Modeling the assessment of a region’s innovative potential

. The paper is devoted to the design and modeling of the system for assessing a region’s innovative potential to justify management decisions in public authorities. The purpose of the study is to substantiate the feasibility of using digital tools and artificial intelligence to formalize and visualize the assessment results. The use of a multi-criteria system for assessing the level of a region’s development, which includes four areas, characterized by 46 indicators, is difficult to interpret to justify management decisions. Based on the theory of fuzzy logic, logical programming methods focused on the application of a system of facts and rules, formal knowledge representation languages for describing subject areas and methodology for developing expert systems for complex problem solving, taking into account the empirical knowledge of experts, a model for assessing the innovative potential of a region is proposed. A case study of one of the Russian regions is illustrated by graphs of 3D visualization of the optimal combination of parameters of the level of innovative development. The formed triad of sustainable and safe development makes it possible to display the behavior of the regional innovation development index as a whole on the basis of social, economic and environmental indicators of sustainability.


Introduction
Digitalization is rebuilding public administration in real time [1][2][3][4][5]. The functionality of state information systems (SIS) provides a single information space for the work of public officers. The use of appropriate technologies in the course of making managerial decisions and monitoring their implementation should be ensured by their digital competencies [6][7][8].
In this case, the operation of SIS ensures the actuality, completeness and relevance of data for the formation of management decisions, largely determining their quality [9][10][11][12].
Published research results indicate that digitalization reduces the unproductive time spent on solving operational tasks [13][14][15]. Thus, the palette of digital tools, on the one hand, is limited by the institutionally regulated set of SIS functions, on the other hand, by specialized software for collecting, storing, analyzing graphical visualization of spatial (geographical) data and related information about objects [16]. There is virtually no description of the use of other digital tools for solving strategic problems, although it is known that they are characterized by incompleteness and inconsistency of information, and the decision-making process is complicated due to the specifics of the subject of labor. Obviously, the work of socio-economic systems should be supplemented with elements of artificial intelligence, predictive analytics and data visualization.
In this study, attention is focused on the use of artificial intelligence methods and data visualization for one of the tasks of a strategic nature -assessing the level of innovative development of Russia's constituent entities. It is assumed that innovations give impetus to the scientific development of the regions, ensuring the accelerated dynamics of the development of all sectors. In this regard, the authors will choose as a working hypothesis that the development of specialized software for solving individual problems of strategic planning can help increase the validity of strategic management decisions.

Materials and methods
The purpose of the study is to develop a prototype tool for solving the problem of automated formation of volumetric surfaces to support the process of regional strategizing in terms of assessing the innovative development of a territory. Achieving the goal of the study required solving the following tasks: 1) localization of complementary components for the development of specialized software, analysis of its completeness and staging accuracy for the automated solution of spatial planning problems; 2) software implementation of a prototype digital tool for visualization of volumetric surfaces; 3) assessment of the prospects for the use of volumetric surfaces for other tasks of spatial planning. The design of the study is based on the consistent implementation of these tasks.
The initial foundations of the study were the provisions of the theory of Fuzzy Logic, methods of Logical Programming, focused on Knowledge Representation and Reasoning, Description Logics and Expert Systems.

Results
Practice shows that at least three complementary components are necessary for the emergence of new software: 1) stakeholders who can describe their user needs and see the opportunity of using the tool in workflows to increase the validity of management decisions, are able to initiate an appropriate project and provide its implementation with resources (financial, human, time); 2) a correct system definition, the implementation of which should be ensured by the developed digital tool, and system realization based on key engineering decisions; 3) a correct description of the way of working scenarios at the level of input parameters with their sources, output parameters with the requirements of future users for their visualization and storage, as well as the proposed technologies (algorithms) for converting inputs into outputs.
Discussion of the tasks of developing specialized software is hampered by the lack of a backlog that supports strategic management processes. It is necessary to focus on the use of digital tools for solving individual problems of economic nature. One of them can be considered the task of assessing the level of innovative development of Russia's constituent entities [17]. Until 2019, the corresponding indicator -Russian Regional Innovation Scoreboard Indicators (RRISI) included 37 normalized indicators grouped into four sub-indicators: Indicators of the Socio-Economic Conditions for Innovation, ISECI), three subgroups, eight indicators; Indicators of the Science and Technology Potential (ISTP), three subgroups, eleven indicators; Indicators of the Innovative Activity (IIA), four subgroups, nine indicators; Indicators of the Quality of Innovation Policy (IQIP), four subgroups, nine indicators. Since 2019, the range of indicators has been expanded to 46 by including the fifth sub-indicator of export activity, two groups of which are focused on assessing the dynamics of knowledge exports (three indicators) and exports of goods and services (four indicators). In addition, five indicators have been added to the ISECI and IQIP sub-indicators.
To work with quantitative and qualitative data in the process of making managerial decisions, it is proposed to use the apparatus of fuzzy logic, where linguistic variables are determined by a set of verbal characteristics of a certain property [18][19][20]. The values of variables are set through fuzzy sets on a basic set of values, for example, qualitative assessments (by the terms "good", "satisfactory" and "unsatisfactory") or the corresponding basic numerical scale (I, II, III). Based on the use of the fuzzy output apparatus, the authors have created a prototype of an expert system. For this, the sub-indices ISECI, ISTP, IIA, IQIP are defined as linguistic variables fed to the input of the fuzzy output system. Next, the ISECI, ISTP, IIA, IQIP inputs were normalized (see Table 1) and the output variable ISECI was designated, which takes the values {I, II, III} according to the rules of qualitative and quantitative assessment presented above. A detailed presentation of the approach is presented for the stakeholder networking interaction using the example of strategic growth points of the South Siberian conurbation [21]. The knowledge base for inference is built on the basis of production models according to the modus ponens rule: "If it is known that A is true, and there is a statement like "IF A THEN B", then B is also true". Its fragment is presented below: 1

. If (ISECI is III) and (ISTP is III) and (IIA is III) and (IQIP is III) then (RRISI is III) 2. If (ISECI is II) and (ISTP is III) and (IIA is III) and (IQIP is III) then (RRISI is III) 3. If (ISECI is I) and (ISTP is III) and (IIA is III) and (IQIP is III) then (RRISI is II) 4. If (ISECI is III) and (ISTP is II) and (IIA is III) and (IQIP is III) then (RRISI is III) 5. If (ISECI is III) and (ISTP is I) and (IIA is III) and (IQIP is III) then (RRISI is II) 6. If (ISECI is III) and (ISTP is III) and (IIA is II) and (IQIP is III) then (RRISI is III) 7. If (ISECI is III) and (ISTP is III) and (IIA is I) and (IQIP is III) then (RRISI is II)
The choice of this type of knowledge representation model is due to the ease of perception by users. The ease of reading the design of the knowledge base enables to replenish it with new rules by specialists in their workplaces in the process of solving problems. Upon completion of the development of the knowledge base, the result of the fuzzy output system (i.e., the values of the output variable) was obtained for specific values of the input variables.
The implementation of the model was carried out using a case study of Novosibirsk Region (NSR). As an example, consider the values of the ISECI, ISTP, IIA, IQIP indicators for NSR. The following values were submitted to the input of the expert system prototype: ISECI = 0.435, ISTP = 0.465, IIA = 0.298, IQIP = 0.672. At the output for the indicated parameters ISECI, ISTP, IIA, IQIP, the value RRISI = 0.523 was obtained, which in terms of "good", "satisfactory" and "unsatisfactory" corresponds to the assessment "satisfactory". The use of the prototype makes it possible to assess the innovative potential of NSR by visualizing the impact of input indicators on the resulting RRISI value. The formation of four 3D surfaces of the fuzzy output model localizes the ranges of input parameters to obtain optimal RRISI output values. Thus, the visualization of triads provides the process of modeling the assessment of the innovative potential of NSR on the entire possible range of input indicators in combinations: 3D surfaces of influence on the regional innovation index of sub-indicators: RRISI -ISECI -ISTP (Fig.  1), RRISI -ISECI -IIA (Fig. 2), RRISI -ISECI -IQIP (Fig. 3), RRISI -ISTP -IQIP (Fig. 4).
The aligned 3D surfaces enable to visualize the optimal combinations of parameters of the level of innovative development. This is an opportunity to consider several options for achieving the goals set on the basis of solving direct and inverse problems. In the first case, the task is to obtain the resulting RRISI value for a certain combination of input parameters ISECI, ISTP, IIA, IQIP. In the second, the inverse problem is solvedidentifying the values of ISECI, ISTP, IIA, IQIP to achieve a given RRISI output parameter. Thus, it becomes possible to lay down such parameters for the innovative development of regions that are significant, specific, achievable without excessive optimism in the planned period, and ensure the sustainable development of the regional economy.
This approach, combined with the dynamic adjustment of the knowledge base of the expert system to subject areas, makes it possible to increase the adaptability of managerial decisions to changes in the economic situation and ensure their effectiveness.

Discussion
The presented digital 3D surface visualization tool shows one of the many applications of artificial intelligence elements, allowing spatial planners to make more informed, rational decisions based on the visualization of 3D surfaces of quantitative indicators. In turn, the expansion of the basic system of indicators will allow building innovative profiles of territories, macroregions, conurbations, algomerations, and other associations at the federal, regional and municipal levels.
The developed knowledge base makes it easy to visualize, for example, the index of sustainability of spatial development based on the triad's sustainable development component, proposed in [22]. At the same time, it becomes possible to display the behavior of the index as a whole based on the social, economic and environmental indicators of sustainable development of each individual region, as well as work with their components.

Conclusion
In the future, proactive management decision-making will be based on unified technological solutions: the Gostech digital platform [23], all applications of which will be available on the Gosmarket state marketplace [24], the Gosoblako state cloud platform and an automated working position of a public officer ARM GS [25]. The presented prototype can be included as one of the elements of the development of the functionality of the