Fuzzy topology representation for MV-algebras

&
Mathematical Logic Quarterly 55 (3):259-270 (2009)
  Copy   BIBTEX

Abstract

Let M be an MV-algebra and ΩM 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 ≤ v for any v ∈ ΩM. Then one can introduce in a natural way a fuzzy topology δ on ΩM. 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

Categories

Add categories

Keywords

Reprint years

DOI

10.1002/malq.200810005

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Fuzzy topology representation for MV‐algebras.Jialu Zhang & Quanfa Chen - 2009 - Mathematical Logic Quarterly 55 (3):259-270.
On (∈, ∈ ∨ q)‐fuzzy filters of R0‐algebras.Xueling Ma, Jianming Zhan & Young B. Jun - 2009 - Mathematical Logic Quarterly 55 (5):493-508.
Fuzzy propositional logic. Algebraic approach.Slava Meskhi - 1977 - Studia Logica 36 (3):189 - 194.
Zariski‐type topology for implication algebras.Manuel Abad, Diego Castaño & José P. Díaz Varela - 2010 - Mathematical Logic Quarterly 56 (3):299-309.
Regular opens in constructive topology and a representation theorem for overlap algebras.Francesco Ciraulo - 2013 - Annals of Pure and Applied Logic 164 (4):421-436.
Fuzzy Preorder, Fuzzy Topology and Fuzzy Transition System.S. P. Tiwari & Anupam K. Singh - 2013 - In Kamal Lodaya (ed.), Logic and its Applications. Springer. pp. 210--219.
Birkhoff variety theorem and fuzzy logic.Radim Bělohlávek - 2003 - Archive for Mathematical Logic 42 (8):781-790.
On some properties of quasi-MV algebras and $\sqrt{^{\prime }}$ quasi-MV algebras.Francesco Paoli, Antonio Ledda, Roberto Giuntini & Hector Freytes - 2009 - Reports on Mathematical Logic:31-63.
Hyper-Archimedean BL-algebras are MV-algebras.Esko Turunen - 2007 - Mathematical Logic Quarterly 53 (2):170-175.
The $L\Pi$ and $L\Pi\frac{1}{2}$ logics: two complete fuzzy systems joining Łukasiewicz and Product Logics. [REVIEW]Francesc Esteva, Lluís Godo & Franco Montagna - 2001 - Archive for Mathematical Logic 40 (1):39-67.
Commutative basic algebras and non-associative fuzzy logics.Michal Botur & Radomír Halaš - 2009 - Archive for Mathematical Logic 48 (3-4):243-255.
Eq-algebra-based Fuzzy Type Theory And Its Extensions.Vilém Novák - 2011 - Logic Journal of the IGPL 19 (3):512-542.
Boolean deductive systems of BL-algebras.Esko Turunen - 2001 - Archive for Mathematical Logic 40 (6):467-473.
Fuzzy closure systems on L-ordered sets.Lankun Guo, Guo-Qiang Zhang & Qingguo Li - 2011 - Mathematical Logic Quarterly 57 (3):281-291.
A type of fuzzy ring.Hacı Aktaş & Naim Çağman - 2007 - Archive for Mathematical Logic 46 (3-4):165-177.

Analytics

Added to PP
2015-10-24

Downloads
12 (#1,062,297)

6 months
3 (#1,002,413)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Deduction Theorem for Many‐Valued Inference.Mingsheng Ying - 1991 - Mathematical Logic Quarterly 37 (33‐35):533-537.
Deduction Theorem for Many‐Valued Inference.Mingsheng Ying - 1991 - Mathematical Logic Quarterly 37 (33-35):533-537.

Add more references