:||1-Sep-2015||Rank:||M23||ISSN:||1562-2479||DOI:||10.1007/s40815-015-0057-9||Abstract:||
A new definition of a fuzzy lattice (L-E-fuzzy lattice) as a particular fuzzy algebraic structure is introduced in the framework of fuzzy equalities and fuzzy identities. The membership values structure is a complete lattice. An L-E-fuzzy lattice is defined on a bi-groupoid M, as its fuzzy sub-bi-groupoid μ equipped with a fuzzy equality E, fulfilling fuzzy lattice identities. It is proved that the new notion is a generalization of known lattice-valued structures. Basic properties of the introduced new fuzzy lattices are presented. In particular, it is proved that the quotients of cuts of μ over the corresponding cuts of E are classical lattices. By a suitable example, it is shown how the new introduced structures can be applied.
|Keywords:||Complete lattice | Fuzzy congruence | Fuzzy equality | Fuzzy identity | Fuzzy lattice||Publisher:||Springer Link||Project:||Development of methods of computation and information processing: theory and applications
Provincial Secretariat for Science and Technological Development, Autonomous Province of Vojvodina, Grant “Ordered structures and applications”
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