International Journal of Computational Intelligence Systems,
Год журнала:
2024,
Номер
17(1)
Опубликована: Ноя. 28, 2024
In
this
paper,
we
introduce
the
concept
of
fuzzy
zero
divisor
graph
(FZDG)
for
a
commutative
ring
$$R$$
denoted
by
$${\Gamma
}_{f}\left(\text{R}\right)$$
.
We
explore
multiset
dimension
(Mdim),
new
variant
metric
(MD),
specifically
in
context
FZDGs.
To
illustrate
our
findings,
analyze
FZDG
$${\mathbb{Z}}_{n}$$
integers
modulo
$$n$$
,
}_{f}\left({\mathbb{Z}}_{n}\right).$$
compute
all
possible
values
}_{f}\left({\mathbb{Z}}_{n}\right)$$
providing
significant
theoretical
insights
into
its
structure.
Our
results
not
only
advance
understanding
FZDGs
and
their
dimensions
but
also
have
practical
implications
across
various
fields,
including
cryptography,
coding
theory,
network
analysis.
This
study
lays
groundwork
future
research
on
application
concepts
theory
algebraic
structures.
International Journal of Computational Intelligence Systems,
Год журнала:
2024,
Номер
17(1)
Опубликована: Ноя. 28, 2024
In
this
paper,
we
introduce
the
concept
of
fuzzy
zero
divisor
graph
(FZDG)
for
a
commutative
ring
$$R$$
denoted
by
$${\Gamma
}_{f}\left(\text{R}\right)$$
.
We
explore
multiset
dimension
(Mdim),
new
variant
metric
(MD),
specifically
in
context
FZDGs.
To
illustrate
our
findings,
analyze
FZDG
$${\mathbb{Z}}_{n}$$
integers
modulo
$$n$$
,
}_{f}\left({\mathbb{Z}}_{n}\right).$$
compute
all
possible
values
}_{f}\left({\mathbb{Z}}_{n}\right)$$
providing
significant
theoretical
insights
into
its
structure.
Our
results
not
only
advance
understanding
FZDGs
and
their
dimensions
but
also
have
practical
implications
across
various
fields,
including
cryptography,
coding
theory,
network
analysis.
This
study
lays
groundwork
future
research
on
application
concepts
theory
algebraic
structures.
