Malaysian Journal of Mathematical Sciences,
Journal Year:
2023,
Volume and Issue:
17(4), P. 629 - 644
Published: Dec. 14, 2023
This
paper
introduces
an
innovative
concept
known
as
n-polar
Z-hesitant
Anti-Fuzzy
Soft
Sets
(MZHAFSs)
within
the
framework
of
BCK/BCI-algebras.
set
theory
originates
in
captivating
field
fuzzy
theory.
Our
approach
is
a
harmonious
synthesis
anti-fuzzy
theory,
soft
models,
and
sets,
skillfully
applied
effort
leads
to
introduction
new
variant
sets
termed
MZHAFSs
(n-polar
sets)
context
Additionally,
we
elucidate
provide
comprehensive
understanding.
Furthermore,
introduce
define
various
related
concepts,
including
subalgebras,
ideals,
closed
commutative
establish
meaningful
connections
between
them.
We
also
present
rigorously
prove
several
theorems
that
are
pertinent
these
newly
introduced
notions.
Symmetry,
Journal Year:
2024,
Volume and Issue:
16(3), P. 260 - 260
Published: Feb. 20, 2024
Circular
q-rung
orthopair
fuzzy
sets
(FSs)
were
recently
considered
as
an
extension
of
FSs
(q-ROFSs),
circular
intuitionistic
(Cir-IFSs),
and
Pythagorean
(Cir-PFSs).
However,
they
are
only
for
some
simple
algebraic
properties.
In
this
paper,
we
advance
the
work
on
q-ROFSs
(Cirq-ROFSs)
in
Dombi
aggregation
operators
(AOs)
with
more
mathematical
properties
laws.
These
include
(Cirq-ROF)
weighted
averaging
(Cirq-ROFDWA),
Cirq-ROF
ordered
(Cirq-ROFDOWA),
geometric
(Cirq-ROFDWG),
(Cirq-ROFDOWG)
operators.
Additionally,
present
idempotency,
monotonicity,
boundedness
proposed
context
artificial
intelligence,
symmetry
analysis
plays
a
significant
efficient
role
that
can
refer
to
several
aspects.
Thus,
compute
major
aspect,
identify
multi-attribute
decision-making
(MADM)
technique
based
numbers
(Cirq-ROFNs)
enhance
worth
evaluated
Finally,
use
existing
techniques
comparison
our
results
show
validity
supremacy
method.
AIMS Mathematics,
Journal Year:
2025,
Volume and Issue:
10(1), P. 460 - 498
Published: Jan. 1, 2025
<p>Solid
waste
management
(SWM)
protects
public
health,
the
environment,
and
limited
resources
in
densely
populated
urbanized
countries
such
as
Singapore.
This
work
presents
an
advanced
framework
for
optimizing
SWM
using
mathematical
models
decision-making
techniques,
including
circular
$
q
$-rung
orthopair
fuzzy
set
(C$
$-ROFS)
data,
combined
with
Choquet
integral
(CI)
logarithmic
percentage
change-driven
objective
weighting
(LOPCOW)
methods,
enhanced
by
aggregation
operators
(AOs)
Einstein
weighted
averaging
$-ROFECIWA)
geometric
$-ROFECIWG)
operators.
By
conducting
a
systematic
evaluation,
these
methods
classified
different
alternatives
to
SWM,
evaluating
them
according
criteria
their
environmental
impact,
cost-effectiveness,
reduction
efficiency,
feasibility
of
implementation,
health
safety,
acceptance.
The
C$
$-ROFECIWA
$-ROFECIWG
perform
better
than
previous
approaches
effective
multifaceted
dynamic
scenarios.
comparison
study
demonstrates
that
integration
LOPCOW
offers
conclusions
are
more
reliable
sustainable.
conducted
Singapore
successfully
finds
most
feasible
emphasizes
possibility
implementing
environmentally
sustainable
practices
urban
environment.
research
practical
insights
policymakers
need
improve
enhance
various
environments.</p>
Demonstratio Mathematica,
Journal Year:
2025,
Volume and Issue:
58(1)
Published: Jan. 1, 2025
Abstract
The
circular
Pythagorean
fuzzy
set
is
an
expansion
of
the
intuitionistic
(CIFS),
in
which
each
component
represented
by
a
circle.
Nevertheless,
even
though
CIFS
improves
representation,
it
still
restricted
to
inflexible
interpretation
triangle
(IFIT)
space,
where
square
sum
membership
and
nonmembership
environment
cannot
exceed
one.
To
overcome
this
restriction,
we
provide
fresh
extension
called
n,m
-rung
orthopair
(C
-ROFS),
allows
IFIT
region
be
expanded
or
contracted
while
maintaining
features
CIFS.
Consequently,
decision
makers
can
assess
items
over
wider
more
flexible
range
when
using
C
-ROFS,
allowing
for
making
delicate
decisions.
In
addition,
define
several
basic
algebraic
arithmetic
operations
on
such
as
intersection,
union,
multiplication,
scalar
discuss
their
key
characteristics
together
with
some
known
relations
-ROFS.
present
study
new
weighted
average/geometric
aggregation
operators
properties.
Further,
strategy
resolving
multicriteria
decision-making
problems
-ROF
provided.
suggested
tested
two
situations:
best
teacher
selection
problem
school
problem.
confirm
illustrate
efficacy
methodology,
comparative
analysis
average,
geometric,
q-rung
averaging,
geometric
PFWA
mathvariant="normal">max
{{\rm{PFWA}}}_{{\rm{\max
}}}
,
mathvariant="normal">min
{{\rm{PFWA}}}_{{\rm{\min
approaches
also
carried
out.
Ultimately,
final
section,
there
are
discussions
ideas
future
research.
AIMS Mathematics,
Journal Year:
2024,
Volume and Issue:
9(5), P. 12259 - 12286
Published: Jan. 1, 2024
<abstract><p>The
circular
intuitionistic
fuzzy
set
(<italic>CIFS</italic>)
extends
the
concept
of
<italic>IFS</italic>,
representing
each
element
with
a
area
on
<italic>IFS</italic>
interpretation
triangle
(<italic>IFIT</italic>).
Each
in
<italic>CIFS</italic>
is
characterized
not
only
by
membership
and
non-membership
degrees
but
also
radius,
indicating
imprecise
areas
these
degrees.
While
some
basic
operations
have
been
defined
for
<italic>CIFS</italic>,
all
thoroughly
explored
generalized.
The
radius
domain
has
extended
from
$
[0,
1]
to
\sqrt{2}]
$.
However,
are
limited
min
max
We
aimed
address
limitations
further
explore
theory
focusing
as
well
domains.
First,
we
proposed
new
\psi]
$,
where
\psi
\in
[1,
called
algebraic
product
(<italic>RAP</italic>)
sum
(<italic>RAS</italic>).
Second,
developed
operators
generalized
union
intersection
based
triangular
norms
conorms,
investigating
their
properties.
Finally,
negation
modal
conditions
examined
characteristics.
This
research
contributes
more
explicit
understanding
properties
capabilities
providing
valuable
insights
into
its
potential
applications,
particularly
decision-making
theory.</p></abstract>
Informatica,
Journal Year:
2023,
Volume and Issue:
unknown, P. 881 - 908
Published: Jan. 1, 2023
ELECTRE
III
is
a
well-established
outranking
relation
model
used
to
address
the
ranking
of
alternatives
in
multi-criteria
and
multi-actor
decision-making
problems.
It
has
been
extensively
studied
across
various
scientific
fields.
Due
complexity
under
uncertainty,
some
higher-order
fuzzy
sets
have
proposed
effectively
this
issue.
Circular
Intuitionistic
Fuzzy
Set
(CIFS)
one
such
set
recently
introduced
handle
uncertain
IF
values.
In
CIFS,
each
element
characterized
by
circular
area
with
radius,
r
membership/non-membership
degrees
as
centre.
This
paper
introduces
CIF-ELECTRE
III,
an
extension
within
CIFS
framework,
for
group
decision
analysis.
To
achieve
this,
we
define
extensions
matrix
weighting
vector
based
on
conditions,
particularly
focusing
optimistic
pessimistic
attitudes.
These
attitudinal
characters
actors
are
constructed
using
conditional
rules
ensure
that
falls
area.
Parameterized
$\alpha
\in
[0,1]$
net
score
degree,
conduct
extensive
analysis
between
illustrate
applicability
model,
provide
numerical
example
stock-picking
process.
Additionally,
comparative
existing
perform
sensitivity
analyses
validate
results
model.
Heliyon,
Journal Year:
2024,
Volume and Issue:
10(17), P. e36799 - e36799
Published: Aug. 26, 2024
Green
industry
development
focuses
on
balancing
economic
and
financial
growth
with
environmental
stewardship
ensuring
that
companies
industries
are
contributing
positively
to
both
sustainability
prosperity.
This
manuscript
aims
develop
the
novel
technique
of
circular
complex
p,
q-quasirung
orthopair
fuzzy
2-tuple
linguistic
(CCp,
q-QOF2-TL)
set
their
operational
laws
based
algebraic
t-norms
Hamacher
t-norms,
where
Einstein
special
cases
for
parameter
