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Fuzzy topology representation for MV-algebras

✍ Scribed by Jialu Zhang; Quanfa Chen

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
288 KB
Volume
55
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

Let M be an MV‐algebra and Ω~M~ be the set of all σ ‐valuations from M into the MV‐unit interval. This paper focuses on the characterization of MV‐algebras using σ ‐valuations of MV‐algebras and proves that a σ ‐complete MV‐algebra is σ ‐regular, which means that a ≤ b if and only if v (a) ≤ v (b) for any v ∈ Ω__~M~. Then one can introduce in a natural way a fuzzy topology δ on Ω~M~__. The representation theorem forMV‐algebras is established by means of fuzzy topology. Some properties of fuzzy topology δ and its cut topology U are investigated (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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