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. There lation among these concepts are investigated and it is proved that under suitable conditions the conceptsofquasi T-fuzzy implicative filter(quasi fuzzy Booleanfilter)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 implicativefilter,andaquasi T-fuzzy fantastic filter if and only if the quotient BL-algebra inducedby it, is a Boolean algebra, a G¨odel algebra, and an MV-algebra, respectively