Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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𝛽-FUZZY FILTERS OF STONE ALMOST DISTRIBUTIVE LATTICES

  • ALEMAYEHU, TEFERI GETACHEW (Department of Mathematics, College of Natural and Computational Sciences, Debre Berhan University) ;
  • GUBENA, YESHIWAS MEBRAT (Department of Mathematics, College of Natural and Computational Sciences, Debre Tabor University)
  • Received : 2021.03.29
  • Accepted : 2021.09.22
  • Published : 2022.05.30
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Abstract

In this paper, we studied on 𝛽-fuzzy filters of Stone almost distributive lattices. An isomorphism between the lattice of 𝛽-fuzzy filters of a Stone ADL A onto the lattice of fuzzy ideals of the set of all boosters of A is established. The fact that any 𝛽-fuzzy filter of A is an e-fuzzy filter of A is proved. We discuss on some properties of prime 𝛽-fuzzy filters and some topological concepts on the collection of prime 𝛽-fuzzy filters of a Stone ADL. Further we show that the collection 𝓣 = {X𝛽(λ) : λ is a fuzzy ideal of A} is a topology on 𝓕Spec𝛽(A) where X𝛽(λ) = {𝜇 ∈ 𝓕Spec𝛽(A) : λ ⊈ 𝜇}.

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References

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