%A LIU Chun-hui
%T Theory of interval valued (∈,∈∨ q)-fuzzy filters in BL-algebras
%0 Journal Article
%D 2014
%J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
%R 10.6040/j.issn.1671-9352.0.2013.648
%P 83-89
%V 49
%N 10
%U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_625.shtml}
%8 2014-10-20
%X The theory of interval valued (∈,∈∨ q)-fuzzy filters in BL-algebras is studied systematically. Firstly, two notions of interval valued (∈,∈∨ q)-fuzzy involution filters and interval valued (∈,∈∨ q)-fuzzy associative filters are introduced and some characterizations of them are obtained. Secondly, the relations among all kinds of interval valued (∈,∈∨ q)-fuzzy filters are discussed. It is proved that an interval valued fuzzy set is an interval valued (∈,∈∨ q)-fuzzy Boolean (implicative) filter if and only if it is both an interval valued (∈,∈∨ q)-fuzzy positive implicative and an interval valued (∈,∈∨ q)-fuzzy involution filter.