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 Fuzzy System Applications,
Год журнала:
2025,
Номер
14(1), С. 1 - 26
Опубликована: Фев. 21, 2025
The
evaluation
of
marine
environmental
concealment
is
crucial
for
underwater
activities.
Traditional
assessment
methods
do
not
fully
leverage
risk
indicators
and
expert
experience.
To
address
this,
this
paper
proposes
a
model
based
on
2-additive
piecewise
linear
Choquet
integral.
This
combines
the
fuzzy
measure
to
aggregate
utility
values
various
indicators,
integrating
both
opinions
objective
data,
while
also
considering
nonlinear
interactions
between
indicators.
Verification
using
real
ocean
data
preferences
shows
that
depth
grid
seabed
terrain
have
most
significant
impact
concealment,
interaction
temperature
gradient,
salinity
current
positively
correlated.
offers
theoretical
contribution
demonstrates
advantages
integral
method
in
handling
complex,
multi-factor
evaluations,
with
practical
application
value.
