Lukasiewicz Fuzzy BE-algebras and BE-filters
DOI:
https://doi.org/10.29020/nybg.ejpam.v15i3.4446Keywords:
\L{}ukasiewicz fuzzy BE-algebra,, \L{}ukasiewicz fuzzy BE-filter,, $\in$-set,, $q$-set,, O-set.Abstract
By applying the concept of Lukasiewicz fuzzy set to BE-algebras, the notions of Lukasiewicz fuzzy BE-algebra and Lukasiewicz fuzzy BE-filter are introduced, and their properties are investigated. Characterizations of Lukasiewicz fuzzy BE-algebra and Lukasiewicz fuzzy BE-filter are discussed, and the relationship between fuzzy BE-algebra (resp., fuzzy BE-filter) and Lukasiewicz fuzzy BE-algebra (resp., Lukasiewicz fuzzy BE-filter) is established. The conditions for the ∈-set, q-set and O-set of Lukasiewicz fuzzy set to be BE-subalgebras are explored. Lukasiewicz fuzzy BE-filter is created by using BE-filter.
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