196
THE SITUATION CATEGORIZATION FOR SUPPORT DECISION
MAKING
V.L. Tokarev1
1Tula
state university, E-mail: [email protected]
The problem of computer aided support of the situations recognition for a conclusion
making is discussed . For decision of this problem is offered the method using building
of the linguistical model.
Introduction
The problem statement
One of the first problems of computer support
decision making is a situations recognition, in
which is found system, comparatively which is
taking the decision.
It is expected that system S, functioning in
surrounding ambience E, has: 1) the
uncontrolled but measuring (or estimating)
entry x; 2) the immeasurable and indefinite
entry w; 3) the controlled (chosen) entry u,
depended from decision d (or directly being
realization of the decision d) of the person
coming to a conclusion (PCC); outputs y
depending from system status (the Fig. 1).
ЛПР
The interaction LPR, systems S and ambiences
E is shown on the Fig.1, 2.
The collection of the conditions of the system
S and ambiences E at the time of k decision
making
dD
form
the
situation
  x, y, z, u, k  . Here k - discrete time, D
- a discrete ensemble of the possible decisions.
Метасистема
x
y
z
u
Информационноизмерительная
система
u
ЛПР
Система S
x
w
y
Среда E
z
Fig.1.
The surrounding ambience interacts with
system, giving on it importance of variable x,
w, depended from ambience status ,
partly hung from y. The surrounding
ambiences usually are considered
as "a
nature", when actions of the ambience do not
carry the goal-directed nature, or counteracting
side ("opponent"), when actions of the
ambience have a purpose to beat PPC.
Fig.2
We expect that ensemble situation ={} is
divide into classes ai, i=1,…,n, (some classes
can consist of one situation).
Each class situation i under any purposes
gG corresponds to the nonblank ensemble of
the decisions ={d}D. The number of the
classes n known moreover classes all ranked
on separate sign from normal situation
(source) before threatening. The Relationship
of the observations y with condition  also
approximate (within -differentially of the
decisions dD) also known: y  H    v .
Here y, v - a vectors to one dimensionality. So
197
class situation possible to match, identical him
classes aiA output yY. That is to say shall
suppose that if it is chose variant of the
partition j, j= 1, ..., n, that ensemble A
subdivides
on
n
classes,
that
is.
ai   j x, u, z ; i  1,...,n . It is required on
information on class i and information
on operation of metasystem {x,y,z,u, k=1,…,N}
for determined length of time (N counting out)
split the ensemble of importance {x,u,z} on n
classes that is build in space {x,u,z}
categorization tree, allowing predict the
attribute of the observations {x,u,z} to that or
other class categorical hung variable y
depending on corresponding to importance one
or several variables.
Rational categorization
In report is offered method of decision of this
problem founded on building models tree
forming rough model of metasystem
bi=F(x,u,z).
The tree contains three levels of the
linguistically models - a models, handling
importance linguistically variable. On lower
level are found models of the ambience,
chosen by importance L(z), on rally-blowing
level - a models, chosen value L(x); on the one
third level - a models, chosen by importance
L(u), but their output is an instruction of a
certain class aiA.
The Rational categorization ensemble А on n
classes is identified n- measured vectorfunction (у) =(1(у) ,..., n(y)), (i(y) - a
function accessories to class ai), satisfying
conditions : first, (y) - measurable on
measure result functions accessories model
output y beside and, in second, for any yY
importance i(y) satisfies standardization
condition
n
 i  y   1, 0 i  y   1.
i 1
As criterion quality to categorizations is
functional
n n



J     b j , ai  b j  yi 
i 1 j 1
(1)
where
 b j , ai  - certain measure to vicinity
between element ensemble B (the thermo
linguistically variable L(y)) and element
ensemble classes А;
- monotonous increasing function , displaying length [0,1] on
itself moreover (0) =0 and (1) =1.
Linguistically models, forming tree, are built
by iteration procedure [1] before achievement
of the minimum criterion
J ò (e M )  ln( st ( )) N kB
- (c M /N)   ln ( k ji  k ji /k B )
(2)
i 1 j 1
where st() - a factor to stability estimation
criterion, calculated on sample data; k ji  ρ(b ji )
- a distance in given metrics ( ) subset bj in iline of the matrix of the observations WN from
begin area of importance output variable y; k B
- a number subset bjВ; cM - a parameter of
regular, intended for increasing her(its)
regular, calculated on one of the expressions
C M  1  n x /N x or C M  1 - n S /N S , where nx, Nx accordingly, number taken into account by
model factor and total number possible factor;
nS, NS - accordingly, number elementary
structured element, comprised of model, and
the total number source structured element,
determined from a priori information.
The Lemma. Distribution of importance
function accessories  b  y , 1  1,...,n , got by
i
means of models bi=F(z,x,u), carries
унимодальный nature.
From lemma follows that maximum
 b  y , 1  1,...,n under some condition can
i
point to attribute of the situations class ai.
The Theorem. If linguistically model
bi=F(z,x,u) answers the minimum a criterion
(2), that such model provides the rational
categorization a situation in the sense of
criterion (1).
As a result adjusted thereby linguistically
model becomes the qualifier ai=f(z,x,u),
herewith in dug the degree to validity to
current categorization emerges resulting
importance of the function accessories
 b  y , 1  1,...,n .
i
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Conclusion
It has been Shown that computer support of
the decision of the problem of situation
categorizations is possible to realize by
buildings of linguistical model describing
metasystem, when ambience, surrounding
system is "a nature" that is to say actions of the
ambience casual and inexpediently.
The Offered method allows to automate the
initial stage of computer support of decision
making.
References
1. Tokarev V.L. Bases of the decisions rationality
provision theory. Tula: Tula state university. – 120
p. (in Russian).