Neutrosophic Vague Binary G – subalgebra of G - algebra

Abstract

Nowadays, human society is using artificial intelligence in a large manner so as to
upgrade the present existing applicational criteria’s and tools. Logic is the underlying principle to
these works. Algebra is inevitably inter-connected with logic. Hence its achievements to the
scientific research outputs have to be addressed. For these reasons, nowadays, research on various
algebraic structures are going on wide. Crisp set has also got developed in a parallel way in the
forms as fuzzy, intuitionistic fuzzy, rough, vague, neutrosophic, plithogenic etc. Sets with one or
more algebraic operations will form different new algebraic structures for giving assistance to these
logics, which in turn acts to as, a support to artificial intelligence. BCH/BCI/BCK- are some algebras
developed in the first phase of algebraic development output. After that, so many outputs got
flashed out, individually and in combinations in no time. Q- algebra and QS –algebra are some of
these and could be showed as such kind of productions. G- algebra is considered as an extension to
QS – algebra. In this paper neutrosophic vague binary G – subalgebra of G – algebra is generated
with example. Notions like, 0 – commutative G - subalgebra, minimal element, normal subset etc.
are investigated. Conditions to define derivation and regular derivation for this novel concept are
clearly presented with example. Constant of G – algebra can’t be treated as the identity element,
generally. In this paper, it is well explained with example. Cosets for neutrosophic vague binary
G – subalgebra of G - algebra is developed with proper explanation. Homomorphism for this new
concept has been also got commented. Its kernel, monomorphism and isomorphism are also have
discussed with proper attention.