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SỐ11
On quick reading of the attached paper
I would guess that the author is a mathematician
with considerable depth. ( not a biologest ormedical
and freight
man by primary intered) this substantive
area is one in which the Sonicte are way shong
but a US graduate student in mathematics or
information theory could have done this work.
The translation is unusually good on the author
is very familiar with English,
The work as
presented is more of theoretical than practiced
interest. Perhaps" sanitization" means not
disclosing the specific problem attached. when
was it.
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SYSTEMS ENGINEERING ANALYSIS OF DECISION MAKING RELIABILITY
Leningrad SISTEMOTEKHNICHESKOYE ISSLEDOVANIYE NADEZHNOSTI PRINYATIYA RESHENIY
in Russian 1972 pp 1-20
Thanks
[Author's abstract of a dissertation in pursuit of the candidate of techni
sciences degree by A. M. Shtern, specialty 05.252 -- Computer Technology, RSFSR
Ministry of Higher and Secondary Special Education, Northwestern Correspondence
Polytechnical Institute]
[Text]
The reliability of decision making is acquiring special significance
in modern production and in transportation and special systems. This problem
has not only a certain amount of scientific significance but also considerable
economic significance, since unreliable, ineffective decisions could lead to
significant material losses and irreversible damage to the system.
Decision making is the most complex and least studied operation in the over-
all process of information processing. Decision making reliability is a
function of many factors, and analysis of their influence upon decision
making reliability is the topic of many researchers.
Because these problems are rather new, most research in this area has been
basically devoted to particular problems associated with a particular tech-
nical system or particular characteristics of the operator. The task of
developing and revealing decision making reliability criteria which would
be universal, independent of the concrete type of information processing
system, arises quite naturally. The effectiveness of the criteria revealed
is dependent on the degree to which they permit control and prediction of
the reliability of a systems engineering complex.
The present work,
which analyzes decision making reliability from a systems
engineering standpoint, deals with a number of tasks having the objective
of producing practical recommendations on particular problems in reliable
organization and planning of man-machine systems.
Basic Concepts
The decision making process can be described by a trajectory in a configura-
tional search space. The search space is given by the set of states {N}
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and the relationships existing among them.
The decision structure can vary
significantly depending on the nature of the relationships associating dif-
ferent points in the search space.
This work shows that in the case where the search space is a successive
linear system, decision making is determined, and it assumes one of the
following forms -- maze, formal, convergence, closed, and interpolational.
When the probability element is introduced to the structure of relationships
among states in the search space, decision making acquires a probabilistic
structure and assumes the following forms -- search, heuristic, divergence,
open, and extrapolational.
These types of decision making can either be used separately, or they can be
formed into complex combinations and sequences. In this case the determined
and probabilistic types of decision making are always the polar types, and
they are described by various mathematical tools. In the first case we use
logical functions and determined networks, while in the second case we use
statistical probability models and the theory of random processes. The
determined approach presupposes that in all situations the system implements
a certain given logical function, and all of its decisions are error-free.
In the probabilistic approach we reject presence of an entirely error-free
decision beforehand, substituting it by the probabilities of reaching accep-
table decisions.
Special difficulties arise in formalizing the problem when the decision making
process simultaneously possesses the qualities of both determined and proba-
bilistic processes. In this case the search space may be determined in rela-
tion to a universal assessment and statistical in relation to a local one.
This situation is the one most often encountered; however, formal methods
for assessing the reliability of combined types of decision making are poorly
developed. This is why we are forced to limit ourselves to examining just
the polar type in practical situations. This dissertation demonstrates that
use of a quasiclassical approach opens up a number of new possibilities for
analyzing determined-probabilistic types of decision making. In this approach,
the reliability of decisions can be assessed by the appropriate quasiclassical
probability distributions.
It becomes much simpler to assess the reliability of decision making if we
introduce the distance measure into the search space under analysis. This
measure need not be defined as geometric length; in some measurable way it
must relate points in the configurational space together. The units of
distance measurement in the models examined here could be steps,
bits, and
so on.
This work does not assess distances in concrete units; instead, rela-
tive distances are examined.
This permits comparison of experimental results
obtained in different informational environments.
The reliability of decision making depends on, in addition to the structure
of the search space, the internal information characteristics of the system
making decisions. The number of these information characteristics is
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sufficiently large, and in the general case it is not as yet possible to
find their optimum values. For the moment we are forced to limit ourselves
to examining one or a few characteristics and revealing how the changes
they experience. influence the system's reliability. " Two important factors
defining the reliability of decision making are analyzed in this work:
1) The memory's information capacity Q,
2) the level of prediction processes P.
The Basic Problem
Let the configurational search space be given with the appropriate metrics.
The decision making process consists of a transition from some initial
state to some final state (a goal). Let the generalized distance between
the initial state and the goal be |R|.
We need to determine the range of variables @ and P producing a maximum
in the reliability functions
max F = max F(IRI,Q)
max F = max
F (IRI,P)
where F is a function of the reliability of decision making.
The limits are:
Q < 2 |R|
F & [0,1]
Fp € (0,1]
P & IRI
This problem was solved by means of phenomenological experiments and digital
modeling of the decision making process with a BESM-6 digital computer. In
parallel, the need arose for solving a number of background problems, the
content of which will be presented below.
-
The Phenomenological Solution
The phenomenological analysis had an applied nature. Its tasks included
determining a quantitative criterion of decision making reliability and
developing the appropriate procedure permitting prediction of decision
making reliability.
The configurational search space consisted of associated environments of
varying complexity in this case. The decision process involved transforma-
tion of a certain initial situation into some final situation according to
particular rules:
×1x2X3,X3×4 ×2
x,x,x, x, ›››,
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This transformation could be made with the assistance of a fixed number of
substitutions, for example:
X2 X3X5-×3 ×4 × 10
×2×;x3~ ×2 ×3× 5
-
Inasmuch as the possibility for making a direct transition from the initial
to the final situation was absent, the problem was solved in stages, in a
prescribed number of steps.
The decision process was assumed to be reliable when the final situation was
reached with a minimum number of steps and in minimum time, and it was assumed
to be unreliable in the opposite case.
The distance R|
between the initial and final situations was measured in
units of information capacity in the short-term memory Q, with |R being
given in the interval
0 < | | < Q.
Tests revealed that decision making reliability is dependent in a certain
way on the ratio between the memory's information capacity and the generalized
distance R . When Q and R satisfy the inequality Q/ (R )> 1, the decision
making process is characterized by high reliability.
At the point Q/( R )=] the reliability function experiences a first-order
discontinuity, and the probability of error begins to grow monotonously
as the ratio Q/ ( |R |) decreases.
The Model Solution
The model solution of the problem formulated above was arrived at in digital
form by running the problem in a digital computer. The search space was given
as a quadratic matrix |Ajj with dimensionality n, and it was fed into the
computer's memory.
The values of elements ajj were prescribed by a special
procedure following a random law, in which case
1 ≤ dij ≤ 100.
The algorithm of the model's behavior entailed selection of a trajectory
of movement
from element @11 to element ann that was optimum in a particu-
lar way.
The probability of transition from element to element was prescribed as
follows:
Pajj,(i+1)j+Pa¡jai(j+1)=1.
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Considering this limitation on transitions, the distance |R between the
initial state and the goal was |R =2 (n-1) steps, where n is the dimension-
ality of the matrix.
Inasmuch as with the exception of dead-end points -- that is, when i-n, jin,
in, j=n -- there was a possibility of binary choice at each point on the
trajectory, the set of possible trajectories {T} increased rapidly as the
dimensionality of the matrix increased, in accordance with the law
T
=
(2n-2)!
(n-1): (n=+)]
The values of the elements were summed as movement proceeded along the selec-
ted trajectory. A trajectory with a minimal final sum, Smin, was adopted
as the optimum trajectory. The standard deviation from the minimum sum
served as an indicator of decision making unreliability.
The internal information parameter P, characterizing the depth of prediction,
was also introduced into the examination. Parameter P varied from 0 (random
walk) to |R |(absoute prediction) . Thus each problem was solved |R +1 times.
The minimum sum of all possible P steps was chosen for each value P. As a
result of such choice the trajectory led to a certain state ajj, in which case
if P is the depth of prediction and n is the choice number, then i+j=nP+2.
Consequently the distance
R |between two successive points was:
[R]=(in+1+jn+1)- (in+in).
The result of the model solution consisted of the values:
Do, 1=(Smin-Sp)2,
where Do corresponds to the case in which following several (or one) predic-
tions the remaining number of steps is less than P but the subsequent tra-
jectory is also predicted, and D1 corresponds to the case in which the
final element operates as a "mousetrap" -- that is, whenever this element is
attained the decision is irreversible.
Dispersions Do. 1 obtained by means of the modeling experiments were normal-
ized with respect to the maximum and plotted as a function of the ratio
between prediction depth P and distance [R ].
The most interesting point of the obtained dependence was its similarity
with the results of the phenomenological trials, with the one difference
that in this case the reliability function is continuous. The closeness
of the phenomenological and modeling results indicates that the prediction
'level P depends on the possibility for placing the extrapolation vector in
the short-term memory. If the memory's information capacity is too small
for the required extrapolation vector, the decision making process becomes
unreliable.
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Thus viewing reliability P of decision making as a function of
Q/( R ) on
one hand and as a function of P/ ( R ) on the other, we can say that both
functions are partially equivalent, inasmuch as the information contained
in them is practically identical:
P(B) ~P(R).
Given a fixed distance |R|
between the initial state and the goal, which
must be traveled with a prediction depth not less than P if it is to be
reliable, three types of situations are possible depending on the memory's
information capacity Q:
1) Superreliable operation P<Q.
2) Reliable operation P=Q.
3) Unreliable operation P>Q.
The Background Problems
Functional Assessment of Decision Reliability
The distinct differences between determined reliable and probabilistic
unreliable decisions revealed by solving the basic problem permitted the
hypothesis that these types of decision making also differ in their functional
organization.
To test this hypothesis we developed a procedure for assessing the balance
of controllable and uncontrollable reactions. The main parameters used in
this procedure were the EEG, the EMG, the GSR, the alpha-rhythm, and oscil-
lations of EEG wave asymmetry A(t). Asymmetry oscillations A(t) were com-
puted automatically with an MN-7 analog computer.
The experiments revealed typical differences in the changes experienced by
the parameters analyzed in relation to different types of decision making.
Statistical analysis of reactions of parameter A(t) showed that the determined
types of decision making cause a shift in the balance of controllable and
uncontrollable reactions in the direction of controllable reactions. The
reverse relationship exists in relation to probabilistic types of decisions.
A number of laws were revealed by analyzing changes in alpha-rhythm occurring
during solution of determined and probabilistic problems. Thus the alpha-
rhythm reaction permits us to divide the operators into four groups differ-
ing in reliability. Despite the fact that it does contain some information,
indication of decision reliability on the basis of alpha-rhythm analysis
is rather limited. This index must be used together with others if reliability
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is to be checked and the balance of controllable and uncontrollable reactions
is to be assessed effectively. The table below shows the typical properties
of different groups of operators in relation to depression and activation
of alpha-rhythm in the conditions of determined and probabilistic search.
-
THO
Детерминированный
DONCK
Вероятностный
DONСК
депрессия -
-4
95%
депрессия
98%
I
активация
5%
активация
2%
25%
депрессия
85%
2
депрессия
активация
75%
активация
15%
депрессия
74%
депрессия
30%
3
активация .
.26%
активация
70%
депрессия
депрессия
7%
4
.
активация
89%
активация
93%
Key:
1.
Type
4.
Depression
2.
Determined search
5.
Activation
3.
Probabilistic search
Joint examination of electromyographic and galvanic skin responses produces
a special advantage in assessing decision making reliability. These indices
permit us to obtain quantitative relationships between decision making speed
and reliability in standard situations and in stressful emergency situations.
If we characterize the decision making process in standard conditions by
Pt, where P is decision reliability and t is decision making time, then when
a transition is made to a stressful emergency situation the averaged assess-
ment is:
Pt/6.
The Reliability of Isoentropic and Entropic Decisions
The model solution of the basic problems showed that decision making reli-
ability is dependent in a certain way on prediction level. In cases where
the prediction vector cannot be placed in the memory's configurational
space, it would be suitable to subject it to isoentropic transformation.
This work showed that the methods of graph theory can be used for this pur-
pose. If the search space and the prediction vector are given as the approp-
riate graphs, after normalizing them we can formulate the algorithm of iso-
entropic simplification of the initial graph.
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In this case we examined the graph of the problem G(X,I'), given for the
problem's set of elements {X}, and the graph of the information model G(Y,T)
formed in the decision making process. Here, {Y} is the information model's
set of elements and T is transformation of {Y} into {X} [sic].
The information contained in the graph G(Y,T) is equal to the information
contained in the graph G(X,I), with a precision up to the prediction error.
These errors can differ depending on the extent to which {X} exceeds the
memory's information capacity {Q). When {Q}{{X}, plotting of the final
graph would proceed with certain errors until, by means of equivalent trans-
formations of graph G(X,I'), a transformation is completed to graph G(G,T) ,
where {{} is the set of elements of the memory's configurational space.
In view of the limited nature of {Q), in addition to objective complexity
the problem may be characterized by subjective complexity. The subjective
probability Po of attaining the goal may not coincide with the objective
probability Po, depending on the tip of the problem graph from which the
search for the decision begins. In these cases it would be more effective
to subject the search space to entropic transformation. When this type of
transformation is employed, the information contained in the graph does
not remain constant.
A generalized measure of uncertainty, H, was obtained in the dissertation
for cases in which the search space is subjected to entropic transformation:
Pci
2 Poi
H =
Į Poi
₣ Pci
where Poj is the objective probability of reaching the goal and Poi is the
subjective probability of reaching the goal.
In contrast to other measures of this type, the advantage of the obtained
measure lies in the fact that when the subjective factor is eliminated,
this measure transforms into conventional Wiener-Shannon entropy:
lg
Pci
2Poi
-> Poi lg Poi
-
Į Pci
Q Poi
Pc - Po
Conclusion
Analysis of decision making processes from the standpoint of systems engineer-
ing makes it possible to refine the boundaries of reliable operation of man-
machine systems.
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The revealed laws governing decision making processes indicate the way
information processes should be organized in a man-machine system so that
the system would satisfy the required level of reliability.
The procedures developed here afford a possibility for control and prediction
of the reliability of a systems engineering complex within certain limits.
The research produced the following basic results:
1. Different types of decision making were classified. Determined, prob-
abilistic, and combined types of decision making were analyzed. It was
demonstrated that these types differ in different situations in relation to
the reliability criterion.
Thus determined decisions are characterized by
complete reproducibility. As a rule, probabilistic decisions are not re-
producible.
Partial reproducibility is a unique feature of combined types.
The methods for formalizing determined and probabilistic types of decision
making are examined. Quantum-mechanics probabilities are suggested for
assessment of the reliability of combined determined-probabilistic types.
2. It is established that the reliability of decision making is dependent
on the relationship between the information capacities of the short-term
memory and the environment of the problem. When the memory's information
capacity exceeds the quantity of information processed, the decision making
process is characterized by high reliability. If, however, the volume of
information processed is greater than the memory's information capacity,
the reliability function experiences a first-order discontinuity, and the
probability of error grows monotonously as the information capacity of the
environment of the problem increases.
A procedure for assessing decision making reliability accounting for both
the characteristics of the information environment and the characteristics
of the operator is developed on the basis of the revealed law. Use of this
procedure in the planning of man-machine systems insures at least quasi-
optimum organization of the system.
3. A digital model of the decision making process accounting for the predic-
tion factor is developed. It is demonstrated that the reliability of decision
making depends significantly on prediction depth. The reliability function
grows monotonously with increase in the prediction vector, attaining a maxi-
mum when the prediction level becomes comparable with the generalized dis-
tance between the initial state and the goal. Inasmuch as prediction depth
depends on the possibilities for placing the prediction vector within the
short-term memory, transition from superreliable to unreliable operation
occurs to the extent that the memory's configurational state is inadequate
to hold the assigned prediction vector.
4. A method is proposed for assessing the balance of the operator's control-
lable and uncontrollable reactions, relying upon the use of electrophysiological
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procedures.
This method can be used both for occupational selection and
for control of the reliability level during operation.
It is demonstrated that the reaction balance shifts in the direction of
uncontrollable reactions in probabilistically organized environments. In
determined environments, meanwhile, optimization of decision making is in-
sured predominantly by controllable reactions. In this connection, if we
are to heighten the reliability of a systems engineering complex we must
make use of operators characterized by a maximum proportion of controllable
reactions.
5. Objective criteria for detecting emergency states are revealed.
These
criteria permit determination of the relationship between decision making
reliability and speed in ordinary conditions and in emergency conditions.
In emergency conditions, stress functions significantly increase decision
making speed but decrease reliability.
A method of controllable decision reproduction making it possible to surmount
dead-end states in emergency situations is proposed on the basis of an analysis
of stressful decision making. This method is ineffective when the lack of
time is sizable.
6. The mechanisms of isoentropic and entropic information transformation
are examined. The language of graph theory is used to formalize isoentropic
processes. An algorithm of equivalent simplification of the environment
of the problem, given in the form of a normalized graph, is proposed in
application to isoentropic decision making processes.
A generalized information measure is introduced for cases of entropic infor-
mation transformation. The proposed measure accounts for both the objective
characteristics of signals depending on the technical components of the
systems engineering complex, and the subjective characteristics dependent
upon the operator's properties. The advantage of this measure lies in the
fact that when the subjective factor is eliminated, it transforms into
the conventional Wiener-Shannon measure of entropy.
7.
Practical application of the procedures developed as a result of solving
the basic problem demonstrated their economic effectiveness in relation to
automated control systems.
The principal research results are presented in the following works:
1. "Effectiveness of Decision Making Processes," in "Nadezhnost' i effektiv-
nost' kompleksnykh sistem 'chekovek-tekhnika'" (Reliability and Effec-
tiveness of Integrated Man-Machine Systems), Leningrad, 1971.
2.
"Prediction of Operator Errors," in "Ispol'zovaniye EVM v geofizike"
(Use of Computers in Geophysics) , VIEMS, Moscow, 1971.
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3.
"The Brain as a Measuring System," in "Biologicheskaya i meditsinskaya
kibernetika i bionika" (Biological and Medical Cybernetics and Bionics),
Issue 3, Kiev, 1970.
4.
"A Stochastic Model of Brain Function," in "Materialy 4 Vsesoyuznoy konfer-
entsii po neyrokibernetike" (Proceedings of the Fourth All-Union Con-
ference on Neurocybernetics), Rostov-on-Don, 1970.
5.
"The Problem of Determined and Probabilistic Thinking," in "Materialy 4
Vsesoyuznogo simposiuma po kibernetike" (Proceedings of the Fourth All-
Union Symposium on Cybernetics), Tbilisi, 1968.
6.
"Information Quality as a Measure of Activity," in "Materialy konferentsii
molodykh uchenykh" (Proceedings of the Young Scientists Conference),
Izd-vo MGU, Moscow, 1968.
7.
"Informational Interpretation of the Measurement Process," in "Materialy
4 nauchnoy konferentsii NGU" (Proceedings of the Fourth Scientific Con-
ference of Novosibirsk State University), Novosibirsk, 1968.
SG1A
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