Prime fuzzy (implicative) MP-filters of R₀-algebras

Article type: Research Article

Authors: Li, Wan^{a; b} | Hu, Bao Qing^{a; b; *}

Affiliations: [a] School of Mathematics and Statistics, Wuhan University, Wuhan, P.R. China | [b] Computational Science Hubei Key Laboratory, Wuhan University, Wuhan, P.R. China

Correspondence: [*] Corresponding author. Bao Qing Hu. Tel.: +86 27 68775350; Fax: +86 27 78752256; E-mail: [email protected].

Abstract: The filter, also called a “deductive systems”, is the basic tool in the study of logical algebras and the completeness of the corresponding non-classical logics. The aim of this paper is to investigate prime fuzzy MP-filters and prime fuzzy implicative MP-filters of R0-algebras. In the absence of the condition that A˜ is a fuzzy filter, the equivalent conditions of A˜ being a (prime) fuzzy implicative filter which it necessitates to satisfy are concretely investigated and whose some related properties are specifically enumerated. Meanwhile, we also point out a little mistake occurred in Liu and Li’s paper.

Keywords: Filters, R₀-algebras, fuzzy MP-filters, prime fuzzy (implicative) MP-filters

DOI: 10.3233/IFS-151902

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 4, pp. 1915-1925, 2016