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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>Journal of
Physics: Conference Series</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.1109/WSC.2006.322972</article-id>
      <title-group>
        <article-title>Problems of Construction of Smart Innovative Enterprises</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Mykola Odrekhivskyі</string-name>
          <email>Mykola.V.Odrekhivskyi@lpnu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Liubomyr Vankovych</string-name>
          <email>Liubomyr.Y.Vankovych@lpnu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Orysya Pshyk-Kovalska</string-name>
          <email>Kovalska@lpnu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Lviv Polytechnic National University</institution>
          ,
          <addr-line>12 S. Bandera St, Lviv, 79013</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2006</year>
      </pub-date>
      <volume>62</volume>
      <issue>7</issue>
      <fpage>25</fpage>
      <lpage>30</lpage>
      <abstract>
        <p>The purpose of the scientific work is to study problems of smart management and design of integrated intelligent information management system of smart innovative enterprises. The approaches to formation of the smart management process are studied. These approaches investigation additionally proofs the importance for modern business conditions to design the management model that provide economic efficiency of enterprises. The interpretation of the concepts of digital factory, smart factory and virtual factory has been further developed. To perform the tasks of the "virtual factory" for the management of smart innovative enterprises in general, it is proposed to use the intelligent information management system of innovative enterprises as part of integrated intelligent information innovative enterprises. Based on the system intelligent management system of smart innovative enterprises has been developed. It will make it possible to design, construct and restructure the intelligent management systems of smart innovative enterprises as a whole and their units in to adapt them to modern business conditions. The study of smart and sustainable manufacturing of enterprises based on its integral index was tested. The methodological basis of the investigation is a set of general and special methods of scientific researches. The implementation of these methods is caused by the goal and logic of problems solving for smart management and design the system of smart innovative enterprises that are based on the using of Industry 4.0 concept. The theory of Markovian stochastic processes using the Chapman-Kolmogorov equation systems was used as a mathematical tool to evaluate efficiency of smart management. Based on this mathematical tool, the software for evaluation and prediction of state of smart innovative enterprises development was presented and tested for adequacy. The prediction results can be used to support managerial decision-making, developed software can be incorporated into the structure of the intelligent management system of smart innovative enterprises and applied for the study of sustainable manufacturing of enterprises.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>4.0
Smart innovative enterprises, smart management, sustainable manufacturing, digital factory,
smart factory, virtual factory, integrated intelligent information management system, Industry</p>
    </sec>
    <sec id="sec-2">
      <title>1. Introduction</title>
      <p>Smart enterprise today is Smart Management, IT data platforms and real management knowledge,
sources of business processes (production, distribution, sales) combined. Knowledge management IT
platforms provide: read measurement values from all data sensors and import data from the database;
processes, calculates all indicators and models of business/production/sales; evaluates the results and
condition of business facilities (products, customers, suppliers, technology, finance, social networks,
environment, quality and enterprise in general); corrects results in smart management on regular
mobile devices with clear identification and if "yes", then "where" and "why". Smart management
EMAIL:</p>
      <p>
        2022 Copyright for this paper by its authors.
takes into account real events and, if something is "wrong" in accordance with the planned goals,
analyzes business processes and implements management influences aimed at achieving goals. It is
worth noting that over the past few decades, production has progressed rapidly, it has become more
automated, computerized and complex, thanks to improved information technology, production
methods and technologies, equipment and facilities, new and improved materials, improved
understanding of process characteristics through analysis big data. This allowed the use of new
production methods (cyber production and distributed production), new production processes
(production of various additives and hybrid production) [35]. Modern methods of production and
organization of technological processes equipped with sensors, computational methods, new
materials, data analytics, artificial intelligence, organizational management and communication
technologies form a smart manufacturing [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. That is, smart manufacturing is a new form of
production that combines today's and tomorrow's production assets with sensors, computing
platforms, communication technologies, modeling, intelligent engineering, data intensive modeling,
and management. It uses the concepts of cyber-physical systems, the industrial Internet of Things,
cloud and service-oriented computing, artificial intelligence and data science [
        <xref ref-type="bibr" rid="ref2">2, 41</xref>
        ]. Smart
manufacturing systems are fully integrated production processes that respond in a timely manner to
the changing requirements and conditions of the enterprise, supply chain, consumer needs [38]. Smart
manufacturing allows you to get all the information about the production process, when it is needed,
where it is needed, and in the form in which it is needed throughout the production chain, to make
optimal decisions [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. Such technological progress will allow a wide range of industries to reduce
costs, improve quality, increase productivity, improve material management, increase efficiency,
reduce energy consumption and improve the health and safety of workers [
        <xref ref-type="bibr" rid="ref3">3, 40</xref>
        ]. Continuous
monitoring and improvement of key performance indicators (KPIs), improvement of sustainability
indicators of smart manufacturing systems will help in this. Sustainable manufacturing requires a KPI
balance, covering economic, environmental and social efficiency [11]. However, smart and
sustainable manufacturing systems are complex in nature, often due to diverse, heterogeneous
technological processes that form quantitative indicators of the production process, ensuring data
integrity, so to establish the relationship between systems and subsystems is extremely difficult [
        <xref ref-type="bibr" rid="ref1">1,
39</xref>
        ]. The evolution of manufacturing, new processes, materials and assistive technologies are
developed based on the needs of today. Additional efforts are being made to quantify metrics, model
systems and subsystems, and to develop methods for quantifying performance indicators. To address
these shortcomings, the US National Institute of Standards and Technology (NIST) is working on
[53]: developing standard intelligent methods of measuring production; modeling and characterization
of smart manufacturing; developing guidelines on methods, metrics and tools that enable production
stakeholders to assess and ensure the cybersecurity of smart manufacturing systems; developing
methods and approaches to the integration of smart manufacturing systems. In addition, the developed
standards of ASTM (American Society for Testing and Materials) led by NIST (National Institute for
Standards and Technology) [42, 43] guide companies to assess and characterize the sustainability of
manufacturing processes and supply chains. That is, the essence of smart manufacturing is based on
intelligent technologies and production processes, its monitoring, materials, data, sustainability,
resource and network sharing. Since today smart enterprises are divided into smart manufacturing,
digital and virtual enterprises [37, 44], in the work, based on the concept of smart manufacturing,
digital and virtual enterprises, it is proposed to develop projects to build smart innovative enterprises.
The structure of the innovation process is proposed to be based on the structure of the innovation
process, which includes: idea generation, knowledge transfer, research (basic and applied research),
design and research work, diffusion of innovations and technologies, technological preparation of
production, production, marketing and commercialization of innovative products, its implementation,
use, modernization and renovation. This will help build smart innovative enterprises (SIE) through the
effective integration of digital, smart and virtual enterprises.
      </p>
    </sec>
    <sec id="sec-3">
      <title>2. Literature Review</title>
      <p>
        Many scientists have studied the problems of building smart enterprises based on the concept of
smart manufacturing, digital and virtual enterprises, which is the basis of Industry 4.0 [8, 10]. Andrew
Kusiak [
        <xref ref-type="bibr" rid="ref2 ref3">2, 3</xref>
        ], Shreyanshu Parhi, Kanchan Joshi, Milind Akarte [38], Zakoldaev D.A.,
Korobeynikov A.G., Shukalov A.V., Zharinov I.O. [54] explore concepts "smart factory", "smart
manufacturing" and "factory of the future". D. Kibira, M.P. Brundage, S. Feng, and K.C. Morris [12],
Hugh Boyes, Bil Hallaq, Joe Cunningham, Tim Watson [21], Sathyan Munirathinam [37], Steve
Ranger [45] argue that "smart manufacturing" and "industrial Internet of Things" are at the heart of
Industry 4.0 today. Y. Lu, K.C. Morris, and S.P. Frechette [54] point out that attempts are being made
today to divide the factories of the future into three main types − digital factory, smart factory and
virtual factory. Stephen Furber [44] emphasizes the use of artificial intelligence, machine learning and
the Internet to construct smart enterprises. Erum Mehmood, Tayyaba Anees [14], Saeed Shahrivari,
Saeed Jalili [36], Tongya Zheng, Gang Chen, Xinyu Wang, C.Y. Chen, Xingen Wang, Sihui Luo [50]
explore intelligent big data processing technologies that provide new knowledge for decision making
in the form of more objective and scientifically sound smart decisions. David Tegarden, Barbara
Haley Wixom, Alan Dennis [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], Maria Rashidi, Maryam Ghodrat, Bijan Samali and Masoud
Mohammadi [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ], Deepika Verma [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] think that distributed artificial intelligence, integrated intelligent
information systems as multi-agent systems are the most suitable class of models for the
implementation of smart management functions.
      </p>
      <p>Based on the analysis of recent research and publications, it can be concluded that the key aspect
of constructing a SIE can be attributed to:
• the concept of smart industries, digital and virtual enterprises, their effective integration;
• intellectualization of all SIE activities;
• big data mining and multicriteria decision analysis;
• construction of an integrated intelligent information system (IIIS).</p>
    </sec>
    <sec id="sec-4">
      <title>3. Methods</title>
      <p>To construct smart innovative enterprises in the work used: the concept of smart manufacturing,
digital and virtual enterprises; methodology of structural design, which combines natural and artificial
intelligences and allows: to intellectualize all the processes of SIE; to carry out intellectual analysis of
big data and multicriteria analysis of decisions; intellectualize the organizational management of the
SIE in general; take into account the possibilities of intellectualization of all stages of management
and, accordingly, to build an integrated intelligent information system (IIIS).</p>
      <p>The theory of Markovian stochastic processes using the Chapman – Kolmogorov equation
systems, based on them dynamic and static mathematical models solved by computer technology,
used to support decision-making on the condition of development of SIE or any element of their
hierarchy and on the choice of managerial influences on these states.</p>
      <p>Cognitology methods have been used to develop the intelligent information system (IIS),
according to which IIS is proposed to be considered as a logical-cognitive model of a social agent,
and integrated IIS as multi-agent systems based on synthesis of natural and artificial intelligence and
take into account adequate formalization of decision-making processes.</p>
    </sec>
    <sec id="sec-5">
      <title>4. Results and Discussion</title>
      <p>
        It is proposed to build smart innovative enterprises on the basis of the concept of smart industries,
digital and virtual enterprises, their effective integration. The concepts of "smart factory", "smart
manufacturing", "factory of the future" [
        <xref ref-type="bibr" rid="ref3">3, 38, 54</xref>
        ] appeared very recently and do not yet have clear
definitions. Now they are used as synonyms, although the concept of "factory of the future" is more
voluminous and includes not only "smart manufacturing", but also digital and virtual enterprises.
      </p>
      <p>The concept of "smart production" means fully integrated corporate production systems that are
able to respond in real time to changing production conditions, supply chain requirements and
satisfy customer needs. That is, in real time, as quickly as possible, the planned goals are achieved
through the intensive and comprehensive use of information technology, "Industrial Internet of
Things" and cyberphysical systems at all stages of production and supply products. "Smart
manufacturing" and "Industrial Internet of Things" are today the basis of Industry 4.0 [12, 37, 45],
which is characterized by fully automated production, where management of all processes is
carried out in real time and taking into account changing external conditions. Industrial Internet of
Things (IIoT) [21, 37] means a system of integrated computer networks and connected industrial
(production) facilities with built-in sensors and software for collecting and exchanging data, with
the possibility of remote control and management in an automated mode, without human
intervention.</p>
      <p>The concept of "smart manufacturing" is quite vague (sometimes it means active robotics,
automation of most production and management processes and even just innovat ion), and the
transition to it occurs in several stages, which takes more than one year. Today, attempts are being
made to divide the factories of the future into three main types - digital, smart and virtual [46, 54].</p>
      <p>The main task of the "digital factory" - the development of models produced using digital
design and modeling [26, 34, 52]. These tools begin to be used at the stage of research and
development, and end with the creation of digital mock-up (DMU), digital twin, research sample,
production of small series or individual products to customer requirements.</p>
      <p>"Smart factories" are aimed at mass production, but while maintaining maximum flexibility of
production. This is ensured by a high level of automation and robotics of the enterprise.
Automated control systems for technological and production processes are widely used. Industrial
Internet of Things (IIoT) technologies provide machine-to-machine interoperability, integration of
Digital Factory with Smart Factory [30]. The production assets of an ent erprise equipped with
sensors and means of communication are able to produce products almost (or not at all) without
human intervention. Big Data technologies allow to cope with sharply increased information flows
coming from sensors and automated control systems [14, 36, 50].</p>
      <p>"Virtual factory" is an integrated structure for the design and analysis of production systems
[47], which is a network of digital and "smart" factories, which also includes suppliers of
materials, components and services. A number of automated enterprise management systems are
used in such a factory to manage global supply chains and distributed production assets. With the
right degree of integration, they allow you to develop and use a virtual model of all organizational,
technological, logistics and other processes that take place not only in the enterprise but also at the
level of distributed production assets and global supply chains, up to after -sales service. This
provides integrated management of business processes, products and development of production
systems, the implementation of the functions of smart management.</p>
      <p>With the emergence of digital ecosystems, manufacturing enterprises from isolated systems,
which independently perform all the necessary business processes for production, will be
transformed into open systems that connect different market participants. The means of production
of such systems will be managed not by personnel, but by cloud services. The ultimate goal of all
these transformations is not production, but the provision of services to consumers [37, 45].
Therefore, today, based on the concept of digital factory, smart factory and virtual factory, it is
advisable to develop projects to build new enterprises and such enterprises could be SIE.</p>
      <p>Smart innovative enterprise (SIE), therefore, is a management approach focused on the use of
new technologies for the development of innovative enterprises. Because today, entrepreneurs
need new creative ideas and solutions that would accord the requirements of a world t hat is
changing every second. We are talking about the use of artificial intelligence, machine learning
and the Internet [44, 46] – all the latest technologies that help to more effectively implement
innovative processes of innovative enterprises. All this will provide employees of the innovative
enterprises: the ability to automate innovation processes and implement machine learning
algorithms in all areas of the innovative enterprises; digital platform that will facilitate data
management and integration of components of the innovation process; intelligent technologies that
analyze data and provide the most accurate real-time results for the required transactions. It should
be noted that the use of artificial intelligence in the innovative enterprises will help to more
quickly analyze a variety of situations and make more informed decisions, closely link analytics
with semantic and logical processes of information processing.</p>
      <p>Because only information based on reliable data is the basis for a variety of tactical and strategic
operations, this leads to lower costs, reduced risks and reliable data that provides a deeper
understanding of the innovation process. Therefore, the structure of the SIE is proposed to be based
on the structure of the innovation process, which would be managed at all stages of its organization by
an integrated intelligent information management system of smart innovative enterprises (IIIMS SIE)
(Fig. 1).</p>
      <p>Integrated intelligent information management system of smart innovative enterprises (IIIMS SIE)
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      <sec id="sec-5-1">
        <title>Intelligent research information system (IRIS)</title>
        <sec id="sec-5-1-1">
          <title>Ideas</title>
        </sec>
        <sec id="sec-5-1-2">
          <title>Information</title>
        </sec>
      </sec>
      <sec id="sec-5-2">
        <title>Research work</title>
      </sec>
      <sec id="sec-5-3">
        <title>Basic research</title>
      </sec>
      <sec id="sec-5-4">
        <title>Applied research knowledge</title>
        <p>Transfer of
innovations
technologies</p>
        <sec id="sec-5-4-1">
          <title>Discovery</title>
          <p>Inventions
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IIMS</p>
        </sec>
        <sec id="sec-5-4-2">
          <title>Innovative products</title>
        </sec>
      </sec>
      <sec id="sec-5-5">
        <title>Marketing</title>
      </sec>
      <sec id="sec-5-6">
        <title>Commercial sales</title>
        <p>Innovative
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        <p>M</p>
      </sec>
      <sec id="sec-5-7">
        <title>Technological preparation of manufacturing</title>
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        <p>According to the given structure, the components of the innovation process include: generating
ideas; knowledge transfer; research work, which includes basic and applied research; design and
research work; technological preparation of manufacturing and manufacturing; marketing and support
of innovative products for consumers during its operation, modernization and renovation; audit of
innovative goods and services in order to complete i (i = 1, 2,…) innovation cycle (ІЦi), start ІЦi+1
and ensuring the spiral development of innovative enterprise (Fig. 2), where І1, І2, …− idea 1, idea 2,
…, idea і, … .</p>
        <p>It is impossible to organize a full innovation cycle in some enterprises, so it is proposed to include
innovation units in the structure of such enterprises, which would be engaged in the transfer of
knowledge, technology and innovation (resource, process, product, marketing, management,
organizational, diffusion etc.).
• APS (Advanced Planning and Scheduling) – synchronous (advanced) manufacturing
planning;
• MES (Manufacturing Execution Systems) – manufacturing executive system designed to
solve operational tasks of design, production and marketing management;
• SCADA (Supervisory Control and Data Acquisition) – a system that performs dispatching
functions (collection and processing of data on the state of equipment and technological processes)
and helps to develop software for embedded equipment;
• CNC (Computer Numerical Control) – system of direct software control of technological
equipment on the basis of controllers (specialized (industrial) computers) built into technological
equipment with numerical software control;
• IIoT (Industrial Internet of Things);
• Big Data.</p>
        <p>The tasks of the "virtual factory" can be implemented by IIRMS and IIMS based on the
following systems and technologies:
• AEMS – automated enterprise management systems;
• ERPII (Enterprise Resource Planning) – supports all business processes of the enterprise:
planning, financial management, sales, production, logistics, operations, relationships with customers
and suppliers, reporting, etc., developed on the basis of ERP (Enterprise Resource Planning) –
enterprise planning and management and includes SCM (Supply Chain Management) and CRM
(Customer Relationship Management).</p>
        <p>The intermediate position between automated enterprise management systems and automated
process control systems is occupied by the production executive system MES (Manufacturing
Execution Systems), designed to solve operational problems of design, production and marketing
management. Data management in the integrated information space during all stages of the product
life cycle is entrusted to the product lifecycle management system PLM (Product Lifecycle
Management). A characteristic feature of PLM is the interoperability of different automated systems
of many enterprises, i.e. PLM technologies (including CPC technologies, collaborative product
commerce) is the basis that integrates the information space in which CAD, ERP, PDM, SCM, CRM
and other automated enterprise systems operate. That is, the PLM system can be the basis for the
construction of IIIMS SIE.</p>
        <p>The world is changing faster and faster, there are no more adequate ideas and ways of working
yesterday. This is due to the rapid commercialization of products and services, convergence of
strategies. Firms that rely on yesterday's ideas, yesterday's products and yesterday's assumptions are
very vulnerable today [49]. Creative thinking and generating ideas are at the heart of innovation
today. Intelligent information systems of scientific research today must formulate qualitative ideas,
expand opportunities for the formation of new questions based on available answers, including
questions that have not been asked before. The ideas here should be understood as a general idea of a
possible innovative product that the SIE could offer to the consumer [20].</p>
        <p>The process of generating ideas, which in SIE should be based on modern methods of generating
ideas [32, 51] on innovative goods and services, begins with their emergence (emergence, creation),
constant and systematic search, accumulation, selection and formation of a portfolio or bank of ideas
[23, 33] in IRIS.</p>
        <p>The sources from which ideas can come in IRIS are proposed to be divided into two groups:
• external, which may include entities with which the SIE interacts or which influence its
activities. At the SIE among the divisions that work with external sources and where they get ideas
for new products, we can single out the divisions of R&amp;D, diffusion of innovations and
technologies, marketing, sales and supply;
• internal, which include processes in SIE, namely the results of the units on the basis of which
employees form ideas for a new product or service. In this case, it is proposed to include in this
group units of strategic planning and development, research, design and experimental work,
technological preparation of production and production units. These are the most important
departments that are well aware of the advantages and disadvantages of SIE, its financial, technical
and production capabilities assess the current state and prospects.</p>
        <p>Smart innovative enterprises need to constantly look for new ways to generate ideas in order to
become more competitive. Researchers and practitioners advocate open approaches, involving
outsiders, crowdsourcing platforms for innovation and ideas, where crowdsourcing is an opportunity
to get ideas from external sources [29]. That is, IRIS with the right tools and features should not only
speed up the quantity but also the quality of ideas. Outsiders in the innovation process are seen as a
powerful tool to increase success and revenue from new proposals.</p>
        <p>IRIS is an intelligent support system for research conducted in order to formulate and store ideas,
their selection and implementation. IRIS can use a variety of platforms, including online platforms for
crowdsourcing and identifying the best of a number of ideas. It is important here to use modern
research methods to substantiate the further promotion of ideas at all stages of the innovation process.
IRIS models expert opinions and takes into account the specifics of the problems to be solved. She
uses advances in artificial intelligence and machine learning to conduct her chosen experiments to
increase the accuracy and effectiveness of her research. This fundamentally changes the paradigm of
scientific research from the search for laws based on hypotheses to the construction of empirical
models based on data on the objects of study. Many systems to be studied have too many variables
and are too complex for people to comprehend and use in a timely manner. Therefore, IRIS is
becoming relevant as a set of automated methods for building empirical models based on intelligent
processing of big data in real time.</p>
        <p>Today, there are two categories of technologies that take into account the processing of big data, it
is batch and streaming [14, 36, 50]. Streaming deals with continuous data and is a tool for converting
big data into fast data. The batch model requires a set of data collected over time. Streaming requires
the receipt of data in IRIS micropackets or in real time. Batch processing is often used when working
with large amounts of data or legacy data sources where data cannot be delivered by streams. In both
cases, all data must be uploaded to a specific type of storage, database, or file system, and then
processed. Data streams can also be involved in processing large amounts of data, but batch mode
works best when real-time analytics are not required. Streaming is responsible for processing data in
dynamics and fast delivery of analytical results, it generates almost instantaneous results.</p>
        <p>Both models are valuable, and each can be used to solve different situations. Therefore, IRIS is
proposed to be used as an intelligent real-time data processing system based on obtaining, processing,
analyzing and making real-time decisions. IRIS as an intelligent real-time data processing system
must be equipped with a big data package platform, data analysis tools and machine learning models.</p>
        <p>Research sometimes has to be conducted in areas with poorly formalized knowledge, but the
analysis of empirical data in order to make optimal decisions in these areas is necessary. In this case,
it is advisable to use information systems that perform intelligent analysis of empirical data, in
particular intelligent systems based on the JSM-method [24, 28]. Existing intelligent JSM systems
(IntJSM) are proposed to be integrated into IRIS and they should include:</p>
        <p>IntJSM = Task solver + Information environment (fact base (BF) and knowledge base (BK) +</p>
        <p>Intelligent interface (dialogue + presentation of results + work training).</p>
        <p>
          To perform the tasks of the "virtual factory" to implement the functions of smart management, it is
proposed to use the appropriate intelligent information management system of smart innovative
enterprises (IIMS SIE), the structure of which is shown in Fig. 3 and which can be integrated into the
IIMS SIE. Object-oriented integrated and distributed databases and knowledge bases, expert systems,
decision support systems (DSS), integrated neural networks and fuzzy logic tools can form the basis
of the tools needed to design and operate IIMS SIE. DSS allows you to model and automate
decisionmaking processes, model and automate SIE management processes in general. Distributed artificial
intelligence, integrated intelligent information systems as multi-agent systems [
          <xref ref-type="bibr" rid="ref5 ref6 ref7">5-7</xref>
          ] are the most
suitable class of models for the implementation of integrated IIMS SIE. Therefore, it is advisable to
consider IIMS SIE as a logical-cognitive model of a social agent, and integrated IIMS SIE as a
multiagent system.
        </p>
        <p>A modular structure was chosen to build the IIMS SIE, which will provide it with flexibility,
adaptability to environmental conditions and survivability. The structure of decision support modules
(modules M3 and M4), which are able to support decision making and explanation, is proposed to
include: subsystems of knowledge accumulation of the first and second kind, knowledge base, user
interface, subsystems of decision making and explanation. Necessary decisions when using IIMS SIE
will be made on the basis of expert knowledge, which, respectively, can be highly qualified specialists
in relevant fields of knowledge (knowledge of the first kind), as well as knowledge obtained based on
a priori information and research results of SIE (knowledge of the second kind).</p>
      </sec>
      <sec id="sec-5-8">
        <title>Module to support decision-making on</title>
        <p>the condition of innovation activities (М3)</p>
      </sec>
      <sec id="sec-5-9">
        <title>Module to support decision-making on managerial influences (М4)</title>
      </sec>
      <sec id="sec-5-10">
        <title>Knowledge base</title>
      </sec>
      <sec id="sec-5-11">
        <title>Knowledge base</title>
      </sec>
      <sec id="sec-5-12">
        <title>Machine conclusions</title>
      </sec>
      <sec id="sec-5-13">
        <title>Explanation decisions</title>
        <p>Accumulation of
knowledge 1st kind
Accumulation of
knowledge 2st kind
Accumulation of
knowledge 1st kind
Accumulation of
knowledge 2st kind</p>
      </sec>
      <sec id="sec-5-14">
        <title>Machine conclusions</title>
      </sec>
      <sec id="sec-5-15">
        <title>Explanation decisions</title>
      </sec>
      <sec id="sec-5-16">
        <title>Expert</title>
      </sec>
      <sec id="sec-5-17">
        <title>User interface</title>
      </sec>
      <sec id="sec-5-18">
        <title>Expert</title>
      </sec>
      <sec id="sec-5-19">
        <title>User interface</title>
      </sec>
      <sec id="sec-5-20">
        <title>Database</title>
      </sec>
      <sec id="sec-5-21">
        <title>Module for assessing and forecasting conditions of innovative enterprises (М2)</title>
        <p>Assessment of
conditions of
innovation activities</p>
      </sec>
      <sec id="sec-5-22">
        <title>Information processing</title>
        <p>Forecasting of
conditions of
innovation activities</p>
      </sec>
      <sec id="sec-5-23">
        <title>Storage information</title>
      </sec>
      <sec id="sec-5-24">
        <title>System interface</title>
        <p>. . .</p>
      </sec>
      <sec id="sec-5-25">
        <title>Module of states modeling of innovative enterprises (М5)</title>
      </sec>
      <sec id="sec-5-26">
        <title>Block of information</title>
      </sec>
      <sec id="sec-5-27">
        <title>Bank of models</title>
      </sec>
      <sec id="sec-5-28">
        <title>1 – model</title>
      </sec>
      <sec id="sec-5-29">
        <title>2 – model ... n - model</title>
      </sec>
      <sec id="sec-5-30">
        <title>Synthesis models</title>
      </sec>
      <sec id="sec-5-31">
        <title>Submission of models</title>
      </sec>
      <sec id="sec-5-32">
        <title>User interface</title>
      </sec>
      <sec id="sec-5-33">
        <title>Module for diagnosing conditions of innovative enterprises (М1)</title>
      </sec>
      <sec id="sec-5-34">
        <title>Diagnosis</title>
      </sec>
      <sec id="sec-5-35">
        <title>Data collection</title>
      </sec>
      <sec id="sec-5-36">
        <title>Primary data processing</title>
        <p>. . .
(IIMS SIE)
Source: own elaboration.</p>
        <p>This knowledge can be formalized and entered into the knowledge base as knowledge on the basis
of which the M3 module supports decisions about the state of SIE, and the M4 module - about the
managerial influences on them, which are implemented by the module. М6.</p>
        <p>
          Management decisions about SIE states in general, or any element of their hierarchy, in IIMS SIE
with the proposed structure can be supported by using Monte Carlo modeling, discrete modeling,
modeling dynamics and statics of systems [
          <xref ref-type="bibr" rid="ref7">7, 10</xref>
          ], digital business models and visual modeling,
operations research (simulation, business games, stochastic programming), decision trees, impact
diagrams, fuzzy logic tools, agent-based and multi-agent modeling [12, 13, 16, 17].
        </p>
        <p>Research of dynamic and static characteristics of real states of SIE with the subsequent acceptance
of administrative decisions is carried out by means of IIMS SIE. Data collection, their initial
processing, in order to clarify management problems, is carried out by means of the M1 module - the
module for diagnosing SIE conditions. Storage and processing of collected data, further assessment
and forecasting of SIE conditions is carried out by means of the M2 module. If real research cannot be
implemented then it is proposed to use virtual information from the information block and modulate
virtual states of SIE by means of the M5 module. This will facilitate further assessment and
forecasting of possible conditions, situational decision-making and their implementation by means of
the M6 module. If the information on SIE states is well structured, mathematical methods are used to
process this information and further choose management solutions, and if the problem is poorly
structured or unstructured, it is suggested to use expert judgments and evaluations to prepare solutions
[15, 18, 19]. Given that the dynamics of SIE conditions is stochastic [31], to predict SIE conditions in
order to further make optimal decisions, the most suitable models may be based on mathematical
methods of the theory of Markovian stochastic processes using systems of the Chapman–Kolmogorov
differential equations [22, 25 , 27, 48].</p>
        <p>This mathematical apparatus was tested in the study of the sustainability of the Public Joint Stock
Company "Concern Electron" (PJSC "Concern Electron", Lviv) on the index of sales of innovative
goods and services (% compared to the previous year, 2017-2021). In a study of 9 enterprises, we
found that 2 enterprises in 2017 were in status S1(BC), 4 enterprises - in status S2(C), 3 enterprises - in
status S3(HC). In this case: BC - the number of enterprises in which the index of sold innovative
goods and services was higher than average; C - the number of enterprises in which the index of sales
of innovative goods and services was within the average value; HC - the number of enterprises in
which the index of sold innovative goods and services was less than average. Thus, the initial
conditions of the studied process will be the following values of the probabilities of statuses: P0(S1) =
2/9 = 0,222; P0(S2) = 4/9 = 0,444; P0(S3) = 3/9 = 0,333. During the study period, the status of
development of enterprises of PJSC "Concern Electron" changed according to the index of the volume
of sold innovative goods and services. Intensities of transitions of enterprises from status to status,
indicated by the corresponding values over the arcs of transitions of the graph presented in Fig. 4.
2
S1
3
7
5</p>
        <p>4
S2
9</p>
        <p>S3</p>
        <p>Studies of the dynamics of development of PJSC "Concern Electron" on the index of the volume
of sold innovative goods and services were conducted by calculating with the help of computer
technology system of the Chapman–Kolmogorov differential equations (1), where λij (i, j = 1, 2, 3; i ≠
j) – intensity of transitions from status i to status j. For t →∞ and dP/dt = 0, the system of differential
equations (1) is transformed into a system of algebraic equations. This allows us to study the state of
development of PJSC "Concern Electron" in a stationary mode and make appropriate forecasts.
P
P1
P2
P3
 1/ = −( 12 +  13) ∙  1( ) +  21 ∙  2( ) +  31 ∙  3( );</p>
        <p>2/ =  12 ∙  1( ) − ( 21 +  23) ∙  2( ) +  32 3( ); (1)
 3/ = −( 31 +  32) ∙  3 +  13 ∙  !( ) +  23 ∙  2( ).</p>
        <p>When analyzing the obtained dynamic and static characteristics of the probabilities of the
enterprises of PJSC "Concern Electron" on the index of sold innovative goods and services (Fig. 5)
we can conclude that the most likely for PJSC "Concern Electron" is an increase in sold innovative
goods or services, since the dynamics of characteristics revealed that the probability of the first status,
in which the index of sold innovative goods and services is greater than the average value, becomes
the largest and reaches a static value of 0.444. That is, the development of PJSC "Concern Electron"
is projected to be relatively stable.</p>
        <p>H- integration steps (time)</p>
        <p>Thus, the proposed mathematical apparatus and developed on its basis mathematical and software
IIMS SIE adequately describe the status and sustainable development of the studied PJSC "Concern
Electron" and can be widely used in the study of statuses and sustainability of innovative enterprises
in general.</p>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>5. Conclusions</title>
      <p>A smart innovative enterprise (SIE) is a management approach focused on the use of new
technologies for the development of innovative enterprises. As individual entrepreneurs today need
new creative ideas and solutions that would meet the requirements of a changing world, the structure
of the SIE is proposed to be based on the structure of the innovation process, which would be
managed at all stages of its organization by integrated intelligent information management system of
smart innovative enterprises (IIIMS SIE).</p>
      <p>In the development of integrated intelligent information management system of smart innovative
enterprises it is advisable to use innovative methodologies and tools inherent in Industry 4.0. In
particular, those that would provide all stages of the innovation cycle: generating ideas and research;
designing; production planning and preparation; production; marketing; implementation; installation,
commissioning and operation; technical support and modernization, diffusion of innovations,
utilization and recycling. In other words, integrated intelligent information management system of
smart innovative enterprises can be used to implement the tasks of "digital factories", "smart
factories" and "virtual factories". The tasks of the "digital factory" can be performed by IRIS,
ICADF, ICAD-E and ICAD-T, and the tasks of "smart factories" can be performed by IIPMS.</p>
      <p>The generation of ideas in the CEE should be based on modern methods of generating ideas for
innovative goods and services. It begins with their emergence (emergence, creation), constant and
systematic search, accumulation, selection and formation of a portfolio or bank of ideas in IRIS.
Therefore, the sources from which ideas can come from IRIS are proposed to be divided into:
external, which include entities with which smart innovative enterprise interacts or which influence its
activities; internal, which include processes in smart innovative enterprise.</p>
      <p>IRIS is proposed to be considered as an intelligent support system for research conducted in order
to formulate and store ideas, their selection and implementation. IRIS should be used as an intelligent
real-time data processing system based on obtaining, processing, analyzing and making real-time
decisions. Therefore, IRIS must be equipped with a big data package platform, data analysis tools and
machine learning models. Since research sometimes has to be conducted in areas with poorly
formalized knowledge, it is advisable to use information systems that perform empirical analysis of
empirical data, in particular intelligent JSM systems.</p>
      <p>To perform the tasks of the "virtual factory" for the management of innovative enterprises in
general, it is proposed to use intelligent information management system of smart innovative
enterprises (IIMS SIE) as part of integrated intelligent information management system of smart
innovative enterprises. The tools needed to design and operate IIMS SIE can be based on
objectoriented integrated and distributed databases and knowledge bases, expert systems, DSS, integrated
neural networks and fuzzy logic tools. Since distributed artificial intelligence, integrated intelligent
information systems as multi-agent systems are the most suitable class of models for implementing
integrated intelligent information management system of smart innovative enterprises, it is advisable
to consider IIMS SIE as a logical-cognitive model of a social agent, and integrated IIMS SIE as a
multi-agent system. Therefore, a modular structure has been proposed for the construction of IIMS
SIE, which will provide it with flexibility, adaptability to environmental conditions and survivability.</p>
      <p>To predict the statuses of smart innovative enterprise in order to further make optimal decisions,
the most suitable models may be based on mathematical methods of the theory of Markovian
stochastic processes using systems of the Chapman–Kolmogorov differential equations. The proposed
mathematical apparatus and developed on its basis mathematical and software IIMS SIE adequately
describe the status and sustainable development of the studied PJSC "Concern Electron" and can be
widely used in the study of statuses and sustainability of innovative enterprises in general.</p>
    </sec>
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