Zhang Xiaohong
College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, China.
ScientificWorldJournal. 2014;2014:718972. doi: 10.1155/2014/718972. Epub 2014 Apr 8.
Some new properties of fuzzy associative filters (also known as fuzzy associative pseudo-filters), fuzzy p-filter (also known as fuzzy pseudo-p-filters), and fuzzy a-filter (also known as fuzzy pseudo-a-filters) in pseudo-BCI algebras are investigated. By these properties, the following important results are proved: (1) a fuzzy filter (also known as fuzzy pseudo-filters) of a pseudo-BCI algebra is a fuzzy associative filter if and only if it is a fuzzy a-filter; (2) a filter (also known as pseudo-filter) of a pseudo-BCI algebra is associative if and only if it is an a-filter (also call it pseudo-a filter); (3) a fuzzy filter of a pseudo-BCI algebra is fuzzy a-filter if and only if it is both a fuzzy p-filter and a fuzzy q-filter.
研究了伪BCI代数中模糊关联滤子（也称为模糊关联伪滤子）、模糊p滤子（也称为模糊伪p滤子）和模糊a滤子（也称为模糊伪a滤子）的一些新性质。利用这些性质，证明了以下重要结果：(1) 伪BCI代数的模糊滤子（也称为模糊伪滤子）是模糊关联滤子当且仅当它是模糊a滤子；(2) 伪BCI代数的滤子（也称为伪滤子）是关联的当且仅当它是a滤子（也称为伪a滤子）；(3) 伪BCI代数的模糊滤子是模糊a滤子当且仅当它既是模糊p滤子又是模糊q滤子。
