Some types of T-fuzzy filters in BL-algebras

Some types of fuzzy filters with respect to a t-norm, in a BL-algebra, are introduced such as quasi T-fuzzy filter, quasi T-fuzzy positive implicative filter, quasi T-fuzzy implicative filter and quasi T-fuzzy fantastic filter. Several properties are investigated and some equivalent conditions for these fuzzy filters are obtained. The relation among these concepts are investigated and it is proved that under suitable conditions the concepts of quasi T-fuzzy implicative filter (quasi fuzzy Boolean filter) and quasi T-fuzzy positive implicative filter are equivalent. Furthermore, it is proved that a quasi T-fuzzy filter in a BL-algebra is a quasi T-fuzzy implicative filter, a quasi T-fuzzy positive implicative filter, and a quasi T-fuzzy fantastic filter if and only if the quotient BL-algebra induced by it, is a Boolean algebra, a G¨odel algebra, and an MV-algebra, respectively

Keywords:

Many-Valued logics , BL-algebra , T-norm , T-fuzzy filter