a fuzzy decision model for command and control process

8/11/2019 A Fuzzy Decision Model for Command and Control Process

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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

649


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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.

650


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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

6 52


5/5

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

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Toncrka,Teteuji 0- and Kiyoji

Ami

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a fuzzy decision model for command and control process

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