Fuzzy anti-grouped filters and fuzzy normal filters in pseudo-BCI algebras

Article type: Research Article

Authors: Zhang, Xiaohong^{a; b; *}

Affiliations: [a] School of Arts and Sciences, Shaanxi University of Science & Technology, Xi’an, P.R. China | [b] College of Arts and Sciences, Shanghai Maritime University, Shanghai, P.R. China

Correspondence: [*] Corresponding author. Xiaohong Zhang. E-mails: zxhonghz@263.net, zhangxh@shmtu.edu.cn.

Abstract: The notions of fuzzy anti-grouped filter and fuzzy normal filter in pseudo-BCI algebra are introduced, some properties and equivalent conditions are presented. A counterexample is constructed to show that a fuzzy anti-grouped filter may be not a fuzzy p-filter, by this, a mistake in some literatures is revised. The relationships among some special kinds of fuzzy filters are discussed, the following results are proved: (1) a fuzzy filter of a pseudo-BCI algebra X is fuzzy p-filter if and only if it is both a fuzzy normal filter and a fuzzy anti-grouped filter of X; (2) a fuzzy filter of a pseudo-BCI algebra X is a fuzzy associative filter if and only if it is both a fuzzy anti-grouped filter and a fuzzy T-type filter of X, if and only if it is both a fuzzy anti-grouped filter and a fuzzy q-filter of X. Moreover, a method for constructing new fuzzy anti-grouped filter via any fuzzy filter is proposed.

Keywords: Fuzzy logic, pseudo-BCI algebra, anti-grouped pseudo-BCI algebra, fuzzy anti-grouped filter, fuzzy normal filter

DOI: 10.3233/JIFS-17006

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 3, pp. 1767-1774, 2017