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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>An  Approach  to  Security  Environment  Forecasting  Based  on  Structuring  of  Foresight  Process  and  on  the  Method  of  Goal  Dynamic Evaluation of Alternatives </article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Vitaliy Tsyganok</string-name>
          <email>tsyganok@ipri.kiev.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Oleksandr Hryhorenko</string-name>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Viktor Holota</string-name>
          <email>v.holota@ukr.net</email>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Maksym Konovaliuk</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Olha Tsyhanok</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Institute for Information Recording of National Academy of Sciences of Ukraine</institution>
          ,
          <addr-line>Kyiv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"</institution>
          ,
          <addr-line>Kyiv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>State University of Trade and Economics</institution>
          ,
          <addr-line>Kyiv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff3">
          <label>3</label>
          <institution>Taras Shevchenko National University of Kyiv</institution>
          ,
          <addr-line>Kyiv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff4">
          <label>4</label>
          <institution>Yevheniy Bereznyak Military Academy</institution>
          ,
          <addr-line>Kyiv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <fpage>158</fpage>
      <lpage>168</lpage>
      <abstract>
        <p>   In 2021 the Assessment of the Future Security Environment of Ukraine (the forecasting period - till 2030) was elaborated and published for the first time. However, the methodology of strategic forecasting and planning in the national security and defense sphere still needs to be further developed and improved. That is why we propose to use the Method of Goal Dynamic Evaluation of Alternatives and its modifications to elaborate and process the Future Security Environment model, built by experts and analysts. According to our approach, prediction process should be structured into series of steps, and thoroughly consider the international experience of strategic geopolitical forecasting.</p>
      </abstract>
      <kwd-group>
        <kwd>1  forecasting</kwd>
        <kwd>prediction process</kwd>
        <kwd>foresight</kwd>
        <kwd>future security environment</kwd>
        <kwd>structured analytic techniques</kwd>
        <kwd>goal dynamic evaluation of alternatives</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction </title>
      <p>
        Forecasting of the future security environment (FSE) of Ukraine is one of the top-priority tasks of
analytical activity of governmental bodies responsible for conducting the Defense Review. It is based
on the elaboration of probable scenarios of military escalation within midterm and long-term
perspective [1]. The solution of this problem is the key to building of effective national resilience
system, providing the ability to quickly adapt to security environment changes and maintain sustainable
functioning through minimization of external and internal threats [
        <xref ref-type="bibr" rid="ref1">2</xref>
        ].
      </p>
    </sec>
    <sec id="sec-2">
      <title>2. Context </title>
      <p>
        In 2021, for the first time, Ukrainian experts elaborated and published the Assessment of the Future
Security Environment of Ukraine for the period till 2030. According to their understanding, the security
environment should be considered as a combination of factors that may influence national interests and
pose a threat, which must be neutralized by national defense and security forces. Security environment
is comprised of states with their national interests (economic, political, military etc), natural
environment, specific physical and legal entities, political parties, national information space etc [[
        <xref ref-type="bibr" rid="ref2">3</xref>
        ]].
      </p>
      <p>
        At the same time, according to Ukrainian doctrines, one of the main tasks of national defense force
capabilities development is the introduction of a network-centric approach to implementation of modern
systems for management, obtaining and exchange of information, as well as building of a unified
information environment through automation of collection, processing and dissemination of
information [[
        <xref ref-type="bibr" rid="ref2">3</xref>
        ]].
      </p>
      <p>While considering the problem of security environment forecasting, we have to take into account
foreign experience in this field. The United States of America, as one of the leading superpowers, has
a very diversified network of government entities and nongovernment “think tanks” which develop
different forecasts. In this context, analytic units of the US Intelligence Community are among the most
powerful segments of the US defense and security sectors (which are responsible for strategic
forecasting).</p>
      <p>
        On many occasions, the US experts were trying to reconsider the problems of prediction. In 2008,
such a leading American “think tank” as the RAND Corporation (in its report “Assessing the Tradecraft
of Intelligence Analysis”) illustrated intelligence “failures” related to some unsuccessful attempts of
US Intelligence Community experts to predict historical events, that significantly influenced further
development of security environment [
        <xref ref-type="bibr" rid="ref6">7</xref>
        ], including:
 incorrect forecasts concerning the development of nuclear weapon in the Soviet Union (1940s);
 inability to predict the quick collapse of the Soviet Union (1980s);
 incorrect estimate of the consequences of Y2K issue (1990s);
 wrong assessment on Iraqi WMD program (2000s) and others…
      </p>
      <p>Taking into account more recent developments, we may supplement this list with the incorrect
forecasts concerning Russia’s armed aggression against Ukraine (2014, 2022), emergence of “Islamic
State in Syria and Levant” (2014), the results of the referendum on the withdrawal of the United
Kingdom from the European Union (2016) and COVID-2019 pandemic (2020).</p>
      <p>
        That is why the US Intelligence Community is routinely raising the issue of improving the
procedures for forecasters. In this context it would be very interesting and fruitful to look into the
research conducted in 2011-2013 by Philip Tetlock, the Professor at the University of Pennsylvania,
and other scientists and analysts. The study was designed as a large-scale forecasting tournament under
request of the Intelligence Advanced Research Projects Activity (IARPA), the research and
development branch of the Office of the Director of National Intelligence (US). Some results of the
research were published in an article “The Psychology of Intelligence Analysis: Drivers of Prediction
Accuracy in World Politics” [[
        <xref ref-type="bibr" rid="ref3">4</xref>
        ]] and in Philip Tetlock’s and Dan Gardner’s book “Superforecasting:
The Art and Science of Prediction” [[
        <xref ref-type="bibr" rid="ref4">5</xref>
        ]].
      </p>
      <p>The aim of the research was to empirically determine the factors, which could contribute to
improvement of accuracy and credibility of the forecasts, developed by analysts. More than 750
American analysts from government and non-government institutions (particularly, those developing
geopolitical forecasts and, thus, closely related to security environment forecasting tasks) took part in
the experiment. For two years they were giving answers to probabilistic questions concerning some 200
different geopolitical events of different significance (close to issues of security environment).</p>
      <p>As a result of the research, Philip Tetlock and his colleagues concluded that the accuracy of the
forecasts depended on a set of individual and professional skills such as:</p>
      <p>Dispositional Variables – inductive reasoning; cognitive control; numerical reasoning;
openminded style of thinking; greater tolerance to ambiguity allowing to make correct choice in favor of
certain interpretation of events; readiness to change paradigm accepting new information; capability to
determine the level of uncertainty of forecaster’s judgments and/or probability of future events; political
knowledge;</p>
      <p>
        Situational Variables – the research indicated that professional environment matters. The most
beneficial environment is when analysts have an opportunity to cultivate their skills and receive
feedback on the subject of forecasting. The other key to success is the formation of problem-solving
teams or groups of forecasters united by the same goal. This leads to information and experience
sharing, diversity of knowledge, and “cognitive altruism”: forecasters in teams shared news articles,
argued about the evidences, and exchanged rationales using self-critical epistemic norms. Forecasters
who worked alone were less accurate [[
        <xref ref-type="bibr" rid="ref4">5</xref>
        ]]. While working in groups (teams), analysts were more
adequately reacting to external critiques and were more self-critical, so it made their forecasts more
objective and accurate.
      </p>
      <p>
        It is worth admitting that American scientists Daniel Kahneman and George Klein hold a similar
view. They think that professional environment provides analysts with possibility to develop their
predictive skills and better opportunities to practice by sharing of their experience, knowledge, ideas,
and judgments [[
        <xref ref-type="bibr" rid="ref5">6</xref>
        ]].
      </p>
      <p>
        Behavioral Variables – reflect the ability of a forecaster to self-develop and to question his own
analytical paradigm concerning conducted forecasting. In this context analysts “should spend more time
researching, discussing, and deliberating before making a forecast” [[
        <xref ref-type="bibr" rid="ref3">4</xref>
        ]]. They have to permanently
check permanently their key assumptions, search for new questions, and debate with colleagues. In
general, it is a routine movement towards self-development by means of self-analysis.
      </p>
      <p>
        At the same time Philip Tetlock admitted that a key feature of forecaster’s activity is making
nonnumeric (verbal) forecasts “that are vague and hard to score for accuracy, so feedback is often
absent” [[
        <xref ref-type="bibr" rid="ref3">4</xref>
        ]]. That is why automation process of verbal information processing is significantly
complicated (in contrast to numeric data processing).
      </p>
      <p>In order to solve this problem, we propose to use Ukrainian experience as well as best foreign
practices in the sphere of forecasting. In this article we would like to describe:</p>
      <p>(1) some results of the trainings of Ukrainian national security and defense analysts dealing with
prediction of security environment;</p>
      <p>(2) the use of the Method of Goal Dynamic Evaluation of Alternatives (MGDEA) for automation of
strategic geopolitical forecasting.
3. Practical results of national security and defense analysts’ trainings </p>
      <p>In 2016-2021 dozens of seminars (trainings) were held with the representatives of Ukrainian national
security and defense sector, which led to some important conclusions. The most accurate and argued
forecasts were built as a result of creative combination of Structured Analytic Techniques (SAT). The
most efficient techniques included the following ones: Structured Brainstorming; Cognitive Mapping;
Force Field Analysis, DIMEFIL/PMESII Analysis; SWOT Analysis; Alternative Futures Analysis etc.</p>
      <p>So, it makes sense to break the forecasting process into the following phases:
1. pre-forecasting orientation;
2. preparation of formalized incoming information;
3. key problem (question) formulation;
4. key problem (question) decomposition;
5. determination of key trends in security environment;
6. build-up of security environment cognitive model;
7. generation of security environment scenarios;
8. evaluation of these scenarios in the context of their probability and level of threat to the national
interests of the state.
4. Application  of  the  method  of  goal  dynamic  evaluation  of  alternatives  to 
automation of the proposed action algorithm </p>
      <p>
        The method was developed for evaluation of decision alternatives based on the goal hierarchical
model [
        <xref ref-type="bibr" rid="ref7 ref8">8, 9</xref>
        ] and improved to provide new opportunities, such as evaluating alternatives of actions when
building strategic plans [
        <xref ref-type="bibr" rid="ref9">10</xref>
        ] and evaluating the importance and probabilities of alternative scenarios
during their generation [
        <xref ref-type="bibr" rid="ref10">11</xref>
        ]. These methods are realized and implemented in respective software
systems in the laboratory for decision support systems of the Institute for Information Recording of the
National Academy of Sciences of Ukraine. Particularly, we should mention the decision support system
"Solon-3" [
        <xref ref-type="bibr" rid="ref11">12</xref>
        ] and the system for conducting examinations by distributed groups of experts
"Consensus-2" [
        <xref ref-type="bibr" rid="ref12">13</xref>
        ]. It is the latter software system that allows you to structure the security environment
through building its goal-oriented model with the involvement of expert-analyst groups in the process.
      </p>
      <p>Usage of these software tools enables us to:
 create a network environment for remote work of forecasters as members of object-oriented
analytical groups;
 ensure administration and recording/backlogging of all actions of analysts involved in the
forecasting process;
 automatically perform pairwise comparisons of importance and influence of various
alternatives (hypotheses, scenarios, trends, decision options, measures, etc.), which is extremely
effective when working with verbal (non-numerical) information;
 create cognitive models of the development of a security environment or a specific situation;
 determine (through a distributed expert assessment) the degree of probability of the security
environment development scenarios and the level of danger to the national interests of the state.</p>
      <p>
        MGDEA [
        <xref ref-type="bibr" rid="ref7 ref8">8-9</xref>
        ] is primarily intended for evaluating alternatives (decision options, projects,
measures) at a time interval in decision support systems (DSS). Evaluation is carried out based on an
expert-constructed model of the subject domain. The method makes it possible to use the most general
models of weakly structured subject domains, which sufficiently fully and adequately reflect the
peculiarities of one or another subject domain. Models, in this case, represent knowledge bases (KB) –
hierarchies of goals that are conveniently represented in the form of a connected directed graph. The
vertices of the graph correspond to the goals formulated by the experts, and the arcs represent the
existing relationships between them. Among the goals, the main goal of the problem (root vertex of the
graph), intermediate goals, as well as projects (terminal vertices of the graph, goals of the lowest level
of the hierarchy) are usually distinguished. In order to achieve the greatest adequacy of the model to
the subject domain and to ensure the opportunity to take into account the dynamics of changes in the
relative estimations of alternatives over time, the arcs of the graph are “loaded” with the values of time
delays of influences determined by experts.
      </p>
      <p>
        Unlike other existing methods, for example, multi-criteria ones [
        <xref ref-type="bibr" rid="ref13">14</xref>
        ], where appropriate optimization
methods are used [
        <xref ref-type="bibr" rid="ref14 ref15">15, 16</xref>
        ], MGDEA allows us to evaluate heterogeneous projects for which it is difficult
or impossible to formulate a single set of evaluation criteria. In addition, MGDEA does not require an
expert to master the entire problem as a whole; it allows us to construct a subject domain model, using
a group of experts, each of whom has full knowledge only of some part of the domain. Due to the listed
properties, MGDEA can be positioned as one of the fundamental methods in the area of expert
decisionmaking support.
      </p>
      <p>The method envisions performing a set of procedures (involving experts), related to construction of
the KB (knowledge base) of the subject domain with the determination of a number of numerical
parameters regarding the degree of influence of goals, delays in the spreading of influences, the duration
of project implementation, etc. When the construction of the KB (i.e. hierarchy of goals) is completed,
the method allows us to calculate the ratings (estimates) of decision variants (actions, measures,
projects) based on the KB.
4.1.</p>
      <p>The essence of the method application and its modifications  </p>
      <p>It is appropriate to single out the following main stages in the course of applying the MGDEA. In
addition, we will consider a number of concepts related to the operation of the method.</p>
    </sec>
    <sec id="sec-3">
      <title>4.1.1. Building a model ‐ a hierarchy of goals</title>
      <p>The construction process begins with the formulation of the main goal of the problem and possible
options for its solution, which ultimately need to be evaluated. The main goal is subject to
decomposition into simpler components – sub-goals that affect the main goal. In the future, these
formulated goals are also subject to decomposition. Moreover, the list of goals that affect the
achievement of the current goal, in addition to the newly formulated goals, may include those already
present in the hierarchy (previously formulated during the decomposition of other goals). The
decomposition process continues until the sets of goals that affect the formulated goals consist only of
the evaluated decision options and the already formulated goals. That is, the decomposition process
stops when there are no undisclosed goals left.</p>
      <p>The hierarchy of goals, which is built by experts, is presented in the form of a directed graph, the
vertices of which are marked with goal formulations. Every arc in the graph signifies the influence of
achievement of one goal on achievement of another. Thanks to the described process of building a
hierarchy of goals, the graph corresponding to it is one-way connected, since from any vertex of the
graph there is a path to the vertex that denotes the main goal. Each vertex (goal) is matched with an
indicator of the degree of achievement 
∈ ℝ,  ∈
1. .  ,  – the number of goals in the hierarchy.
0 
1 , moreover, 
1
when the i-th goal is fully achieved, and 
0
process in its achievement. It should be noted that each influence (represented by an arc in the graph)
can be both positive and negative for achieving one or another goal. The degree of influence of one goal
on the achievement of another is expressed by the corresponding indicator – the partial coefficient of
– when there is no
influence (PCI). In MGDEA, the change in PCI over time is taken into account, therefore, the PCI 
of the i-th goal on the j-th at the moment of time t is determined by the expression:


0, if  

, otherwise
, </p>
      <p>is an expert assessment of the delay of the influence of the i-th goal upon the j-th goal. For
goals such as projects (variants of decisions), the delay in their influence on one or another goal is
usually increased by the duration of the project, determined by the expert.</p>
    </sec>
    <sec id="sec-4">
      <title>4.1.2. Formation of subsets of compatible goals  </title>
      <p>MGDEA provides for the possibility of determination of PCI by expert means. To increase the
reliability of such expert assessments, as a rule, the method of pairwise comparisons is used. Regarding
the comparison of the degrees of influence of a set of goals on some defined goal, it should be noted
that within the described model, compatible and incompatible goals are distinguished, which jointly
influence some defined goal. Goals are considered compatible, if the achievement of one of them does
not exclude the necessity and possibility of achieving the other, and incompatible – in the opposite case.</p>
      <p>
        Since any comparisons and corresponding comparative estimates are worth applying only among
sets of mutually compatible objects, there is a need to find such maximum-cardinality subsets of objects,
that each of them
would include only
mutually compatible objects. In [
        <xref ref-type="bibr" rid="ref16">17</xref>
        ], the
method and
corresponding algorithm for determining subsets of compatible objects is proposed; it is iterative and
involves determination of compatible subsets in the process of gradually obtaining information about
the incompatibility of pairs of objects from the original set of objects.
      </p>
      <p>
        The algorithm that implements the method is characterized by significantly lower computational
complexity compared to the method described in [
        <xref ref-type="bibr" rid="ref7 ref8">8-9</xref>
        ], where the solution of the problem is associated
with the search for a set of simple paths of the maximum length in the compatibility graph. This task
was formulated as follows:
      </p>
      <p>What is given: a set of objects A={ ai }, iI, where I={1,2,…,n} is a set of indices; P is the set
of pairs of compatible objects, i.e. pairs &lt;ai;aj&gt;, [ai,ajA], for which ai * aj = "true" ('*' is the introduced
binary operation of compatibility).</p>
      <p>We should find: As  A (s I), such that m[(amAs)( * am = "true")]  k[(ak As)(akA)]
mI
equality holds: ak  * am  = "false".</p>
      <p>

 ammAIm


</p>
      <p>The proposed method of finding subsets of As in the set A assumes the determination of these subsets
in the process of successive exclusion of elements from the set of pairs of incompatible objects. The
algorithm of the method is iterative and the number of iterations is equal to the number of elements in
(1) 
the aforementioned set of pairs. Before starting the execution of the algorithm, we assume that all pairs
of objects are compatible, while, naturally, the set of compatible objects coincides with the original set
(As=A). Let us assume, that, as a result of some experiment, the pair &lt;ak; al&gt; is deemed incompatible,
so this pair is excluded from the set of compatible pairs.</p>
      <p>
        It was proved in [
        <xref ref-type="bibr" rid="ref16">17</xref>
        ] that for the set A of compatible objects of power n, when the pair &lt; ak; al &gt; is
excluded from the set of compatible pairs, we obtain two subsets of compatible objects:
A1={ai | iI, ik}, and A2={ai | iI, il} of power (n – 1) each, and that this power is the maximum
possible. In this way, each iteration of the proposed method is performed over all subsets obtained at
the previous step. In addition, in order to minimize the number of obtained subsets of compatible
objects, at each iteration of the algorithm, all possible absorptions by the obtained sets of those sets that
are subsets of the first ones are performed. The iterative process stops when the set of pairs of
incompatible objects has no remaining elements and becomes empty.
      </p>
      <p>In addition to lower computational complexity of the algorithm, the proposed method provides an
opportunity to determine (select) compatible subgroups of goals while providing information on the
pairwise compatibility of these goals. A useful feature of the method is the ability to redefine compatible
subgroups of goals after editing information about the compatibility of pairs of goals, when adding or
removing some goal from the hierarchy. It is especially useful for MGDEA in the expert construction
of a hierarchy of objectives that the redefinition of compatible subgroups of objectives occurs without
reusing or entering information about the compatibility of those pairs that remained unchanged.
4.1.3. Determining the partial coefficients of influence  </p>
      <p>As mentioned above, the determination of the PCIs, denoted in (1) by 
,  ∈ 
– the coefficients
of the influence of goals with index j on some goal with index i in the hierarchy, takes place within the
already defined compatible subgroups. Such PCIs are normalized values and for each k-th group of
compatible goals satisfy the condition:

1,  
(2) 
where 
number of compatible goals in the k-th group.</p>
      <p>is the PCI of the j-th goal upon the i-th goal in the k-th group of compatible goals; K is the
Since goals can have both positive and negative influence, which is reflected by the sign of the
corresponding PCI, before performing influence comparisons, goals that have a negative influence are
replaced by opposite values (i.e., their logical negations). As a result, when determining PCI, all goals
j in the k-th subgroup of compatible goals have a positive effect on the achievement of the i-th goal.</p>
      <p>
        To determine PCI, it is suggested to use the methods of group pairwise comparisons, which
sufficiently satisfy the requirements to reliability of obtained results [
        <xref ref-type="bibr" rid="ref17">18</xref>
        ]. Thanks to development of
innovative expert evaluation methods (which, in comparison to existing ones, allow decision-makers to
obtain evaluations from experts more fully and without pressure), we can suggest using the method of
paired comparisons with feedback to determine the PCI, which gives the expert the opportunity to
perform evaluations in the scale, the detail of which adequately reflects his knowledge (competence) in
the area of expertise [
        <xref ref-type="bibr" rid="ref18">19</xref>
        ]. The expediency of using this technology of expert evaluation, in particular
for determining PCI of hierarchy goals, was confirmed by a comparative experimental study [
        <xref ref-type="bibr" rid="ref19">20</xref>
        ].
      </p>
    </sec>
    <sec id="sec-5">
      <title>4.1.4. Degrees of achievement of goals </title>
      <p>
        The basis of MGDEA is a generalized procedure for determining the degree of achievement of an
arbitrary goal of the hierarchy at a given moment in time t. As stated in [
        <xref ref-type="bibr" rid="ref7 ref8">8-9</xref>
        ], when determining the
degree of achievement of a certain goal, it is necessary to analyze the degree of achievement of goals
that have a direct influence upon this goal for each alternative subset of mutually compatible goals. So,
expression:
  , that is the degree of achievement of the i-th goal at the moment of time t, is determined by the
 


⎧
⎪
⎪
⎨
⎪
⎪
⎩

0,
 ,
1,
 ,
if
if
if
if 
1







1





1
,
 
(3) 
where 

is the threshold of achievement the i-th goal; 

is the
function of the degree of achievement of the i-th goal at time t; 
k-th group of compatible goals, which has a negative effect on the i-th goal.
is the PCI of the j-th goal in the
      </p>
    </sec>
    <sec id="sec-6">
      <title>4.1.5. Rating calculation  </title>
      <p />
      <p>of solution variants –</p>
      <p>The essence of the calculation with the help of MGDEA of the rating (relative estimate) of the
alternative (decision variant) corresponding to the l-th goal of the hierarchy at some point in time t is
reduced to the determination of the difference between the degrees of achievement of the main goal –
under condition of full achievement of all goals that correspond to those defined for comparison
0. That is, the rating of one or another alternative is the difference between the degree of achievement
of the main goal in the presence of the influence of this alternative on the main goal and without it.</p>
      <p>In order to expand the application area of MGDEA, it was proposed to improve the method with the
possibility of calculating the rating of alternatives not only in relation to the contribution to the
achievement of the main goal of the hierarchy, but also in relation to any other chosen goal. This allows
comparing the influence of alternative decision variants on intermediate goals in the general domain
1 ,  ∈ ,  
. . 
and under condition  
1 ,  ∈ \
 , 

model.</p>
      <p>The process of calculating</p>
      <p>– the degree of achievement of the selected i-th goal at the moment
of time t can be described as follows. The goal hierarchy graph is searched for goals that do not influence
other goals of this hierarchy, i.e., a set of vertices that do not include any arc of the graph is selected.
From this set of goals (they are usually alternatives / projects), the calculation of degrees of goal
achievement begins. The initial values of the degrees of achievement of the goals from this set are
assigned, as just noted, equal to 1 or 0, although intermediate values are also possible, in case it is
necessary to consider the incomplete realization of a project at a given moment in time. It is advisable
to take into account the expert estimation of the degree of project realization when analyzing the
intermediate states of the model and in the case of partial resource allocation for (financing of) projects.</p>
      <p>
        It should be noted that, in general, the graph may have vertices that do not have incoming arcs.
Although, according to the logic of model construction, this is unlikely, and such a scenario was not
considered in [
        <xref ref-type="bibr" rid="ref7 ref8">8-9</xref>
        ], it is worth noting that when constructing a hierarchy, it is advisable to include the
goal called "Other factors", which influences all those goals of the hierarchy, the achievement of which
is insufficiently determined by the set of goals, available in the hierarchy. If this recommendation is
followed, the initial set of goals when determining the degrees of goal achievement will not be empty,
because it will include the goal "Other factors", not influenced by any other goals.
      </p>
      <p>Subsequently, a set of goals is formed that can be achieved directly from the goals belonging to the
set formed at the previous step. The formation process is carried out through inclusion of all goals
(graph vertices) that are directly influenced by goals from the previous set (which include arcs coming
from the corresponding vertices). This set may also include goals belonging to the previous set.</p>
      <p>For each goal from the formed set, the degree of its achievement at the moment of time t is
determined. In fact, in the process of determining the degrees of achievement of goals, there is progress
along the graph of the hierarchy from the goals of the lower level to the goals of the upper levels and,
finally, to the main goal of the problem. In the case of the presence of reverse connections in the graph
(arcs coming out from the vertices of higher levels and incoming the vertices of lower levels), the
iterative process of determining the degree of achievement of goals is terminated in the case when the
absolute value of the difference between the calculated values of the degree of achievement of the
selected goal at adjacent iterations (x) and (x+1) does not exceed the specified accuracy ε:
 


.</p>
      <p> 
4.1.6. Input parameters and reference time points  </p>
      <p>The accuracy of ε calculations, as well as the planning period, are entered as input parameters. Based
on the specifics of the tasks solved with the help of this DSS, the minimum unit of measurement of time
intervals is a day (twenty-four hours), that is, planning is carried out with an accuracy of one day. By
default, a recommended planning period is entered into a special form as the time period over which
the relative ratings of the selected projects are calculated. This value (in days) is calculated according
to the graph of the hierarchy of goals by moving from the vertices of the lower level to the upper level,
similar to the process of determining the degrees of achievement of goals, but during this process, the
sum of the delays in the spreading of influences forms the value of the maximum duration of the time
period, beyond which changes in the relative project ratings’ calculation results no longer occur.</p>
      <p>Although the MGDEA allows you to calculate the relative ratings of projects at any point in time
from the start of their realization, since the calculated values of the ratings change only in the so-called
reference points of the time axis, it is suggested to determine these points a priory (in advance) and only
once, and not determine them before each iteration. In contrast to the iterative method proposed in
[89] for determining the next</p>
      <p>moment of time for calculating the degrees of goal achievement:


, 

,  ∈
1,2, … ,  1
,  </p>
      <p>is the value of the delays of the effects of the goals in the hierarchy, which contains n goals,
it is currently proposed to pass from the goals of the lower level to the upper level with the calculation
and addition to the list of all possible delays of the effects of the goals in the hierarchy. The passage is
organized simultaneously with the process of determining the degree of achievement of the main goal
of the hierarchy, and in the presence of feedback, it continues until condition (4) is fulfilled. In fact, the
formation of the list of goal influence delays is performed together with the calculation of the
abovementioned recommended planning period, the value of which corresponds to the maximum value
among the calculated influence delays.</p>
    </sec>
    <sec id="sec-7">
      <title>4.1.7. Integral index </title>
      <p>In addition to the calculated ratings of alternatives at reference time points, for analyzing the
dynamics of changes in the ratios between these ratings, an additionally developed viewing mode, the
so-called integral assessment, proves extremely useful. In this mode, the graphs display the integral
index of project efficiency i(t):</p>
      <p>,  
which in essence is the integral over time t of the rating (relative estimation) function of the project r(t).</p>
      <p>In the integrated evaluation view, the intersection points of the graphs (curves) reflect the moments
of time since the start of the projects, when the ratio between the projects is changed in the sense of
their dominance compared to others. Thus, it can be concluded that in a certain time perspective,
preference should be given to the project whose graph turned out to be higher on the chart at a certain
period of time.
(4) 
(5) 
(6) 
5. Proposed  technology  application  for  the  forecasting  of  future  security 
environment </p>
      <p>In the course of this scientific research, the possibility of forecasting future security environment
was practically confirmed. The purpose of the forecasting is to determine the main factors affecting the
security of the state, as well as, in the future, to determine directions and measures to increase security.
The proposed technology makes it possible to structure a complex system, which is the general security
situation in the country, in the constructed model through sequential decomposition of the system. After
creating a model of the security situation, the mechanism embedded in the technology allows us to
calculate priorities (through determining the degrees of achievement of the goals - components of the
system), make forecasts, predict the development of the security situation.</p>
      <p>
        According to the technology, at the initial stage, structuring is performed through group work on the
decomposition of the problem. It is performed by knowledge engineers, as well as expert analysts, who
are joining the knowledge engineers in the decomposition process if necessary. The system of
distributed collection and processing of expert information “Consensus-2” [
        <xref ref-type="bibr" rid="ref12">13</xref>
        ] allows for organizing
the process of group decomposition, which is the basis of building the model. In the course of group
construction of the model, in addition to decomposition, expert analysts may be involved in the group
evaluation (expertise) of the relative importance of influences of the goals (PCI) in the hierarchy,
determination of time delays in the spreading of influences, and other parameters of the model. In the
system, under group evaluations, methods of information processing are used. These methods were
previously tested as to reliability of their results [
        <xref ref-type="bibr" rid="ref19">20</xref>
        ]. The general result of such collective work is a
model of the security environment, which (for the sake of clarity) it makes sense to present in the form
of a graph of the goal hierarchy. The main goal – the root vertex of the hierarchy graph – can be
formulated, for example, as "Ensure State Security". The upper level of decomposition by the
responsible knowledge engineer can be represented without the involvement of analysts in the form of
the well-known decomposition DIMEFIL: Diplomatic, Information, Military, Economic, Financial,
Intelligence and Law Enforcement (see Fig. 1).
      </p>
      <p>Figure 1: Screenshot with an image of the goal hierarchy graph in the “Consensus‐2” system </p>
      <p>
        At a later stage, when the model of the future security environment is built completely, including
the determination of all key parameters, its usage is connected with the application of the “Solon-3”
DSS [
        <xref ref-type="bibr" rid="ref11">12</xref>
        ]. The DSS software provides a toolkit for the state of the security environment forecasting by
determining the ratings and effectiveness of projects (measures, alternative solutions), rational
distribution of resources between them in the sense of their impact on the main goal achievement or
achievement of other (intermediate) goals in the goal hierarchy. The basis of the implemented
mathematical calculations in the “Solon-3” DSS (Fig. 2) is the MGDEA, which was created to process
the information from hierarchical-goal models of this same type, taking into account the dynamics of
the development of the security environment.
      </p>
      <p>Figure 2: Screenshot with the image of the model and calculations in the “Solon‐3” DSS </p>
    </sec>
    <sec id="sec-8">
      <title>6. Conclusions </title>
      <p>The combination of international and domestic experience of information and analytical activities
makes it possible to develop approaches to solving certain problems of forecasting the security
environment through structuring of the forecasting process itself and the application of the method of
goal dynamic evaluation of alternatives.</p>
    </sec>
    <sec id="sec-9">
      <title>Acknowledgement</title>
      <p>This work was supported by the ECHO project which has received funding from the European
Union’s Horizon 2020 research and innovation programme under the grant agreement no 830943.</p>
    </sec>
    <sec id="sec-10">
      <title>References </title>
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