FILTERS OF BE-ALGEBRAS BASED ON FUZZY SET THEORY
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The fuzzification of filters in BE-algebras is discussed. Characteriza-tions of a fuzzy filter of BE-algebras are given. An answer to the following question is provided. Question. Let A be a subset of [0; 1] containing a maximal element m > 0 and let F := {F_alpha | alpha ∊ A}be a decreasing chain of filters of a BE-algebra X: Then does there exist a fuzzy filter ¹ of X such that ¹(X) = ¤ and F¹ = F?
Abstract
The fuzzification of filters in BE-algebras is discussed. Characteriza-tions of a fuzzy filter of BE-algebras are given. An answer to the following question is provided. Question. Let A be a subset of [0; 1] containing a maximal element m > 0 and let F := {F_alpha | alpha ∊ A}be a decreasing chain of filters of a BE-algebra X: Then does there exist a fuzzy filter ¹ of X such that ¹(X) = ¤ and F¹ = F?
참고문헌 (3)
- S.S. Ahn, "On ideals and upper sets in BE-algerbas", Sci. Math. Jpn, 68, pp.279~285 (2008)
- H.S. Kim, "On BE-algerbas", Sci. Math. Jpn, 66, pp.113~116 (2007)
- A. Walendziak, "On commutative BE-algerbas", Sci. Math. Jpn, 69, pp.281~284 (2007)