=Paper=
{{Paper
|id=Vol-3171/paper71
|storemode=property
|title=Information Support of Intelligent Decision Support Systems for Managing Complex Organizational and Technical Objects Based on Markov Chains
|pdfUrl=https://ceur-ws.org/Vol-3171/paper71.pdf
|volume=Vol-3171
|authors=Marharyta Sharko,Natalia Petrushenko,Olga Gonchar,Nataliia Vasylenko,Kateryna Vorobyova,Iryna Zakryzhevska
|dblpUrl=https://dblp.org/rec/conf/colins/SharkoPGVVZ22
}}
==Information Support of Intelligent Decision Support Systems for Managing Complex Organizational and Technical Objects Based on Markov Chains==
<pdf width="1500px">https://ceur-ws.org/Vol-3171/paper71.pdf</pdf>
<pre>
Information Support of Intelligent Decision Support Systems for
Managing Complex Organizational and Technical Objects Based
                      on Markov Chains
     Marharyta Sharko1, Natalia Petrushenko2, Olga Gonchar3, Nataliia Vasylenko4,
                    Kateryna Vorobyova5, Iryna Zakryzhevska6

1
  State Higher Educational Institution “Pryazovskyi State Technical University”, 7, Universytets’ka st.,
Mariupol, 87500, Ukraine
2
  Ukrainian Academy of Printing, Pidholosko st., 19, Lviv, 79020, Ukraine
3
   Khmelnytsky National University, Instytuts’ka str., 11, 29016, Ukraine
4
   Kherson State Agrarian and Economic University, Stritenska st., 23, Kherson, 73006, Ukraine
5
   Limkokwing University of Creative Technology Malaysia, Inovasi 1-1, Jalan Teknokrat 1/1, Cyber 3,
Cyberjaya, Selangor, 63000, Malaysia
6
  Khmelnytsky National University, Instytuts’ka str., 11, 29016, Ukraine


                 Abstract
                 Management of multilevel organizational and technical systems under the influence of
                 environmental factors is a complex process that uses both structured and semi-structured data.
                 For information support of management decisions in such systems, the use of probabilistic
                 mathematical models based on Markov processes is proposed. In contrast to the traditional use
                 of Markov chains, it is proposed to replace equal step intervals with a discrete sequence of
                 states determined by environmental influences. This approach makes it possible to model and
                 regulate the process of making relevant decisions when managing multi-level organizational
                 and technical objects and increase its efficiency in difficult operating conditions.

                 Keywords
                 information support, intelligent systems, semi-structured problems, control, uncertainty,
                 Markov chains 1

1. Introduction
   The typology of solving complex semi-structured problems of managing multilevel control systems
requires taking into account quantitative and qualitative characteristics with the dominance of
uncertainty and fuzzy ideas about the influence of unpredictable environmental factors. The appearance
of a hierarchical structure in intelligent semi-structured control systems is due to the presence of a large
amount of information about the controlled processes in the system, the impossibility of processing this
information and making decisions by one control center, as well as the decentralization of the decision-
making process. One of the important problems of decision-making under conditions of uncertainty is
the lack of a common methodology for constructing probabilistic models for regulating the process of
making relevant decisions and information support for intelligent control systems for complex multi-
level organizational and technical objects.
   Decision-making information support models in the management of simple organizational and

COLINS-2022: 6th International Conference on Computational Linguistics and Intelligent Systems, May 12–13, 2022, Gliwice, Poland.
EMAIL: mvsharko@gmail.com (M. Sharko); natalia.velikaya@gmail.com (N. Petrushenko); o.i.gonchar@i.ua (O. Gonchar);
neve80@ukr.net (N. Vasylenko); katrin.vorobyova@gmail.com (K. Vorobyova); zg_ira@ukr.net (I. Zakryzhevska)
ORCID: 0000-0003-2321-459x (M. Sharko); 0000-0001-7383-8558 (N. Petrushenko); 0000-0003-3917-7586 (O. Gonchar); 0000-0001-7910-
5013 (N. Vasylenko); 0000-0002-3990-730X (K. Vorobyova); 0000-0003-0918-9949 (I. Zakryzhevska)
                ©️ 2022 Copyright for this paper by its authors.
            Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
                CEUR Workshop Proceedings (CEUR-WS.org)
technical objects are used to analyze systems in which decision-making is of a one-time nature, and
system components are described by static quantities. Most management models for complex
organizational and technical objects are characterized by the fact that the processes they describe are
dynamic in nature. Dynamic models of hierarchical control systems for complex organizational and
technical objects operating under conditions of uncertainty are of particular interest due to the need to
take into account controllable and uncontrollable factors.
    Phenomenologically, the choice of the first step to change the current situation of managing complex
organizational and technical systems is associated with a quantitative assessment and adjustment of one
of the determining factors, which leads to a shift in the starting point of the management transformation
process. After performing operations related to the adjustment of the subsequent factor, the starting
point will again shift towards the reduction of the process. Thus, the process of changing the position
of the reference point is random in nature, characterized by an arbitrary choice of a corrected factor
with discrete time characteristics of the duration of the first and subsequent steps and a countable set of
states. Such a process will be Markovian, since subsequent states of the starting point of the process of
transformational transformations do not depend on past states.
    The unresolved parts of the general problem of managing complex objects include the formalization
of the accumulated knowledge and experience in managing them, taking into account the influence of
uncertain destabilizing environmental factors on the cognitive component of the decision maker.
    The aim of the work is to develop information support tools for intelligent decision-making systems
in the management of multi-level organizational and technical objects under conditions of uncertainty.


2. Relative Works

    The Markov process model applied in the construction of logical networks of the information space
is presented in [1,2]. In [3], the Markov process model is used to calculate the probabilities of transitions
between states of patients as a set with deviations in the anatomy of the lymphatic drainage system. The
construction of the architecture of information support for the management of organizational and
technical systems is presented in [4]. The use of the theory of artificial intelligence and computational
linguistics to enhance the semantic connection of uncontrolled terms of knowledge representation in
information systems of engineering regulations is presented in [5,6]. The procedure for information
support of decision-making systems with a limited number of observations, based on interval estimates
of probabilities, is presented in [7]. The information-entropy model of the basis for making managerial
decisions under conditions of uncertainty is presented in [8]. The information support system for
minimizing losses in the management of information systems with the analysis of the results of
management decisions is presented in [9]. In [10], a description of information support for managing
uncertainty by taking into account the requirements, opportunities and recommendations for the
implementation of projects in corporate systems is given. Information support of mechanisms and types
of control with a gradation of categories of possibilities and classes of uncertainties is presented in [11].
The use of information technologies for risk and uncertainty management in complex projects is
presented in [12,13]. The influence of information systems on business efficiency is reflected in the
works [14-17]. In [18], a number of new functions and influences on management activities are
proposed. The adoption of preventive measures to minimize threats and risks is reflected in [19]. The
work [20] is devoted to setting priorities and reducing uncertainties by digital data transformation. The
use of a heterogeneous hidden Markov chain for the characteristics of wavelet coefficients is considered
in [21], feature extraction based on the Markov chain for anomaly detection in time series in [22], the
use of Markov chains in complex multilevel control chains in [23]. Modeling using Markov chains for
a wide range of applications is presented in [24-28].
    The variety of ways to study uncertainty has caused fragmentary ideas about the parameters of
uncertainty and approaches to its management, inconsistency in conceptualization and measurements.
The formation of a modern information support system in system research should be aimed at
modernizing the tools for managing organizational and technical systems in the context of dynamic
transformations.
3. Materials and Methods

   The properties of information support for decision-making under conditions of uncertainty were
used as research materials:
 Information security
 Protection from the influence of the external environment
 Controllability, i.e. the possibility of adjusting control actions
 Structural heterogeneity, i.e. the presence in the system of various elements with different weight
   contributions
 Effectiveness, i.e. the emergence of a new quality in the combination of a specific set of elements.
   Probabilistic mathematical Markov processes models are used as methods of information support
and decision-making modeling.

4. Methodology

   The dynamics of a hierarchical control system can be described using the equations

                                           dx
                                           dt
                                              = f(𝑥, 𝑢, 𝑣1 , 𝑣2 , … , 𝑣𝑛 ), x(t0)=x0                     (1)

    where xEm – vector of phase variables, Em – state space at a moment in time t.
    The change in the state of information support of the management system occurs under the influence
of the control center u(t)U and control subsystems v1(t), v2(t), …, vn(t), vi(t)Vi. Assuming that the
control parameter of the center u changes continuously in time, the resulting function u(t), t[t0, t],
u(t)U, will be measured by t. Sets U, V1, V2, …., Vn will be the sets of admissible controls.
    Every program control u(t), t[t0, t] determines the trajectory of the control system x(t), t[t0, t].
The set of ends of the trajectories of the differential equation (1) represents the reachability set starting
from the initial state for all possible program controls u(t)U, t[t0, t]. Each new event depends only
on the previous one and does not depend on all other events. Thus, the resulting control trajectory ends
with a point x(t), into which the system passes at time t. This point will be the starting point of the
Markov process. The original probability distribution can be represented by the equation:

                                            P(𝑥0 = S) = 𝑞0 (S)𝑆𝐸                                       (2)

       where ∀ – universal quantifier,
        S – discrete states,
        q0 – probability distribution at a moment in time t0 = 0.
       The set E represents a finite number of possible states.

                                              E = {𝑒1 , 𝑒2 , … , 𝑒𝑛 }                                    (3)

        Range of random variable {xn}, the values of which determine the parameters of information
support of intelligent control systems, is the state space, and the value n, characterizing the movement
of this parameter in the control system, – is the step number. The probabilities of transition from one
state to another are represented as square matrices.

                                   𝑃𝑖𝑗 (n) = P(𝑥𝑛+1 = j⃒𝑥𝑛 = i)                                          (4)
                                               s1   s2 ... sn
                                    s1      p11    p12   ...   p1n 
                               P  s2      p       p22   ...   p2 n 
                                            21                                                        (5)
                                     .      .       .    ...    . 
                                                                     
                                    sn      pn1    pn 2 ...    pnn 

       Elements, pij denote the probability of transition from the state si into the next.
       The transition probability matrix expresses the probability that the state of the control system at
time n + 1 is subsequent to other states.

                        P(xn+1 = 𝑆n+1 ⃒xn = 𝑆n ) = P(Sn, Sn+1 )∀(Sn+1 , Sn ) ← E ⨯ E                   (6)

       The Markov chain will be homogeneous if the transition probability matrix does not depend on
the step number.

                                               Pij (n) = Pij                                           (7)

       According to the Kolmogorov-Chapman equation, the transition probability matrix for n steps
in a homogeneous Markov chain is the n-th power of the transition probability matrix for one step.

                                         𝑃 (𝑥𝑛 = 𝑆𝑛 ⃒𝑥0 = 𝑆0 ) = 𝑃𝑛                                    (8)



        Markov chain at any moment of time can be characterized by vectors by a row Ci of the matrix
of transition probabilities P.
        Transition probability or conditional probability of an event Skj, upon condition Smj-1 is equal to

                                              Pmkj ≜ [Skj⃒Smj-1]                                       (9)

        Skj – the probability that the system after j-steps will be in the state Sk, ≜ - mathematical equal
sign by definition.
        The probability distribution for identifying the state of information support of the control system
does not depend on time, but only on transitions from the current state to the corresponding control
iterations. By developing the proposed methodological approach, it is possible to establish a sequence
of transitions from the initial current state, creating the necessary control base. The stochastic model
compiled in this way is shown in Figure 1.
           Defining parameters                 Determining the                          Determining the
                and zones                    information support                      characteristics of the
                                                  trajectory                        influence of the external
                                                                                          environment



                                   Determination of the current state         Selection of random variables
                                   of information support parameters                 indexed by time




                               Formation of an information       Establishment of         Defining discrete
                                  situation related to the        transition state          state spaces
                                    reaction to external           probabilities
                                         influences



              Compilation of          Construction of a             Simulation of            Construction of
               the matrix of           directed graph              random events            stochastic models
                 transition
               probabilities


Figure 1: Stochastic model of information support for intelligent control systems for complex objects
based on Markov chains

    The state of the control system can be described by a random process (t). Random process (t) will
be Markovian if its conditional probability distribution function at a future moment of time tn+1 does
not depend on the values of the process in the past moments t1, …, tn-1, and is determined only by the
value (tn)=xn at the present time tn’. Conditional distribution function P{(tn+1)<xn+1|(tn)=xn}=F(xn,
tn; xn+1, tn+1) will be a Markov transition function.

5. Experiment

   Below is an example of using information support for intelligent control systems for complex
organizational and technical objects based on Markov chains, compiled on the basis of an expert
assessment of the management activities of a real production facility (Table 1).

 Table 1
 Probability distribution of the current state of the parameters of information support of the control
 system
   Information         Information        Protection                                          Efficiency
    support            provision         from the         Controllability Structural
  parameters                             external                         heterogeneity
                                      environment
    efficiency              v1                v2               v3                v4                v5
      weight                27                19               17                12               25
contribution,%
     Each combination of information support parameters of intelligent control systems is assigned a
 certain probability, which is written as a line of the state matrix. In this case, the sum of the probabilities
 in the rows of the matrix is always equal to one.

                                       ∑𝑛𝑘=0 𝑃[Skj]= ∑𝑛𝑘=0 𝑝k(j)=1, j≥0                                    (10)

   The values of conditional probabilities of information support parameters at different stages of
 management are presented in Table 2.

 Table 2
 Conditional probabilities of information support parameters of intelligent control systems
Subsequent                      Information     Protection                                                  Efficien
state                           provision      from the       Controllability                                cy
                                                                                Structural
         Current                               external
                                                                                heterogeneity
          state                              environment

 information provision               0,11               0,29              0,14               0,2             0,26
   protection from the               0,12               0,19              0,17               0,25            0,19
external environment
      controllability                0,19               0,25              0,17               0,12            0,27
structural heterogeneity             0,17               0,27              0,19               0,12            0,25
        efficiency                   0,12               0,17              0,27               0,19            0,25


    The initial state vector, according to Table. 1 will be written in the form:


                                       p(0)=(0.27, 0.19, 0.17, 0.12, 0.25)                                 (11)


    The transition probability matrix is the following:


                                         0.11    0.29    0.14   0.2     0.26
                                         0.12    0.19    0.17   0.25    0.19
                                     A=||0.19    0.25    0.17   0.12    0.27||                             (12)
                                         0.17    0.27    0.19   0.12    0.25
                                         0.12    0.17    0.27   0.19    0.25


     Each row in the presented matrix has its own probability distribution. It is necessary to determine
 what is the probability of the influence of the information support parameters of intelligent control
 systems at various stages of their use.
     State S0 characterized by the fact that the working conditions are stable and do not depend on the
 influences of the external environment. Information support at the initial stage will be determined by
 the parameters vi, presented in table 1.
     The state of information support at the first stage of management S1 will be determined by the first
 row vector of the matrix A. The probability of the influence of this parameter p(1), characterizing the
 information security of the management process vi according to the methodology for calculating
 Markov chains will be equal to:
                                         0.11 0.29      0.14     0.2     0.26
                                         0.12 0.19      0.17     0.25    0.19
   p(1)=(0.27, 0.19, 0.17, 0.12, 0.25)х||0.19 0.25      0.17     0.12    0.27||=
                                         0.17 0.27      0.19     0.12    0.25
                                         0.12 0.17      0.27     0.19    0.25
   = (0.1393, 0.2318, 0.1893, 0.1838, 0.2447)                                                          (13)

    The probability that, being in a state S1, information support of the control system will go into the
state S2, characterized by unstable, albeit predictable, changes in the environment is p(2). Information
support at this stage of management will be determined by the parameter v2. The probability of the
influence of this parameter characterizing the security of the control system v2 and its information
support from fluctuations in the external environment is equal to:

                                                    0.11       0.29     0.14    0.2   0.26
                                                    0.12       0.19     0.17   0.25   0.19
                                                  |
   p(2)= (0.1393, 0.2318, 0.1893, 0.1838, 0.2447)х|0.19        0.25     0.17   0.12   0.27||=
                                                    0.17       0.27     0.19   0.12   0.25
                                                    0.12       0.17     0.27   0.19   0.25
   = (0.1392, 0.2218, 0.1915, 0.1763, 0.2374)                                                          (14)

    Comparison of probability parameter values represented by a row vector p(0), with the
corresponding probability distributions of the information support of the control system at the first stage
of control p(1) ed to the formation of a number of practical recommendations. A comparison of identical
values of the parameters presented in (11) and (13) showed their increase at the first stage of
management information support, which can be considered satisfactory, except for the last parameter
"effectiveness" v5, which has decreased. This forces us to move to the next stage of control information
support with the probability p(2).
    In conditions of instability of functioning due to unpredictable pressures of the external environment,
the probability of transition of information support of the control system from the state S2 and S3 is equal
to p(3). Information support at this stage of management will be determined by the parameter v3. The
probability of the influence of this control information support parameter characterizing controllability
v3, that is, the possibility of adjusting control actions is equal to:

                                                0.11      0.29    0.14    0.2      0.26
                                                0.12      0.19    0.17    0.25     0.19
p(3)=(0.1392, 0.2218, 0.1915, 0.1763, 0.2374)х||0.19      0.25    0.17    0.12     0.27||=
                                                0.17      0.27    0.19    0.12     0.25
                                                0.12      0.17    0.27    0.19     0.25

   = (0.1368, 0.2184, 0.1874, 0.1725, 0.2335)                                                          (15)

    Comparison of identical parameters presented in (14) and (15) showed an increase for the parameters
v1 and v3. All other parameters have been reduced. This was the basis for the transition to the next stage
of management information support. It should be noted that the state p(0) characterizes only the initial
state of the system without control. The first control step starts with p(1). In this case, the probability
of the influence of information support parameters at each control step should decrease.
    The probability of transition of information support of the control system from the state S3 into a
state S4 is equal to p(4). Information support at this stage of management will be determined by the
parameter v4. It is determined by cyclic multiplication (12) by the corresponding row of the transition
matrix A.
                                                 0.11            0.29     0.14      0.2      0.26
                                                 0.12            0.19     0.17     0.25      0.19
p(4)=( 0.1368, 0.2185, 0.1874, 0.1725, 0.2335)х||0.19            0.25     0.17     0.12      0.27||=
                                                 0.17            0.27     0.19     0.12      0.25
                                                 0.12            0.17     0.27     0.19      0.25
=(0.1342, 0.2143, 0.1839, 0.1695, 0.2291)                                                             (16)

   Comparison of identical parameters of information support of the control system, presented in (15)
and (16), showed a decrease in all parameters except v3. This served as the basis for the transition to the
next stage of management. The probability of transition of information support of the control system
from the state S4 into a state S5 is equal to p(5).

                                                0.11       0.29   0.14    0.2    0.26
                                                0.12       0.19   0.17    0.25   0.19
p(5)=(0.1342, 0.2143, 0.1839, 0.1695, 0.2291)х||0.19       0.25   0.17    0.12   0.27||=
                                                0.17       0.27   0.19    0.12   0.25
                                                0.12       0.17   0.27    0.19   0.25

= (0.1318, 0.2103, 0.1804, 0.1664, 0.2249)                                                            (17)

   Comparison of identical parameters of management information support, presented in (16) and (17),
showed their decrease in all parameters. This indicates the quality of information support of the
management system.
   Oriented graph of Markov chains for the considered example of information support of intelligent
control systems for complex organizational and technical objects presents on Figure 1.



                                                          0.41                                        0.27
       0.33                                                                       protection from the
                    information
                     provision                                                   external environment
                         ν1                               0.15                              ν2
       0.26                                                                                              0.22
                           0.18                                                            0.43
                                                          0.18

      information support of                                       0.18
                                                 0.46                                        controllability
          control systems
                                                                                                   ν3
      0.36                                                                         0.37                 0.30
                      0.35                                                                  0.35
                                                   0.37
                                                                                   structural
                      efficiency                                                 heterogeneity
                                                                                        ν4
                           ν5                           0.48
                                                                                           0.17
                                0.28


Figure 2: Oriented graph for building Markov chains for evaluating the information support of
intelligent control systems for complex organizational and technical objects

    Since in the presented directed graph the sum of the outgoing probabilities for each parameter of the
information support of the control system is equal to 1, the presented scheme can be considered adequate
to the calculations performed.
    Since in the presented directed graph the sum of the outgoing probabilities for each parameter of the
information support of the control system is equal to 1, the presented scheme can be considered adequate
to the calculations performed.
6. Results and Discussion
    Markov processes are a convenient mathematical model for various technical applications. When
managing complex multi-level organizational and technical objects, depending on the values of a
random process (t) and sets of observation moments Markov processes can be divided into moments
with discrete and continuous time. The transition from one state of the system to another occurs at
regular intervals, which are steps.
    Problem situations arising in the process of managing complex multi-level organizational and
technical objects, caused by the influence of the external environment, can be methodologically reduced
to separate associative homogeneous classes of management decisions, i.e. to some set of strategic
alternatives. If the analyzed problem situation is not associated with the existing classes of control
alternatives, the next hierarchy level procedure for the formation of control information support is
formed, which allows other properties of control information support to be involved in solving the
problem.
    At the initial moment of time, focusing on the initial conditions, the optimal control of the
organizational and technical system is chosen in the time interval [t0, t]. After some time, the state of
the system changes, additional information appears, and there is a transition to the next level of the
hierarchy of information support for the management process. All possible states of information support
process parameters are enumerated. These iterations are carried out for various states of the intelligent
control system with their own parameters and probabilities. Since the processes of transformational
transformations in the control system do not have a continuous time stamp, a sequence of states can be
used as time.
                                                 Start


                                            parameter input




                                          formation of a data
                                           array for analysis



             raw data                     intuition and expert
            extraction                         experience



        use of additional                     application
          information                          software



                                        functioning of software
                                               modules



                               No            assessment of         Yes
                                            implementation                  definition of
                                             opportunities                   restrictions



                                                                 Yes                             No
                                                                         building a directed
                                                                                graph



                                                                           evaluation of
                                                                            alternatives


                                                                          output of results


                                                                                end

Figure 3: Structuring the information space for interactive support of management decisions under
conditions of uncertainty

   The proposed modernization of the use of Markov chains consists in replacing equal step intervals
with a discrete sequence of states, which is determined by unpredictable external environmental
influences. Such modernization of Markov chains is a novelty of use in decision-making information
support in the management of multi-level organizational and technical objects.
    The processes of developing and improving the management of organizational and technical systems
operating under conditions of unpredictable influence of the external environment are determined by
the information space.
    The processes of developing and improving the management of organizational and technical systems
operating under conditions of unpredictable influence of the external environment are determined by
the information space, the structuring of which is shown in Figure 3.
    The performed structuring of the information space for interactive support under conditions of
uncertainty makes it possible to assess the scope of information support for intelligent control systems
for complex multi-level organizational and technical objects, which is based on software and tools,
expert systems, intelligent components, systematization of organizational processes. It is based on
information retrieval, data mining, knowledge search in databases, reasoning based on precedents,
simulation modeling, neural networks, cognitive modeling.

7. Conclusions

1. For information support of decision making in the management of multilevel organizational and
   technical objects under conditions of uncertainty, it is proposed to use probabilistic mathematical
   models based on Markov processes. This makes it possible to simulate and regulate the process of
   making relevant decisions in real time under conditions of uncertainty.
2. In contrast to the traditional use of Markov chains, information support for decision-making in the
   management of multi-level organizational and technical objects under the uncertainty of the
   influence of environmental factors provides for the replacement of equal step intervals by a discrete
   sequence of states determined by unpredictable external environmental influences in the study of
   control operations. This will contribute to solving the urgent problem of increasing the efficiency of
   managing organizational and technical facilities in difficult operating conditions.

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