%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.