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)