Tools for Assessment of Innovation Potential of the Business Environment Development in the Region

The purpose of this study is to assess the innovation potential of the economy and prospects for the innovative development of business environment in a particular economic region. Assessment of the innovation potential was performed using fuzzy set analysis and hierarchy analysis. Innovation level of the business environment and its development priorities were determined by the means of complex numbers. During the study, the authors disclosed the contents of the innovation potential of the regional economy, the allocated groups of the business environment, represented the situational modeling of the dynamics of the development of the innovative activity in the territory (development options and their economic interpretation). In the context of the West Siberian and East Siberian economic regions of Russia, the development of innovation potential of the business environment in the territories was assessed under the author’s system of indicators that reveal the content of components of the business activity potential. Modeling the innovation potential of the region and business environment demonstrates the viability and validity of their application for the analysis of real economic processes. The presented authoring tools to study the extent of development of innovative economy of the regions will help shape the effective areas of state regulation and support of the business environment at the macro and micro level. Prospects for research in this area are to build multivariate models using computer calculations.

Strategic priorities of any territory are the security of the national economy, availability of the goods and services of high quality at the necessary extent, growth of welfare of the population, development of market infrastructure. The economic development of the territory is based on the interaction of two institutional forms: state and private business. The economic theory has different interpretations of the degree of separation of the economy between state and business, their participation in the distribution of resources, in the ownership structure. However, one can't deny the fact that business in the modern world is becoming the engine of economic growth, an indicator of contemporary forms of transformation of the market economy.
In the Russian practice, it is customary to distinguish four groups of entrepreneurs: big business, medium and small businesses and individual entrepreneurs. These entities represent the entrepreneurial sector of the economybusiness environment. The contribution of each of these groups to the Russian economy varies.
According to Rosstat, the contribution of small and medium businesses in Russia's GDP in 2014 was 21%. In 2014, Vnesheconombank's experts conducted a survey of 1,214 managers of this type of business in 16 regions of the country to identify the dynamics of the financial sustainability of the activities and attitudes of entrepreneurs. When asked about the challenges of doing business, 47% of the respondents mentioned the tax burden, 44% -the high level of competition, 26% -the unavailability of financial resources. The highest acceptable rate on loans that allows to speak about competitiveness was marked at the level of 13%. At the same time, over the first half of 2015, the weighted average interest rate on short-term loans amounted to 19%, for loans up to 3-year term -16% (Vnesheconombank, 2014). 2014 was a difficult year to do business. According to analysts, the difficult situation was in lending to small and medium-sized businesses. The negative dynamics deteriorated over the entire 2014 and the first half of 2015, which can be seen from the data in Figure 1.
Many domestic and foreign researchers consider small and medium business the chief conductor of innovations. Lacking the benefits in comparison with large companies and corporations by the scale of production, the size of the customer base, resources and financial capital, a key source of their competitiveness is innovative activity and venture investments. This activity area is risky enough, so if the government is committed to the development of small and medium businesses, it must create the conditions to reduce the risks by providing information, legal and organizational support of innovative activity of the enterprises.
State stimulation of innovation is officially recognized as a key factor in long-term growth of the national economy (OECD, 2010). An important role in the innovative development of the economy is assigned to individual regions. There are studies that empirically confirm a pattern of asymmetric and unequal development of innovative activity in different regions of the state (OECD, 2011, P. 19 ;Foddi, Usai, 2013). In our opinion, it can be explained by the difference in the value of the innovation potential of the territories and the business environment. In terms of the region, the innovation potential should be considered from three perspectives: the possibility of creating innovations, possibility to carry out effective innovative activity, possibility of implementation of innovations by enterprises, as shown in Figure  2.
Hence, the innovation potential of the region (territory) is a set of possibilities of creation and development of effective innovation implementation in the territorial entity.
The business potential of the region is the possibility of increasing the competitiveness  of its own commercial product by implementing innovative technologies in a particular region. In this case, the most important indicators for assessment are the ones that characterize financial, managerial and organizational capacities of enterprises.
The scientific potential of the region is the ability of the regional research organizations to create innovations that have practical application in the industrial and economic activity. In this case, the most important indicators for assessment are the ones that characterize intellectual and material resources of organizations.
These assumptions make it possible to analyze the perspectives of innovative development of the regions by the extent of

Fuzzy set assessment of innovation potential
Innovation potential is suggested to consider as aggregate IP indicator, the value of which will depend on the numerical values of its Table 3. Situational modeling of the dynamics of innovation in the region individual components: SC -scientific component, InC -institutional component, BC -business environment component. Since each component must be described by a set of indicators, the assessment of the innovation potential can be obtained in the analysis of the hierarchy in Figure  3.
Mathematical economic logical model of the innovation potential is written as (Parshukov, 2011): In order to estimate the IP indicator, we need to combine the data collected under the tree hierarchy; the direction of the assessment will match the direction of hierarchy arcs (from the lower-level elements to the root element).
The scale of numeric IP assessments will be given on the interval (0;1) in the form of a standard three-level fuzzy classifier (SFC) in Figure  4. The classifier is built by analogies described in the works on fuzzy modeling (Nedosekin, 2003).
The author's approach to the assessment of the innovation potential involves drawing associations between quantitative estimates of IP model elements and their qualitative economic characteristics.
The  In the formula (2), С -estimated component, row matrix P Ñ =(p 1 , …, p m ) -weights between indicators of the estimated component that we suggest to calculate using the Saati method of matching the weighting factors (Saati, 2008).
K C matrix is a classification matrix. Each row of the matrix corresponds to one of the indicators to assess the component. If the value of this indicator is recognized by the investigator as high, the row is written as (0 0 1), if as medium, i.e. satisfactory, then (0 1 0), and if as low -(1 0 0). The matrix will contain two kinds of numbers 0 and 1, and the sum of the elements in a row is 1. V are the peaks of the SFC classification intervals.
According to the authors, the importance or the contribution of each component to the level of innovation potential is equal. Therefore, the innovation potential is calculated as follows: If the values of the components are different, the weights are determined by Saati method. IP recognition will be made according to Table 1.
The advantage of the proposed tools is the ability to use the agreed indicators measured in different and disparate values (absolute and relative). There is a possibility of quantitative and qualitative interpretation of the values of IP and its components.

Modeling the prospects of development of innovative business environment
Since the ultimate goal of the study is to assess the prospects of innovative development of the business environment, the next stage of the analysis necessary is to determine the necessary tools. The authors chose the means of complex numbers. The study was based on the studies and works of leading Russian economists in this area Svetunkov S.G., Svetunkov M.S., Svetunkov I.G. Selection of these methods is due to the broad economic modeling capabilities and production processes, as well as the ability to describe the non-linear changes in economic indicators. Using the methodological principles outlined in the works (Svetunkov, 2012;Svetunkov, 2011), we obtained the following models and relationships. Let's introduce a complex number Z -the results of the innovation sector of the economy where the real part X is the volume of innovative products and services, and the imaginary part Y is represented by the cost of technological innovation: Yi X Z + = Characteristics of the complex number are the radius vector R and the polar angle [phi].
-scale of the innovation sector of the economy; -profitability of cost.
The exponential notation of the complex number makes complex arithmetic operations between complex numbers impossible: exponentiation, root calculation, calculation of the logarithms. Trigonometric notation allows to describe non-linear and cyclical trends of changing the real and imaginary parts. Notations of Z are the following: Let's introduce a complex number Gresources of innovative activity, where the real part M is the internal costs of innovative activity and the imaginary part N is the number of employees engaged in research and development: We will determine the radius vector of the complex number is the financial support for scientific work.
The exponential and trigonometric notations of a complex number:   Krasnoyarsk Z2 Z2 Z1 Gradual increase in production of innovative products and services has Region attracted additional investments in technological innovation, which contributed to the expansion of the innovation sector of the economy through investment growth. G2 G2 G5 Change of financial flows in favor of technological innovations has reduced the pace of innovation financing, and in the near future it will be implemented at the expense of accumulated scientific creativity. Novosibirsk Z1 Z1 Z2 Investment opportunities in innovative sector of the economy in the Region region reached the limit values, taking into account the development of innovative business environment. Further expansion of this sector will continue at the expense of production possibilities. G3 G6 G7 There is a trend of deterioration in the resource support of innovation, which led to recession and growth of project risks. These trends also partly explain the dynamics of characteristics of the complex number Z.
Relationship between the results of an innovative economy and the results of innovative activity will be represented in the form of the complex function: The parameters [alpha] and [beta] in different processes may be either real or complex numbers. The parameters for each individual case can be assessed according to available statistics of monitoring with an alternative method of least squares of complex econometrics. A detailed description can be found in the work (Svetunkov, 2012).
Since the real and imaginary parts of the complex number Z are measured in monetary terms, there is no need to adjust them to comparable form. The real and imaginary parts of a complex number G are measured in different terms -rubles and number of people, so they should be adjusted to the dimensionless indicators. To do so, we can use the chain or the basic indices. This assumption does not distort the economic logic of the simulation in defining the functional relationship between the complex numbers Z and G. Since the indices describe the dynamics, the functional dependence will show how the change in volume of resources G determines the result of an innovative economy Z.
Let's model and present the economic interpretation of different options of the dynamics of the real and imaginary parts of the complex numbers Z and G, as well as their characteristics, in Table 2.
As you can see from the above table, the use of complex numbers provides ample opportunity not only to describe the current situation, but also to forecast the trends and prospects of development of innovative economy. Table 3 shows a similar interpretation for the complex number G Addition of the calculations using the proposed toolkit to assessment of innovation potential will allow to describe the innovative processes of the development of business environment in the region's economy in more detail.

RESULTS AND DISCUSSION
Testing of the proposed toolkit was carried out according to statistics data obtained from Rosstat. The West Siberian economic region and the East Siberian economic region were chosen as pilot sites. Brief description of the regions is presented below.
The main branches of specialization of the WSER business environment: oil and gas production, chemical and forest industry, metallurgy, agriculture, grain and animal husbandry.
The main branches of specialization of the ESER business environment: electricity, fuel, ferrous metallurgy, non-ferrous metallurgy, chemical and petrochemical industry, machine building and metalworking, timber, woodworking, pulp and paper, light and food industries, production of building materials.
Indicators from Table 4 were chosen to assess the components and the value of innovation potential of the development of business environment of the regions -members of the economic regions.
To determine the level of each indicator (except the indicator "Quality of institutions"), its estimated value was compared with the average for Russia without taking into account the data by regions -members of WSER and ESER. If the calculated value falls within the range (value for Russia minus 5%; value for Russia plus 5%), it is interpreted as an average or sufficient. If the regional value of the indicator goes beyond the range to the left (excluding depreciation of the funds), it is interpreted as low. If the regional value of the indicator goes beyond the boundaries of the interval to the right (excluding depreciation of the funds), it is interpreted as high.
Evaluation of weights according to the Saati method is presented in Tables 5-7.
Analysis of the results shows that in most regions the business environment component has a greater impact on the change in innovation potential. The general conclusion on the results of the assessment is as follows.
Regional indicators of innovation potential and its individual component in the WSER and ESER regions compared with values for Russia are average or below average. There are no advanced regions able in the short term to act as growth drivers of innovative economy of the country in the considered economic regions. This is partly determined by industry specialization of regional economies, in which a key role is played by natural resources and raw materials. The condition for the transition to the innovative type of development is to create conditions for deep processing and diversification of industrial production. The current trend is characterized by the fact that big business and regional authorities focus on receiving natural rent, while financial and institutional conditions in the region do not allow small and medium businesses to develop innovative technologies. Inefficient ownership structure of property and weak institutions, lack of the necessary volume of the state orders make the prospects of development of regional business environment on the basis of innovation unfavorable.
Two regions were chosen to test the modeling tools using complex numbers -Krasnoyarsk and Novosibirsk regions. Calculation of the complex numbers Z and G for the chosen regions is presented in Table 9.
Complex numbers informatively describe the current dynamics and trends in the innovation sector of the business environment and research activities in the regions. Let's analyze the obtained values using the situational models from Table 2 and Table 3. The results and conclusions are presented in Table 10.
The use of the proposed modeling tools of innovation potential of the region and business environment brought informative results. This proves the validity and prospects of their application for the analysis of real economic processes.

CONCLUSION
The indicators chosen by the authors for analysis are not the only definition. At the analytical study of the business environment and innovation potential of other countries and regions of the world, one must take into account the institutional and macroeconomic specificity of the territory.
Characteristic features for the Russian economy are the presence of a strong natural resource base, vast territories, diversity of informal, social and cultural institutions. The contractual relationship between government and business are implicit. Rent-focused behavior of economic agents and the government officials' propensity to opportunism are a real problem for the development of the Russian business environment on the basis of innovation. Government initiatives are indirectly aimed at raising taxes from population and abolition of the social obligations of the state, which ultimately affects the effective demand. Under these conditions, small and medium businesses are focused not on the expansion of innovative activities, but on reducing losses. In terms of game theory, it is a maximin strategy. Given that innovation involves high risks, more and more businessmen refuse to implement it.
The research has shown that the methods of modern mathematical modeling allow not only to describe the theoretical economic models, but also to determine the actual conditions of their implementation. The use of complex numbers is justified by the possible economic interpretation of the results and their use in describing the nonlinear dynamics of cyclical fluctuations. Further research in this area will focus on the construction of the functions of complex variables, revealing a statistical relationship between the change in the value of the innovation potential of individual components and complex variables. This is a complex, time-consuming, but realistic process. Prospects for research in this area is to build multivariate models using computer calculations. Furthermore, fuzzy modeling can be used in combination with nonparametric econometrics tools. Sharing these approaches in the assessment of innovation potential and the development of the business environment will be the focus of our future research.