On Neutrosophic Transitivity and Absorbent Filters of Basic Logic Algebras

Abstract

The vital objective of this article is to explore the neutrosophic nature of transitive and absorbent filters in Basic Logic (BL) algebras. We establish the notion of neutrosophic transitive and absorbent filters in BL-algebras with suitable illustrations and examine a few of their properties. Also, we prove that every neutrosophic transitive filter in BL-algebras is a neutrosophic filter. In addition, we confer some necessary and sufficient conditions for a neutrosophic filter to be a transitive filter and an extension property. Further, we obtain  (i) Every neutrosophic associative filter is an absorbent filter. (ii)  is a neutrosophic positive implicative filter if and only if it is a neutrosophic absorbent filter. (iii) If  is a neutrosophic absorbent filter, then it is a neutrosophic fantastic filter. In the future, the above research can be extended to deductive filters. Moreover, these filters can be applied in fields such as information technology and systems.