a fuzzy decision model for command and control process
TRANSCRIPT
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A FUZZY DECISION MODEL FOR COMMAND AND
CONTROL
PROCESS
Luo,
X u ~ h a n nd Su,jian-zhi
Department of
Sye2em Engineerins and Mathemdics
Nationd
University
of Lkftmw
Techndogy
Chcurgehcr,
Hunan
410073
P.R.CHINA
ABSTRACT
Command and
Control (m
sysfeme are
the kernel
parts
of the Command, Control
Cammunfcation, and hteligence(CI yeteme.
Baaed on the annlysis of the military
dedsionmalning
p r o c e s s i n t h e
proceaa of
command and contro1,the
military
and other
dedeionmakingproceaseaare
regarded as
the
proceecl of
information processing
which
start with
the
states
from
pwcirr to iue~y and then from
fuzzy to
predse. The fuzzy utility dedsion
theoryis
extended to
depict
above
military
decisionmakingp i,nd a
fuzgs decision
model
for command and
control pracese is eatabliahed. This
model was proved
to
be efficient in
land
battle simulation. The essense of the
model is
to
transform the probabilistic
stateahtofuzzy staka and then to
make the decision
stake, and it fife the
human
deaieIonmaking
process
well.
according to the
fuzzy
INTBoDucnoN
The modeling of the military command proceaa
under the combat situation ia very important in
the warfare simulation systems. It playa the
role of the
military
commanders in the warfare
process simulation and ia needed to be carefully
treated.
In
order to
understand the importance
of
decisions in warfare
prooess,
let
UB discuss
The warfare sys tem[
is
compoeed of every
interactive
entity appeared in
the warfare
paocsee. It can
be divided into four
parts
according
to
the functions
and
the
Properties
of
the
entities in
the
conflicting
situations:
troop & weapon system
crws ,
he d&on
&
command
qrstem
(
DCS)
,
the
CSI
&
electronic
warfare eystem ( CayEWS , and the logistic
system (IS).
The general
structure of
the
warfare system is illustrated in Figure 1.
warfare
system first.
the
Human being
uaea
hie e organ to feel the
external world. On the battle field the PI
sys tem act as
the extension
of m e
of the
commanders'
&ense~rgans[~.~J,
he battle field
perceived
by
military commanders i s not the
realistic one but a perceived batt le field with
certain distortions. It is perceived by the
commandemviaCsI systems. Huge quantity
of
warfare information
is
collected
through
various
channels and goes through the process of
filtering, simplifying, and abstraction. The
commandemwouldbaeeon
their
experiencee and
combat doctrine
or
rules
to evaluate
the
situations of this perceived battle field, and
then
to
make the
decisions. Influenced by
simplification, abstxaction, turnover, and the
reliability
of
the
collections
of information,
the perceived battle field
may
be different from
the
real
one. There may even be a
great
difference between them. By eliminating the
fadora of the commanders'
experiences
an
so
on
the good decisions partially depend on the
gap
between the perceived battle field and the
real
oneCB].
From
the information flow in the warfare
system
we know that better decision
will
lead to better
combat result for both sides in conflicting. To
make
good
decisions depend on how to
um
the
information collected efficiently.
So
in the
warfare &nulation systems the modeling
of
command and control proces3e must reflect the
thinking
proceas
of the military commandem.
Lawson presented
a
conceptual model
for
the
command
and control
(C?
procem (Figure
2) . In
Lawson'a model
the command and control(
CY )
ie
d d b e d
as
a
process
including
sensing,
procesSing, comparing, deciding, and acting.
By
futher abstraction
of
this process, we can
ex- the command and control procesa
as
(1-8186-3850-8/933.008 1993 JEEE
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-
R
E
A
L
B
A
T
T
L
E
P
I
E
L
D
-
and
Figure
1.
The Structure of Warfare Systems
a p r o to change data to information,and then
to change information to knowledge, and finally
to
make decision from knowledge@igure 3).
In the wargaming
.systems
developed
before
the so
-called hard margin methods are mostly used
These methods define some threshholds, when the
states considered surpass the threshholds the
decision variables are set to change. These
methods can not reflect the real process of
human decisions obviously. Because in human
decisionmaking
process
the precise
states
are
often transformed into some uzzy concepts after
they come into human mind. The commanders seldom
deal with the precise numbers but the fuzzy
concepts like strong or weak in force strength.
Human decisionmaking process is a process from
precise to fuzzy and then from fuzzy to precise.
T h e
precise states of battle field are changed
into some fuzzy concepts in commanders mind by
situation assessment, and then the decision can
be made by reasoning and comparision of the
t
-J--+c.iI
gnvimnrwnt
t
Figure
3.
Abstraction of C Process
Figure 4. The Fuzzified
procRss
of
Ca
combat doctrine or
rules
basing on these
fuzzy
concept.s,which is the process from fuzzy to
precise. So the fuzzy decision methods can
reflect the commanders decision process much
reasonably.
In the following sections, the fuzzy utility
decision theory
is
reviewed and extended. A
fuzzy dec ision model for military
command
and
control is presented.
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t
EXTENSION OF FUZZY DECISION
THEORY
FOR
COMMAND
AND
CONTROL
PROCEQS
EZ??
A- A1*~*--h)]
The military command and
control
procese
is
very
complicated.
The
direct uae of the
fuzzy
decision theory introduced
by
Tanaka et alcs =xl
can not describe the
mplicacy of the
battle
field. So the theo ry needs to be extended.
First
of a l l the decision in above formulation
is
basing
on
single state
space S ={g en
...,p}.
Obviously the situation
of
the complicated
battle field can not be d d b e d
properly
with
only one state. Therefore the
st
ate space need
8 .
.,S, are fuzzy event
&a used
to
d d b e different
states,
i.e.
l == l
U
I
to be extended to S=&X%X...X& Here &,Ss
,...,
={ ,4,.
.,e,:}
&{s?,&, ...a24
I
1
Figure 6. Diagram of the fuzzy decision model for C
uzzy UTILITY DECISION THEORY
A formulation of fuzzy decision problems was
defi ned
by
Tanaka
et al.C6.ml.
They define
the decision problem
as
a 4-tuple {F,A,P,U},
where F={Fl,Fe,
...
F,} is
a set of fuzzy
states
which are f u z y events on a
probabilistic
space S= ,sa,. . } ,
A= A,,A2,
..., } is a set of fuzzy actions on a
deterministic action
space
D={d,,d2,
...,
p},
and they are also the fuzzy events on
D.
U(.,.)
is an utility function on A S .
Assume
that
F
is orthogonal.
Here
F
is
orthogonal if and only if for all
sk E s
c P F i ( S k ) = l
1
The expected utili ty of a fuzzy action Ai can
be defined as
U(&)= u(Ad'JPPJ
j
An
optimal
decision can
be
defined
as
a fuzzy
action & which maximizes U(AJ,that is,U(&)
..maxU(Ai).
i
The input of the model
is
the probabilistic
state
&{a, ,
. . , s, }
with their
probabilitia
P={p1 p1...,
n}
,
and the
output action
(or
decision
)
is
a
precise
one,
we can find
that
the above
process reflecta
the whole procees first from
prsciSe
to fuzzy
and then from fuzzy
to precise.
...
...
s,={SIM,eaM,...,sxs)
Assume that various actions in the action
set
A
={A1,A2,
..., }
can
be selected
by commanders
while the decision
is
being made. when
selecting
these actions they must eatimate the
effects of these actions
on
the battle field.
Their major referential parameters
are
the
initial
state
datum, i.e., the state parameters
on the
state space sEs,x
Sa
x. .
.
xSM.
The
initial state datum
may be
the
d t s
of a
former action or the initial
state
datum of th e
entire battle. It
is
defined
as S,,={E,S2...,
SG}.
he commanders
estimate
the
m l t s
of
each action
that is assumed to be carried
out
according to the initial datum, and then make
the fuzzy utility
analysis
for each candidate
action by calculating
its
utility value U(& .
Finally they compare the utility values amony
these actions to choose the
optimal
action
&.
This is
the decision
proteas
of the
proposed
model for military command and control. The
concrete estimation
proceas
for finding the
optimal decision can be
treated
in almost the
same way as that used by Tanaka et al.
Figure 5
is the computing diagram of the proposed
model.
COMPUTING PARADIGM OF THE MODEL
Battle Field
Statee
Assume that M
is
the minimum number of the
state variables which
can
express the battle
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field situation properly. The state vaiables
may be the force exponents of both amflic ting
sidea, or the geographical papameters, or
logistical factors, etc.. The states which
every state variable
expr-
can be
partitioned
into
several levels,
that is,
there are ni state valuea for state a,&=
{&,
is the probability distribution of the state
variable on state space a. The initial
slates
of the battle
situation
are
regarded
as
determined, i.e.,
4 ...SA}. *={ la,
(sa,
... 8 3 )
S,={S?,S,..
,S I3
Estimation of Possible
S&tes
Before an action proposal is being chosen, the
commanders must consider the influences of the
excution of the proposal on battle field
situation. But before the proposal is actually
excuted
that
they
can
do
is
only
to
estimate
the influences. Thie estimation
is
done
according to
historical
experiences and
combat rules. In fac t the process
is to
compute
the
probability distribution of battle
field states according
to
the initial states
S,
proposal Ai
s
excuted, i.e.,
={S?,S,
...
S
by assuming
that
the
E E ( ), sa, .e, (a=))
I
==I I
(sa,
(a,... E
(@)
k
'={
k
(sa,
(&,
...
k ( s a )
k
={ 0 m, .., ( s n a }
......
......
They satisfy
nl
I: t ( =I
6
n2
c
t @=I
j=1
......
nM
IW=l
H
This process is called as the process of
randomizing p d g . his is an important
link in the decision loop showed in
Figure 1.
There
may
be many different methods to do
randomizing prowsing
in
different
cases
provided the results of processing f it the
case of military principle. The Lanchester's
Equations
are
efficient
to calculate
the battle
field attritions. So we can
use
Lanchester's
equations to
do the randomizing proceseing.
Fuzy States of the
Battle
Field
Define
the
seta of f u z y states W={Wl,U& ....
U21
U%
{u?,ug,.
..
US},
... uM=
FE,%, ....
U S } . U',Ua,.. . . U are defined on the
probabilistic
spaces
a,&....S respectively.
The elements in
U are all
orthogonal, that
is,
the fuzzy
seta
in U form a set of
fuzzy
partition on S,= (4,s:....
i}.
We
call
U'
a
set
of fuzzy
states
on S.
Fuzzy
states are
a
set of
fuzzy
concepts on
state spat%.For example, if the
s t a t e
space
expressed by S, means the level of blue
force,
then U can be defined as:
Ui={Vl= blue force
is
very strong,
......
U:=blue force is immediate,
U,;= blue force is very weak]
......
The F'robabilitv of
F'uzzv States
The probability of fuzzy states can be
calculated
as
following:
n3
k-1
PWO= c P
UMD
I s i9
The meaning of fuzzy state probability is
obvious, if U1 represents blue force
is
very
weak , the n P(Un
is
the probability
t h a t
the
fuzzy event blue force ?s very weak will
happen.
uzzy Referential tates
Let
Fk is a fuzzy
state
on U'xU %...xuM,
fuzzy referential states.
Because
F
is
defined
on UlxU%...xuM,
it
depends
on
the combination
of the fuzzys tates Ui. In fact F is
a
set of
The
probability of Fk is given below:
then
we call the
set
K={Fl,Fz,....
Fr) the set
of
rnutiple fuzzy relations on U lx U 5 ~ . .. x U ~
P(F,)=
c c
...
P B-k(u&Uj%..,UjSP(v*=,
j,
ja
j,
us,
...
U=
where
j,=1,2
....
;
k1,2
....
z;
... ; jM=1,2,.
..,tM.
II
-(U&US .....U= means the level
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that
the
overall
battle field situation belong to Fk
while the furzy state UI
i
in
U + n d Up ia
in
Us,
...,
UM is in U B .
To
Make the
Decisione
The deciaion
propoeale
can be finally abetracted as
A={A,,As ,...,
}.
For example A, may re-t
attacv,
As
may be 'defense ,
etc..
The selection
of
decision action ia
done
accwrding
to
the values
of utility of the
praposals.
The utility values
of
the
l rr opoe l e can be
computed
(LB
below:
r
i.1
U(&)=
mar
U(A3
i
U(&)= r; U(&,F3P(F3 i=1,2,..
q
The finally ch o proposal satisfies
Before computing the utility values we need
to
determine the utility function
U(.,.).
Thia
i
an
important
parameter
that a f f d the selection of
action propoeals,
and
need
to be
d u l l y
treated
We set the maximum value of U(.,.) ia &and the
m i n ia 0
CONCLUSION
The application
of uzzy
utility decision theory
in
military command and control
P~O(.RBB
presented
in
t h i a
paper.Thie approach was
proved
to
efficient in land battle
simulation.
The
es
of
the
approach ia
to
tranafonn
the probabilistic
states into
fuzzy
statea
and
then
to
make the
decision according
to
the fuzzy
states.
It
f i b
the prooess
of
human decisionmaking.
REFERENCES
h i w a i t y o f Defense Technology, Changaha,
Hunan, China,
Dec. 1991.(In Chinese)
4. Chang Mengxiimg
and
Luo
Xueshan, A
theoretical approach to explore P I and
i ts
modeling,
dleded
Papera
o f
the second
us
-China Defenae Systeme Ananlyaia Se r,25-29,
April 1988,Betheed4,Marrkmd,China
Defenae
Science and Technology Infor Center,
(1988),68.
5.Hideo
Toncrka,Teteuji 0- and Kiyoji
Ami
A formulation o f fuzzy
deciah
p a nd
itsapplication to
an
investment problem,
6 . h Xueshan,An application of fuzzy utility
theory
in
military
dedeion
M i l b y Syatems Engineering, 3(1989) . ( in
Clrineee
7 . h
Xueshun,
Fuzzy decl ei n and
mi l i t a r y
decisi on
8i
n
X u
Guozhi
et
al
(eda.),
Scientific Decision and Systems Engineering,
China Press of Science and Technology, 1990.
(In
Chinese)
8 . h X w h , A n
evaluation
aystem for human
information processing,
Buuetin
f o r
atudiea
and exchanges on ftlzninees and
ita
application(BUSEFAL), No. 44, Oct.1990,
9.
Luo Xueahan, On
the System Laws
for
the
Warfare hocese in u Guazlri et al( e&. ),
Scientific
De ion
and Syatem Engineerins,
China Preiw of Science and TechnolOgy,l990.
( In Chinax
10. h o n , J.S., The State Variubh of a
C o d nd Control
Systems, hoc. or
QluUwam
Assessment
of utility of command
and Control Systems, Offi ce of the Secretary
of Defenae
with
the Cooperation of the MITRE
Corperathn, P Division Waahhgton, D.C.
,
National
Defense
Techndogy, Ft. Leatile, J .
1 1 . A k x ~. evis and M i c M Athans,The
Queet
for a
cd
Theory: Dreame and Realitka,
K Vd.5, pp.25-30,1976.
. .
MC NaiS, J an 1980, 93-99.
1.
Luo Xue-shun, A
research int0 warfare systems:Laboratory for Informution and Decieion Systeme,
Methoddogy and Modeling, Syatem Engineering, Vd . 7M IT , Cambridge,
MA
02139, AD-Al87458.
No.4, Jul y 1989, pp.46-50. (In Chinese).
2. Chung Mengxiong and
Luo
Xueshan,The exploring
of a system theory baaed approach
to
study warfare
procese, Proceedings of national aympoeium on
1988, Beijing, China.(In Chinese)
3. h a
Xueahan,
cdI systems heory reaearch
with
i ta
system engineering
and
crtics, National
methaidogies in&f#We
8Y ?M
d y S G ,
Jan.
appliationa, Ph. D dhertatt on, Department
o