Fuzzy absolute value on a ring

Article type: Research Article

Authors: Mirdar Harijani, Kh. | Anvariyeh, S.M.^*

Affiliations: Department of Mathematics, Yazd University, Yazd, Iran

Correspondence: [*] Corresponding author. S.M. Anvariyeh, Department of Mathematics, Yazd University, Yazd, Iran. Tel.: +98 35 31232705; Fax: +98 35 38210695; E-mail: anvariyeh@yazd.ac.ir.

Abstract: In this paper, fuzzy absolute value on a ring is defined. It is proved that every absolute value can induce a fuzzy absolute value. It is also proved that every fuzzy valued ring induce a fuzzy metric space and a fuzzy norm space. In addition, the notion of a Cauchy sequence and completion of a fuzzy valued ring are given and some of their properties are investigated. Finally, it is proved that every fuzzy valued ring has a completion.

Keywords: Completion, fuzzy absolute value, fuzzy metric space, fuzzy set, fuzzy valued ring

DOI: 10.3233/JIFS-152155

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 1, pp. 435-441, 2017