Application in economics

     Many various problems were solved in the past on the request of the State Planning Committee of Russian Federation, which existed earlier [1]. In one of the problems it was necessary to  edit the table (to find the errors), containing the characteristics of grain production in regions of Russian Federation. The describing properties revealed the data on sowing areas, amount of fertilisers, number of tractors, harvest combines etc. The aim characteristics were related to crop capacity, overall yield of grain and so on. It was discovered, that some characteristics were not connected with each other and this led to significant mistakes in the attempts to recover them. For example, the fact, quite strange at the first sight, was found out that the amount of fertilisers does not influence the crop capacity. The real explanation was that fertilisers were actually used in the production of vegetables only, while grain crops were receiving them in not sufficient quantities. 
     Significant deviations from the general regularity for separate elements of the table were found as well. Some of these deviations were quite clear to the workers of the Planning Committee: «We suspected for a long time, that … region is deceiving us in that index!» We did not knew was it true or not, but became convinced once again, that sometimes the user tends to overestimate the reliability of the computer solutions. It is always necessary to underline the necessity of careful substantial verification of the obtained computer solution, not trying to accept it as indisputable truth, but trying to supplement the computer answers for the question «What?» with human answers to the questions «How?» and «Why?» 
     One of the tables contained the monthly data on average milk yield in the Country for the period from 1946 to 1982. It was required to learn the software to predict the milk yield for one year ahead. ZETMC program was used. It was found out that discovered regularities (similarity of strings and similarity of columns) gave the way to make such forecasts with high enough reliability: the prediction error was not exceeding 1.5%. Practically the prediction was made for 14 months ahead. We were receiving the milk yield data for the period from January to October of the current year and we were sending to the Planning Committee the forecasts for the end of this year and for all months of the next one. During all this period the Committee was sending us the actual data for each month. We were making the prediction for the remaining months of this period. The experience showed, that such method of «sliding» correcting prognosis is the most adequate for the information support of managerial decision making processes. 
      According to the reports of agricultural farms of Novosibirsk region the deviations of their aim production properties (amount of produced grain, milk, vegetables etc.) from the «average-regular» values were defined by means of ZET algorithm. It was found out, that some enterprises were giving higher results than enterprises with similar production conditions. The reason was that they used the existing recourses more efficiently. We also detected «pseudo-leaders» with absolute results higher than for the other farms, but lower than the regularly expected, predicted by ZET algorithm. Such farms used significantly higher resources thus giving the lower production yield per unit of resources, than small middle-level enterprises. 
  

Application in geology and medicine.

     Data tables, revealing the information from few different geological expeditions, usually contain a lot of empty cells. Expeditions had different set of measurement equipment, some device went out of operation, some data were lost etc. So for the usual methods of analysis in the beginning it is necessary to try to fill the gaps in such summary table. 
     The similar situation is typical for the medical data, obtained by means of combination of information from illness records for various patients into one table. During the visits even to the same physician the different symptoms were established. Higher deviation is observed when the documents from other physician or from another hospital are used. As a rule, such tables contain at least 30% of empty cells. 
     The strategy of filling of big amount of gaps was elaborated on such types of tables. The initial conditions for filling of different spaces are not similar. For some gaps it is possible to find the competent submatrix with competency of strings and columns. For others it is impossible, they are less defined. The recommended strategy is the following. Initially it is necessary to fill the empty space with the best certainty. Then, relying upon all elements, including the just filled one, to find the most certain gap from the remaining ones. Such process of filling the most defined element at every step is prolonged until the complete filling of the table. 
     At every step the program outputs the information on expected error of prediction of the filled element value. The process may be interrupted when the expected error becomes higher the fixed limit. 
     We also have met the exotic case, when the table contained 82% of empty cells. At the same time it was an extremely valuable information for geologists and the attempt to fill the gaps was undertaken. Existing 18% were sufficient to fill just a few cells. It was impossible to find competent strings and columns for other gaps. 

 
Technical applications.

     In one of the problems the data revealed the known properties of TV receivers of different types. The TV producing companies give their technical properties, but the sets of these properties do not coincide completely. The combination of such data into one table results in appearance of empty spaces and it is interesting to fill them to discover some properties which are passed over in silence by producer. It was found out that some properties of the receivers are connected with other properties by strong regularity and the predictions of such well defined gaps are very well confirmed. At the same time it was discovered that there are some properties, which do not depend upon other characteristics and cannot be predicted satisfactorily. The example of such independent property is frame material (metal, wood or plastic), which does not depend upon the screen size, scanning frequency etc. 


REFERENCES

1. Elkina V.N., Zagoruiko N.G., Novoselov Yu. A. Mathematical methods of agroinformatics. Published by Institute of Mathematics SB AS USSR, Novosibirsk, 1987.