Neutrosophic General Machine: A Group-Based Study

Abstract

Interval-valued neutrosophic sets have been shown to provide a limited platform for computational
complexity, but neutrosophic sets are suitable for it. The neutrosophic setsare a suitable mechanism for interpreting the philosophical problems of real-life, but not for scientific problems because it is difficult to consolidate.
This study aims to develop the notion of neutrosophic single-valued general machine over a finite group, which
is knows as â€group neutrosophic general machineâ€, for simplicity, GNGM. After that, we present the notions of
max-min GNGM, single-valued neutrosophic subgroup (SVNSG) and single-valued neutrosophic normal subgroup (SVNNSG). We show that if there exists a homomorphism between two GNGMs M1 and M2 and M
is a single-valued neutrosophic fundamental (SVNF) of M2, then f
−1
(M) is a SVNF of M1. Also, if M is a
singe-valued neutrosophic kernel (SVNK) of M2, then f
−1
(M) is a SVNK of M1. Moreover, we prove that if
M is a SVNK and N is a SVNF of M, then M ∗ N is a SVNF of M. In addition, we show that if M and N
are SVNK of M, then M ∗ N is a SVNK of M.