JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (10): 83-89.doi: 10.6040/j.issn.1671-9352.0.2013.648

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Theory of interval valued (∈,∈∨ q)-fuzzy filters in BL-algebras

LIU Chun-hui1,2   

  1. 1. Office of Teaching Affairs, Chifeng University, Chifeng 024001, Inner Mongolia, China;
    2. Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, Inner Mongolia, China
  • Received:2013-12-30 Online:2014-10-20 Published:2014-11-10

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Abstract: 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.

Key words: interval valued (∈,∈&or, interval valued (∈,∈&or, q)-fuzzy involution (associative) filter, BL-algebra, q)-fuzzy filter

CLC Number: 

  • O141.1
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