Research goals and objective: to predict the economic dynamics of the synergetic transformation model of Ukrainian agrarian sector using a neural network on fuzzy data. The object of research: Neuro-Fuzzy Model of Economic Forecasting. The subject of research: forecasting the economic dynamics of the synergetic transformation model of Ukrainian agrarian sector using a neural network on fuzzy data. Research Methods are neuro model, fuzzy logic, assessment of the risk of Voronov and Maksimov Results of the research: We can say that the risk of this forecast, predicted by the neural network, is "very low", we can definitely trust the forecast, and the risk is calculated by the equation of the neuroregression "low", which indicates that we can trust the forecast, but with caution and further monitoring.
Application of optimization methods for fuzzy data is impossible, that`s why neurofuzzy simulation is used as a mathematical methodology, which makes it possible to put forward and solve even those problems which have no complete statistics or in case there are only qualitative factors ensuring the possibility of adapting economic and mathematical models to changing economic conditions.
The purpose of the paper is to predict the economic dynamics of the synergetic transformation model of Ukrainian agrarian sector using a neural network on fuzzy data. Determining the size of synergistic effect of economic, ecological and social nature requires a mathematical interpretation with the use of up-to-date information technology, since the calculation of synergy in economic system is complicated by the random nature of economic phenomena in the conditions of transformation processes. The development of scenarios for transforming the agrarian sector of the economy is possible only with the use of information technology.
The paper is organized as follows: part 2 describes related works concerning neuro-fuzzy models; part 3 describes Neuro-model "Nova Troya"; part 4 describes the results of the neuromodulation; the last part concludes. 2
In market conditions any economic agent during their activities inevitably faces
uncertainty. Even a professional is not able to predict changes that may occur in an
uncertain external environment. Simplification of economic system model in the
framework of traditional methods will inevitably lead to inadequacy of the resulting
decisions due to incomplete consideration of an uncertainty of internal and external
system environment. Consequently, the construction of accurate mathematical models of
innovative development of economic industries, fit for implementation in software
applications to solve analytical tasks of decision-making and its support, based on the
use of traditional methods, can either be difficult or impossible at all [
An alternative way of simulating the behavior of complex economic systems is the
assumption of their fuzziness when describing them. This statement is based on the
principle of incompatibility of accuracy and meaningfulness [
This results in the fact that a number that has a specific meaning for an expert
ceases to have one value (which requires traditional mathematics), but can be
expressed by a set of values with its own probability. In this case, the probability reflects
the impact and strength of possible active factors. The interpretation of fuzzy numbers
is determined on a case-by-case basis and depends on the physical nature of these
numbers, as well as on the factors that affect them. The fuzzy method allows to
dramatically reduce the number of computations, which in turn leads to an increase in the
speed of fuzzy systems [
Artificial Neural Network is a mathematical toolkit that is a universal reproducer of
complex nonlinear functional dependencies, which is based on the principles of the
work of biological neural structures. This toolkit is used in data analysis, time series
forecasting, signal processing, pattern recognition, etc. [
An artificial neuron consists of an adder and a functional converter. The adder performs calculation of weighted signals that arrive via interneuronal connections from other neurons or external input signals. The functional converter transforms the output of the adder by the activation function of the given type. Both natural and artificial neurons can be trained depending on the activity of the processes that take place in them. Also, as a result of training, the weight of the interneuronal connections also changes, which also affects the behavior of the corresponding neuron.
Advantages and disadvantages of neural networks are demonstrated in table 1. Advantages of neural networks Disadvantages and limitations of neural networks - adaptability to environmental changes; - - effective forecasting requires a certain training on examples; minimum number of observation (about 100 observations); - parallel processing of information; - significant time expenditures to achieve a satisfactory result; - insensibility to errors; - only specialists can prepare reliable interpretation of the results; - ability to generalize gained knowledge - learning algorithm can fall into the "trap" of the so-called local minimum error, and the best solution will not be obtained; - inability of traditional artificial neural networks to "explain" how they solve the problem.
One of the areas for application of neural networks is the agrarian industry. In the
research works [
The experience of such models application indicates the possibility to predict the
probable consequences of macroeconomic and industry decisions in the context of
preserving existing relationships [
Modern relationships require new variables to describe them in the economic system, which involves the expansion of characterization methods such as neural modeling and fuzzy logic. The high degree of probability of changes in economic systems is formed under impact of external factors, which makes it impossible to clearly define the goals of the updated system. In this case, the experience of traditional simulation is not enough, so the transition to the neural model of the description of reality becomes relevant. In the transformation model of agrarian sector, the synergetic approach reflects the result of the joint interaction of economic, financial, social and institutional factors (fig.2).
The synergetic effect determined by us is the result of the impact of external
factors. For example, «Е+F=α» under impact of the external factor creates the effect "в",
which with the resulting index "s" (as a result of «F + C = ω») forms the effect "B".
Result of the political and economic component creates the necessary conditions for
the effective functioning of the agricultural sector of the economy [
Taking into account the results of the study, we believe that the synergetic effect of
transformations (S) has to be the sum of the synergetic effect of the components,
which function is close to the maximum under determined level of risk (r). The risks
are natural, climatic, political, demographic, space threats, informational, ethnic,
religious, cultural, social, military conflict risks, terrorism, etc. [
production" inflation
The "Nova Troya" is a neural network model of "inflation-production", which uses a sample of 32 quarterly data for 2009-2016, formed on the basis of the financial statements of PLK TH "Nova Troya" (Ukraine, Kherson region Novotroitsk).
The task is to build a network based on the architecture of a multilayer perceptron using the Excel Neural Package architecture, which bases our data and forms the link between the indicators of economic growth of this enterprise (inputs of the model) and the level of inflation (output of the model), estimated through the quarterly consumer price index (CPI). The model will be used to predict the development of this enterprise for future periods of time (quarters).
Stage One. Introducing the source and placing them in Excel. Stage Two. Using Neural Analysis, we describe the placement of table 3. Stage Three. Identification of inputs (fig. 4)
The All Data window displays a complete list of 8 parameters of the model. As the input parameters we select the last 7. To do this, we perform the Select All command, which will carry all parameters to the Inputs window. Then we return the "extra" CPI parameter back to the All Data window using the adjustment button <. The result obtained is shown below in fig.4.
Stage Four. We perform the preprocessing of input data using the Normalization function. This step allows you to get rid of unnecessary computational problems due to the alignment of the range of variables. We choose the Mean / Variance option, in which the data becomes dimensionless by subtraction of the average value and division by their dispersion. Now all inputs are comparable in order of magnitude.
Stage Five. Next, using the Select Outputs function, we select the output parameter - CPI and normalize it with Mean/Variance result:
Stage Six. We determine the significance of the input parameters. We use the Boxcounting function, and the system by itself, using the Boxcounting algorithm, will determine the statistical significance of the inputs for the specified outputs. In the Boxcounting results window in graphical form we will see that the most significant parameters are x2 and x6 (≈0.4 and 0.3, respectively), and the significance of the parameters x1 and x5 is close to zero and they are insignificant in terms of the effect on the resulting variable. . The rest of the variables occupy an intermediate position by significance. The values of the normalization parameters are shown below: mean predictability = 0.095 and variance (variance) = 0.109. The more their ratio is different from 1, the better the predicted power of the model is. We calculate the ratio Average / Dispersion ≈ 0.87. Apparently, it is close to one, that is, the predicted strength of this network is low. Reducing the number of inputs allows you to shorten the training time of the neural network or allows you to increase its nonlinear properties. So let's go back to the main window and remove the insignificant entries x1 and x5 from the list (fig.7). parison purposes, we estimated the equation of multiple regression: - sales profit, - balance profit, - total profitability. For com117.59 1.96 ∙ 10 ∙ 4.79 ∙ 10 ∙ 1.022 ∙ 10 ∙ 1.96 ∙ .
The relevant statistics are shown in table 3. (1) (2)
The critical value of Fisher test with a confidence probability of 0.95, ν1 = k = 4, ν2 = n-k-1 = 27 is 2.73. Since Ffact = 3.28 > Ftab = 2.73, the regression is adequate. To estimate the independence of errors, we calculated the Durbin Watson criterion: d = Σ (e (t) -e (t-1)) 2 / Σe (t) 2 = 1.41777E-05. As critical table levels for n = 32 and k = 4 for a significance level of 5%, we got critical values di = 1,18 and du = 1,73. The calculated value did not fall into the interval, i.e. estimates can be considered independent. The following table shows the calculation of the coefficients of the neuroregression equation and the Student's statistics (t-criterion): • number of layers without input (Number of layer) = 2; • number of inputs (Number of inputs) = 4; • the number of neurons in the 1st layer (Layer1, neuron) = 3; • order of nonlinearity of the first layer (order) = 1; • type of output function of the first layer (function) = tanh; • the number of neurons in the second layer (neurons) = 1; • the order of nonlinearity of the second layer (order) = 1; • type of output function of the 2nd layer (function) = linear. We get the following neuron network:
Stage nine: Preparation for training the neural network. Before training we set the test set from the whole set of learning examples. Examples from this set will not participate in the training. They will serve as a base for building the estimates for the predicted properties of the trained network. With Edit test set in the window we set the size of the test sample (Number of test examples) = 0, and its character set in the random sample set (Random test set) (fig.10).
Stage ten: Training the neural network. In the course of the network learning you can see the change in the parameters in the field of training information (Training Info). We wait for the learning process to stop by itself or interrupt it artificially by pressing Stop Training button (fig.11).
The learning process stopped by itself. As you can see, 9336 epoches have passed at the moment, and the current training error is 0.2.
Learning outcomes can be assessed visually on the Network responses graph. The corresponding window is shown below (green dotted line shows network feedback, and orange one marks real data).
Stage Eleven. Using Output all data, we output the results of the neural network (table 3). As it can be seen from the table, the results of neuromodeling are well approximated by actual data and the total square error is only 0.01%. The approximate regression equation obtained on the basis of neuromodeling, of course, contains a big mistake, but also only 0.15% (15 times worse). Graphic illustration of the table is given below.
Let’s consider integral assessment of the risk of V & M (Voronov and Maksimov): Rating: • accepts values from 0 to 1; • every investor, based on his/hers investment preferences, can classify the value by allocating a segment of unacceptable risk values for themselves.
Advantages of the method: • the full spectrum of possible scenarios for the investment process is formed on the basis of the fuzzy sets theory; • the decision is made on the basis of the whole set of assessments rather than two assessments of the effectiveness of the project; • the expected efficiency of the project is not a point indicator, but a field of interval values with its distribution of expectations, characterized by the function of belonging to the corresponding fuzzy number.
Using the following graduation (table 5):
Using the Excel Neural Package, a developed network is based on the architecture of the multilayer perceptron, which analyzes the data and forms the link between the indicators of economic growth of analyzed enterprise.
The analysis of existing diagnostic technique of CPI (consumer price index) and the assessment of the financial performance of the enterprise were carried out. It allowed conducting a comprehensive financial and economic analysis of the enterprise with using of fuzzy logic tools, which will enable the formation of an economic and mathematical model taking into account the specificity of the enterprise. Одним з найбільш ефективних математичних інструментів, спрямованих на формалізацію і обробку невизначеної інформації, що інтегрує сучасні підходи і методи, є теорія нечіткої логіки. Даний математичний апарат дозволяє розглянути різні види невизначеності та отримати новий, якісно кращий прогноз розвитку економічних систем.
One of the most effective mathematical tools assigned at formalizing and processing of uncertain information which integrates modern approaches and methods is fuzzy logic theory. This mathematical instrument allows us to consider various types of uncertainty and get a new, qualitatively better forecast of the development of economic systems. 11. Kobets, V., Poltoratskiy, M.: Using an Evolutionary Algorithm to Improve Investment Strategies for Industries in an Economic System (2016), CEUR Workshop Proceedings, vol. 1614, P. 485-501 (Indexed by: Sci Verse Scopus, DBLP, Google Scholar). Available: CEUR-WS.org/Vol-1614/ICTERI-2016-CEUR-WS-Volume.pdf