• Korean Journal of Mathematics
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• v.27 no.3
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• pp.595-612
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• 2019

In this paper, we introduce the concept of ${\beta}$-fuzzy filters in MS-algebras and ${\beta}$-fuzzy filters are characterized in terms of boosters. It is proved that the lattice of ${\beta}$-fuzzy filters is isomorphic to the fuzzy ideal lattice of boosters.

• East Asian mathematical journal
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• v.23 no.2
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• pp.151-158
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• 2007

In this paper we introduce the concept of fuzzy ${\beta}-compact^*$ spaces. Besides giving some interesting properties of fuzzy ${\beta}-compact^*$ spaces we also give a characterization on fuzzy $\beta$-compact spaces by making use of newly introduced concept of fuzzy $\beta$-filters.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.445-460
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• 2022

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 = {X^𝛽(λ) : λ is a fuzzy ideal of A} is a topology on 𝓕Spec_𝛽(A) where X^𝛽(λ) = {𝜇 ∈ 𝓕Spec_𝛽(A) : λ ⊈ 𝜇}.