Neutrosophic interval-valued anti fuzzy linear space

Abstract

In this research paper, we have introduced the concept of Neutrosophic interval-valued anti fuzzy linear space (NIVAFLS) and have also examined its various distinct characteristics. A counter example has demonstrated that the intersection of two Neutrosophic interval-valued anti fuzzy linear spaces (NIVAFLSs) does not possess the capability to be a Neutrosophic interval-valued anti fuzzy linear space (NIVAFLS). Conversely, the union of two Neutrosophic interval-valued anti fuzzy linear spaces (NIVAFLSs) does form a Neutrosophic interval-valued anti fuzzy linear space (NIVAFLS). Additionally, we have defined and provided an explanation for the cartesian product of two (NIVAFLSs). Furthermore, we have performed a study on the homomorphic image and inverse image of Neutrosophic Anti-Fuzzy Linear Space (NIVAFLS), along with investigating some related properties.