R.A. Borzooei

H. Farahani 

M. Moniri

In this paper, we introduce the notions of neutrosophic deductive filter, Boolean neutrosophic deductive filter (BNDF) and implicative neutrosophic deductive filter (INDF) on BL-algebras as generalizations of the fuzzy corresponding versions. We also investigate some properties of these filters and drive some characterizations of them. The relation between BNDF and INDF is investigated and it is proved that every BNDF is an INDF, but the converse is true when certain condition is satisfied. Furthermore, we construct a quotient structure related to the neutrosophic deductive filter and prove certain isomorphism theorems.

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