selection of a set of indicators of estimation of social and economic systems of regional tyPe

2. The main factors that shape the institutional envi­ ronment of the ecological and economic system and their impact on the institutional environment and the dynamics of its development to the state of institutional equilibrium are given. 3. Economic conditions that determine the possibili­ ties of transforming the institutional environment of the market of social­ecological forest services to the state of institutional equilibrium are revealed. 4. Strategies for the behavior of the subjects of the ecological and economic system on the formation of eco­ nomic conditions for achieving the institutional equilibrium of the market for social and ecological forest services are proposed.


. introduction
Among a number of complex systems, socioeconomic systems (SES) occupy a special place, which are divided into SES of different levels and types. The most complex, the most global SES is modern civilization.
The more elementary considered SESs consist mainly of three main elementssubsystems: social groups, economic processes and the environment. A social group is prima rily an individual and a person. Under the environment is understood the ecological, geographic, natural and climatic environment and metasystem environment. The specific ISSN 2226-3780 quantitative and qualitative characteristics of the listed elements and the relationships between them determine the specific properties of a particular local SES [1,2].
Local SESs, functioning in the conditions of Western and Eastern Europe, is being investigated.
Management of the development of such classes of SESs requires the solution of a number of tasks, in par ticular, at the initial stages it is necessary to identify the current state and trends in the development of the system, develop and optimize the scenario of sustainable develop ment at various planning horizons.
The concept of sustainable development requires a com prehensive analysis and consideration of environmental, social, economic, natural and climatic and other factors. And for this it is necessary to solve the problems of de termining sets of indicators of sustainable development.
The solution of these problems allows to objectively assess the state of SES, which should be sufficient to iden tify in full the explicit and indirect properties of SES. Therefore, the tasks of selecting sets of indicators for as sessing socioeconomic systems are quite relevant.

the object of research of technological audit
The object of research is classes of socioeconomic sys tems of a regional type, which include countries, regions of Western and Eastern Europe.
Differences in the natural and climatic conditions of Western and Eastern Europe have a universal complex impact on all aspects of the economy and the life of the individual, society and the state, form a different menta lity of a person (socium), in both Western and Eastern Europe, different durations of the agricultural working season (shorter and requiring considerably more labor, greater intensity and labor costs in Eastern Europe), a much more unprofitable livestock farming with a significantly higher cost of production in Eastern Europe. Industrial and construction production in Eastern Europe is also characterized by high production costs, more expensive infrastructure, higher production costs, longer payback periods than in Western Europe. The basic needs of the individual in Eastern Europe are higher, and the condi tions for their satisfaction are much more modest than in Western Europe.
The climatic conditions of Eastern Europe cause a rise in the cost of life and production and economic activities of man and society.
It should also be taken into account that the society in Eastern Europe does not have sufficient knowledge of natural and climatic factors and differences in climatic conditions in Western and Eastern Europe, as well as in understanding the levels of influence of the FSC on so ciety, economy and culture. The lack of such under standing leads to a decrease in the level of information security of society and the state. Therefore, the task of educating the public is that there are differences in the natural and climatic conditions and they are of a fun damental nature and require extensive coverage of the negative effects of climate on man, society and the eco nomic development of countries and regions and the mass dissemination of scientific and popular science literature, educational and methodological literature on the problems of information security of the society from ignorance and misunderstanding of the impact of natural and climatic conditions on the economy and society. Knowledge and understanding of these differences can play an important role in the development of society, state and globalization of modern society.

the aim and objectives of research
The aim of research is solution of the problems of selecting a set of indicators for estimating the SES, sub stantiating the construction of general criteria for the SES estimation indicators of a regional type, expanding the system of indicators to obtain a more objective picture of SES state estimation.
Evaluation is the identification, comparison of the eva luated object with its idealized image (standard, norm). The SES is assessed, i. e. the region and its condition are diagnosed.

research of existing solutions of the problem
In Eastern Europe, since 1917, it was time to noti ceably weaken the attention of scientists and society to understanding the difference in the natural and climatic conditions of Eastern and Western Europe and the degree of influence of natural and climatic conditions on the his tory and economy of society and the state. The serious impact of natural and climatic conditions (NCC) on the life and economy of society was rejected, it was believed that the geographical environment can't play a major role in the life of society. The situation began to change af ter the 90s of the XX century. Studies of natural and climatic factors in Eastern Europe were carried out by the authors [3][4][5].
It should be noted the American scientistsresearchers, who drew attention to the role of the PCF in the life of the state and society [6,7].
At the present time, the work on the transition to the implementation of the paradigm of «sustainable develop ment of society» is increasingly being carried out, which in turn implies the development of all regions, including individual regions. The term «region» in Russian literature is most often understood as a set of areas of a particular country. Thus, the development of regions as complex socioeconomic systems (SES) is an important component of the development of society.
The transition to the paradigm of sustainable develop ment of society on the example of SES requires the selec tion, analysis and accounting of a large number of indica tors and criteria relating to a variety of areas; Economic, ecological, social, geographic, naturalresource, scientific and technical, labor potential [8][9][10]. A large number of indicators make it difficult to obtain an objective picture of the assessment.
This class of SES is a certain territorially distributed unit that differs from other units of the same level with specific features -geographic, geological, industrial, social, economic, ethnographic, ecological, has a certain integrity, interconnectedness of the elements that form it, solves the problems of multifactorial distributed and hierarchi cal state anticrisis management [2]. To this it is neces sary to add that the SES data are objects with weakly formalized processes.

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The first and most important tasks on the path of researchers are the tasks of selecting the nomenclature and the number of indicators that allow an objective as sessment of the state of SES that should be sufficient to identify in full the explicit, indirect and latent properties of SES relationships [1,2]. 5. methods of research 5.1. feasibility of accounting for climate indicators. At the moment, both domestic and Western researchers do not take into account natural and climatic factors when assessing the state of SES, or when developing management strate gies. At the same time, the need to study and monitor the dynamics of natural and climatic processes is relevant [2,9].
The climate is one of the main environmental factors, its change against the background of complex ecological, social and economic situations in Ukraine and throughout Eastern Europe can cause serious socioeconomic conse quences [2,9,10].
For Eastern Europe, and, consequently, Ukraine is charac terized by more severe and negative NCC than for countries of Western Europe, which hamper the population's living and cause higher production, household and infrastructural costs, which leads to higher production costs, a longer payback period, to rise in price of life and economic activity. In addition, the economy of the country is not as developed as the economy of Western European countries and Ukraine is more strongly expressed social tension, stratification in society, a decline in the standard of living of the popula tion. These factors increase the negative impact of natural and climatic factors on the socioeconomic and production activities of society. All this indicates the advisability of taking into account natural and climatic factors.
As a generalized criterion for assessment can be used: level of sustainability of the regional development, level of investment attractiveness, level of discomfort, etc. The definition of the type of generalized criterion focuses on the appropriate selection of the evaluating positions and indicators [11,12].
5.2. characteristics of the set of indicators. State charac teristic of the object of study of the region is determined by a set of indicators (normalized indicators -mental, specific, etc.). The optimal list of indicators should cor respond to the following: -contain not an infinite, but a limited number of in dicators; -reflect all the basic conditions and properties of the socioeconomic system; -be representative -able to reflect them fully and adequately, including in space (taking into account the objective conditions of the regions) and in time (fixing not only the momentary slice using static indicators, but also the dynamics of the situation with the help of indicators); -be methodically correct -with the values of indi cators ordered in one vector (for example, «the more -the better», but taking into account the meaning of the indicators, for example, unemployment, poverty, crime, etc.); -be structurally mature -without strong dispropor tions in the number and quality of indicators for se lected positions, which can be achieved through ag gregation (the formation of composite indicators).
The task of determining a sufficient number of indica tors characterizing the SES is complex and important, as this affects the quality of diagnosing (assessing) of SES states and the «quality» of «developed» management de cisions [12][13][14].
The large dimension of the set of indicators (up to hundreds and more), the absence and lack of development of a methodology for obtaining generalized indicators makes it difficult to study the dynamics of such systems, the construction of a DSS and the development of optimal management solutions.

research results
The current state of any SES is estimated, as a rule, by a sufficiently large number of particular indicators {x i } n = 1, each of which reflects one of the sides (entities) of the system. This is a multifactor evaluation.
Therefore, the natural next step in the study of such systems is reducing their dimensionality, for example, by translational convolution of particular indicators, i. e. transi tion to an integrated assessment of objects -regions (Fig. 1). In the simplest case, it is the replacement of a certain set of exponents 1 by a single more generalized expo nent I( ). lowering the dimension, it is necessary to exclude loss of information about the system under consideration and therefore a certain «reasonable» averaging procedure is based on the construction of any index, for example, the calculation of the arithmetic mean, mean square, geometric mean, and so on.
Transition to a more generalized integrated assessment allows for a comprehensive review of the state of the region, revealing the positive and negative aspects of its development, and conducting a comparative interregional analysis [15]. In this sequence of actions, it is necessary to distinguish the following stages: the formation of a system of indica tors, the standardization of indicators, the combination of the values of indicators for the integrated assessment, the typology of regions, the ranking of regions, for example, in terms of development level. Based on this, the choice of the method for calculating the integral index takes place.
Any set of parameters {x i } n i =1 can be treated as a vector in an ndimensional Euclidean space. Then every index is a functional on a linear space of dimension n: The most frequently used (as the most convenient from a computational point of view) are the indicators con structed on the basis of linear averaging procedures: com puting the arithmetic mean: Or more generally -weighted mean: where P = {pi} n i=1 , 0 ≤ p i ≤ 1, i = 1, 2…n -given set of weight coefficients.

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The following commonly used index class is constructed on the basis of quadratic averaging procedures (quadratic functionals): calculating the mean square (Euclidean vec tor norm): or more generally -the calculation of the rootmeansquare ratio of the vector X from some given optimal vector: In the literature, there is usually no justification for choosing a particular averaging procedure when calculating indices. Known procedures are conducted either at the level of «plausible reasoning» or at the level of «common sense». Therefore, the problem of theoretical substantia tion of procedures of generalized selectable indices for a class of complex SES of a regional type is posed. The most commonly used averaging procedures and the indices (1), (2), (4) generated by them have a simple geometric interpretation and are related by a quadratic dependence.
Without loss of generality, let's assume that all ad missible states: of the investigated SES are located in the cube: This can always be achieved by appropriate normali zation of the admissible parameters {xi} ni = 1. Let Sa vector in the cube K, all components of which are equal to the unit S = (1, 1, ... 1). Using the approach de scribed in [8][9][10]16], this vector can be called the opti mal vector. Its optimality consists in that it is larger (in the sense of the natural order relation on the space Rn) of any other vector from the cube K. Let's note that the simplest linear index (1) coincides, up to a factor of 1/n, with the scalar product of the current vector X and op timal vector S : Thus, the simplest linear index: Up to a factor of 1 n coincides with the projection of the current vector X on the direction of the optimal vector S. According to [9,10], the angle j between the vectors X and S is called the normalization angle. Let's note that since J X n X ( )= 1 , the indices I(X) and J(X) are related by: Representations (5) and (6) for the linear index I(L) make it possible to introduce one more natural indexthe value of the Euclidean distance from the point X to the straight line generated by the optimal vector S: It is clear that the lower bound in (7)

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The index Г(Х) has a simple meaning: its value at each point X is the rootmeansquare deviation of the components of the vector X from their arithmetic mean.
Further from this triangle it is easy to obtain three connections between the four indexes considered: One of the main purposes of any index of the socio economic system is the rating evaluation of a given set of states X j j m { } =1 of such system. Every functional: R R n → 1 transforms the space Rn into a completely ordered set by means of the convention: X > Y if I(X) > I(Y) for any pair of vectors X, Y∈R n . The ratio of the total order generated by the simplest linear index (1) has a simple meaning: for any pair of vectors X, Y∈R n , the vector whose projec tion onto the direction of the optimal vector is greater than I(X) > I(Y) is the best, or equivalent, that a vec tor that is less distant from the direction of the optimal vector Γ Γ X Y

( )< ( ).
Let's analyze the «reasonableness» of the procedure for constructing linear indices (1), (2). The construction of the index as the mean of the arithmetic meanings of the parameters (1) does not take into account objectively existing differences in the importance of the individual parameters x i . For example, an indicator such as GDP per capita should contribute more to the total value of the index than, for example, the area of paved roads per unit area in rural areas. These differences in the degree of importance of the individual parameters x i can be taken into account by assigning to each of the parameters x i the corresponding weighting factor, i. e., constructing a linear index based on the weighted average calculation I X p ( ) (2).
This raises the problem of a «easonable» choice of the weight coefficients p i i n { } =1 .
Just as the index I(X) is, up to a multiplier, the scalar product of the current vector X X j j m = { } =1 and the optimal vector S = (1, 1, ..., 1), the generalized linear index I X p ( ) is exactly the scalar product of the current vector X and the weighting factor vector: Thus, the problem of a «reasonable» choice of weight coefficients is the problem of choosing in some sense the optimal vector: If the optimality of a vector is understood in the sense of the natural order on the space R n , then in the cube K there is a unique vector that is optimal in this sensethis is the vector S. Therefore, in practical applications, the choice of the «optimal» vector P is carried out with the help of a system of expert estimates [17] that add an element of subjectivism both in the meaning of the index I X p ( ) itself, and of the conclusions on its basis on the current state of the SES.
In this case, assigning the components of the optimal weight factor vector: has an equilib rium point, the center of gravity of this system of vec tors. The vector R n , corresponding to this point should be considered as the natural optimal vector for a given set of states X j j m { } =1 of SES, since the importance of equi librium states of economic states is well known [13,14].
is given and at each point X j the mass M j is concentrated, then the center of gravity of such a system is defined by the equality: . Moreover, among all such indices, the best index is the index constructed on the basis of the center of gravity of the given system of states X K jj m − ∈ 1 (12), since it is unique to the equilibrium state of this system.

sWot analysis of research results
Strengths. Thus, the task of justifying the choice of the nomenclature, the number of indicators and the construc tion of procedures for generalizing the selectable indices for the SES class of the regional type is solved. The obtained results are used in the construction of the DSS by regions of Ukraine, which allows more fully to solve the problems of multifactor estimation and management of complex SES of a regional type. The developed system uses about 70 indicators to assess the sustainability of the region (area) development, more than 80 -to as sess the investment attractiveness of the regions [2,10]. The used indicators relate to the following diverse areas: economicgeographic, resourceresource, labor, economic, infrastructure potential, scientific and technical, health, investment, natural and climatic. For the first time, the natural and climatic potential is introduced into the indicators, which is characterized by 7 partial indica tors (Table 1)  The information technology of SES estimation as ob jects of DSS is shown in Fig. 2. Weaknesses. The large dimension of the set of indica tors requires a decrease in the dimension of the partial indicators, which is realized by progressive convolution of the indicators. This construction of the indices does not take into account the differences in the importance of individual indicators, which, in the analysis, can now be taken into account by assigning the appropriate weight coefficients using the system of expert assessments, using the experience and knowledge of experts for whom the notion of optimality of weight coefficients is not global in nature, but is tied to a particular system (SES) [17][18][19].
Opportunities. This system can be used in the strategy of the development of the regions of Ukraine.
Threats. Insufficient awareness (enlightenment) of the society regarding the importance of natural and climatic factors leads to their underestimation when forming stra tegic plans for the development of regions.

conclusions
Thus, a solution to the complex task of selecting a set of indicators for assessing socioeconomic systems of a regional type is formed and tested. A methodolo gy is developed for selecting a set of SES estimation indicators.