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Fuzzy topology representation for MV‐algebras
Author(s) -
Zhang Jialu,
Chen Quanfa
Publication year - 2009
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200810005
Subject(s) - mathematics , topology (electrical circuits) , representation theorem , fuzzy logic , characterization (materials science) , unit interval , representation (politics) , unit (ring theory) , weak topology (polar topology) , set (abstract data type) , fuzzy set , general topology , discrete mathematics , algebra over a field , pure mathematics , topological space , combinatorics , extension topology , computer science , artificial intelligence , physics , mathematics education , politics , law , political science , optics , programming language
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)