Applied
Soft
Computing
35
(2015)
812–826
Contents
lists
available
at
ScienceDirect
Applied
Soft
Computing
j
ourna
l
ho
me
page:
www.elsevier.com/locate
/asoc
Consistency
of
the
fused
intuitionistic
fuzzy
preference
relation
in
group
intuitionistic
fuzzy
analytic
hierarchy
process
Huchang
Liao,
Zeshui
Xu
∗
Business
School,
Sichuan
University,
Chengdu,
Sichuan
610065,
China
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
18
September
2014
Received
in
revised
form
4
April
2015
Accepted
5
April
2015
Available
online
16
April
2015
Keywords:
Atanassov’s
intuitionistic
fuzzy
set
(A-IFS)
Intuitionistic
fuzzy
preference
relation
Multiplicative
consistency
Group
decision
making
Group
intuitionistic
fuzzy
analytic
hierarchy
process
(GIFAHP)
a
b
s
t
r
a
c
t
Intuitionistic
fuzzy
preference
relations
(IFPRs),
which
are
based
on
Atanassov’s
intuitionistic
fuzzy
sets
(A-IFS),
have
turned
out
to
be
a
useful
structure
in
expressing
the
experts’
uncertain
judgments,
and
the
intuitionistic
fuzzy
analytic
hierarchy
process
(IFAHP)
is
a
method
for
solving
multiple
criteria
decision
making
problems.
To
provide
a
theoretical
support
for
group
decision
making
with
IFAHP,
this
paper
presents
some
straightforward
and
useful
results
regarding
to
the
aggregation
of
IFPRs.
Firstly,
a
new
type
of
aggregation
operator,
namely,
simple
intuitionistic
fuzzy
weighted
geometric
(SIFWG)
operator,
is
developed
to
synthesize
individual
IFPRs.
It
is
well
known
that
for
traditional
comparison
matrices,
if
all
individual
comparison
matrices
are
of
acceptable
consistency,
then
their
weighted
geometric
mean
complex
judgment
matrix
is
of
acceptable
consistency.
In
this
paper,
we
prove
that
this
property
holds
for
IFPRs
as
well
if
we
use
the
SIFWG
operator
to
synthesize
the
individual
IFPRs.
A
numerical
example
is
given
to
verify
the
theorems.
It
is
pointed
out
that
the
well-known
simple
intuitionistic
fuzzy
weighted
averaging
(SIFWA)
operator,
the
intuitionistic
fuzzy
weighted
averaging
(IFWA)
operator,
the
intuitionis-
tic
fuzzy
weighted
geometric
(IFWG)
operator
and
the
symmetric
intuitionistic
fuzzy
weighted
geometric
(SYIFWG)
operator
do
not
have
this
property.
Finally,
the
group
IFAHP
(GIFAHP)
procedure
is
developed
to
aid
group
decision
making
process
with
IFPRs.
©
2015
Elsevier
B.V.
All
rights
reserved.
1.
Introduction
In
many
practical
decision
making
situations,
such
as
choosing
a
car
to
buy
or
selecting
a
person
for
higher
managing
position,
the
decision
makers
or
experts
may
prefer
to
express
their
preference
information
by
comparing
each
pair
of
objects
and
construct
a
preference
relation
which
stores
their
preference
information
over
a
set
of
alternatives
or
criteria
in
a
matrix.
There
are
many
different
types
of
preference
relations,
such
as
multiplicative
preference
relations
(MPRs)
[1],
fuzzy
preference
relations
(FPRs)
[2],
and
intuitionistic
fuzzy
preference
relations
(IFPRs)
[3]
which
are
based
on
Atanassov’s
intuitionistic
fuzzy
sets
(A-IFSs).
Xu
[4]
made
a
survey
on
different
kinds
of
preference
relations
and
discussed
their
properties.
The
goal
of
establishing
a
preference
relation
is
to
derive
the
priority
weights
of
objects
from
the
preference
relation
and
then
rank
the
objects
according
to
the
priority
weights
[5].
However,
in
many
cases,
the
preference
relation
may
not
be
consistent.
Consistency
of
a
preference
relation
requires
that
the
expert’s
judgments
yield
no
contradiction.
Due
to
the
fact
that
the
lack
of
consistency
for
a
preference
relation
can
lead
to
inconsistent
or
incorrect
conclusion,
the
consistency
of
a
preference
relation
turns
out
to
be
a
very
important
research
topic,
which
has
been
attracting
more
and
more
scholars’
attention.
The
earliest
work
on
consistency
was
done
by
Saaty
[1],
who
proposed
a
consistency
ratio
from
a
MPR
and
suggested
that
a
MPR
is
of
acceptable
consistency
if
its
consistency
ratio
is
less
than
0.1.
He
also
presented
that
it
is
difficult
to
obtain
such
MPR,
especially
when
the
MPR
has
a
high
order.
For
the
inconsistent
MPR,
two
ways
can
be
used
to
deal
with
such
kind
of
MPR:
one
is
to
return
such
an
inconsistent
MPR
to
the
decision
maker
to
reconsider
constructing
new
MPR
until
the
acceptable
consistency
is
reached
[6];
the
other
way
is
to
improve
the
inconsistent
MPR
automatically
by
some
iterative
algorithms
[7,8].
The
first
method
is
accurate
and
reliable
but
wastes
a
lot
of
time,
and
in
some
settings,
if
the
decision
makers
do
not
want
to
interact
with
the
experts,
or
if
they
cannot
find
the
initial
experts
to
re-evaluate
∗
Corresponding
author.
E-mail
addresses:
liaohuchang@163.com
(H.
Liao),
xuzeshui@263.net
(Z.
Xu).
http://dx.doi.org/10.1016/j.asoc.2015.04.015
1568-4946/©
2015
Elsevier
B.V.
All
rights
reserved.
剩余14页未读，继续阅读
资源评论
