Bauman Moscow State Technical University
Author list of organization
List of articles written by the authors of the organization
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MULTIFORMITY OF OBJECTS OF NON-NUMERICAL NATURE
01.00.00 Physical-mathematical sciences
DescriptionIn accordance with the new paradigm of mathematical statistics the statistics of objects of nonnumerical nature (statistics of nonnumerical objects, non-numerical data statistics, non-numeric statistics) is one of the four main areas of mathematical statistics. Statistics of objects of nonnumerical nature consists of a central core - statistics in spaces of arbitrary nature - and statistical theories of analysis of specific types of non-numeric data. To identify possibilities of application of statistics of objects of nonnumerical nature it is useful to explore the multiformity of objects of non-numeric nature. This is the subject of this article. We have considered the results of measurements at scales other than absolute; binary relations; dichotomous (binary) data; sets. We have also analyzed the objects of non-numerical nature as statistical data, and their importance in the formation of statistical or mathematical model of a real phenomenon, as a result of data analysis
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THE DIVERSITY OF CONTROLLING DOMAINS AND INSTRUMENTS
DescriptionIn modern conditions of quantitative and qualitative degradation of science in general and economics in particular, especially in our country, the scientific direction of "Controlling" stands out not only for its activity, but also the rapid intensive and extensive growth. This work is the summary of the main publications of scientific results on controlling obtained at the Laboratory of economicmathematical methods in controlling of Scientific and Educational Center "Controlling and management innovations" of Bauman Moscow State Technical University. We discuss the concept of "method", "tool", "mechanism", "algorithm" in relation to the Controlling. Adequate use of these terms is necessary for the formulation of sound scientific results, and to provide their perception of the scientific community. Innovations in the field of management in industry and other sectors of the economy based, in particular, on the use of new adequate organizational and economic methods. Controlling in this area - it is the development of relevant management procedures used and the newly established (implanted) organizational and economic methods to the task. Development, systematization and application of modern mathematical tools of controlling are the main theme of our work. We have considered the problems of controlling new areas - controlling risks, quality controlling, controlling organizational and economic support for control tasks in the aerospace industry, controlling research activities. We have also obtained new scientific results in controlling personnel and ecological safety controlling
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METHODS OF REDUCING SPACE DIMENSION OF STATISTICAL DATA
01.00.00 Physical-mathematical sciences
DescriptionOne of the "points of growth" of applied statistics is methods of reducing the dimension of statistical data. They are increasingly used in the analysis of data in specific applied research, such as sociology. We investigate the most promising methods to reduce the dimensionality. The principal components are one of the most commonly used methods to reduce the dimensionality. For visual analysis of data are often used the projections of original vectors on the plane of the first two principal components. Usually the data structure is clearly visible, highlighted compact clusters of objects and separately allocated vectors. The principal components are one method of factor analysis. The new idea of factor analysis in comparison with the method of principal components is that, based on loads, the factors breaks up into groups. In one group of factors, new factor is combined with a similar impact on the elements of the new basis. Then each group is recommended to leave one representative. Sometimes, instead of the choice of representative by calculation, a new factor that is central to the group in question. Reduced dimension occurs during the transition to the system factors, which are representatives of groups. Other factors are discarded. On the use of distance (proximity measures, indicators of differences) between features and extensive class are based methods of multidimensional scaling. The basic idea of this class of methods is to present each object as point of the geometric space (usually of dimension 1, 2, or 3) whose coordinates are the values of the hidden (latent) factors which combine to adequately describe the object. As an example of the application of probabilistic and statistical modeling and the results of statistics of non-numeric data, we justify the consistency of estimators of the dimension of the data in multidimensional scaling, which are proposed previously by Kruskal from heuristic considerations. We have considered a number of consistent estimations of dimension of models (in regression analysis and in theory of classification). We also give some information about the algorithms for reduce the dimensionality in the automated system-cognitive analysis
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PREDICTION METHODS FOR THE ROCKET AND SPACE INDUSTRY
01.00.00 Physical-mathematical sciences
DescriptionWe have allocated the basic sources of uncertainty in various industrial and economic situations. We have also considered the role and the tasks of forecasting in the management of industrial companies, particularly in the rocket and space industry. We have discussed the methods of organizational and economic forecasting - statistical, expert, combined, including foresight and given some suggestions for improving the forecasting and planning mechanisms for practical use when creating space systems
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METHODOLOGY OF CONTROL PROCESSES MODELING IN SOCIO-ECONOMIC SYSTEMS
01.00.00 Physical-mathematical sciences
DescriptionThe article introduces the basic concepts of control theory. It has also noted the multicriteriality of real control problems. After reviewing the basic concepts of the theory of modeling we have analyzed postwar history and current status of mathematical modeling of control processes. We have also discussed the modeling methodology. As an example of a real model of the management process we have considered a model of allocation of time between the acquisition of knowledge and development of skills
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PRICING METHOD BASED ON THE ESTIMATION OF DEMAND FUNCTION
08.00.13 Mathematical and instrumental methods of Economics
DescriptionWhen solving some problems of economics and management at an enterprise, it becomes necessary to determine the retail price of a product or service at a known wholesale price or producer price. We offer to determine the retail price based on an analysis of a survey of potential consumers about the maximum possible price for the product or service in question. We calculate the retail price on the basis of optimizing the economic effect equal to the product of the result from the sale of one unit of goods by the demand function, which we estimate by interviewing consumers. To solve the optimization problem, we approximate the demand function using the least squares method. As examples, the linear and power models of the demand function are analyzed. Ways of further development of the proposed approach are discussed. Unresolved scientific problems are formulated. Methods for estimating the demand function in the context of a large number of repetitions of respondents and their tendency to “round numbers” require further elaboration, as a result of which the Kolmogorov criterion cannot be used to determine the accuracy of the restoration of the demand function. Various parametric and non-parametric approaches of regression analysis should be adapted to the problem of restoring the dependence of demand on price, as well as methods for solving the corresponding optimization problems
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01.00.00 Physical-mathematical sciences
DescriptionWe have proposed the method for testing of independence of two alternative variables on the basis of statistics of non-numeric data. The method is aimed at application in problems of statistical quality control. Testing of independence is based on set of small samples, i.e., in the Kolmogorov’s asymptotics, when the number of unknown parameters of the distribution increases in proportion to the data size
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MATHEMATICAL METHODS OF CLASSIFICATION THEORY
01.00.00 Physical-mathematical sciences
DescriptionThis article gives a review of mathematical methods of construction and using of classifications. The main approaches to solving the problems of cluster analysis and grouping are discussed. We have also proposed global and local natural classification criteria. The methods of discriminant analysis (diagnosis, pattern recognition with the teacher) are discussed in connection with the construction of generalized indicators (ratings)
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MATHEMATICAL METHODS IN SOCIOLOGY DURING THE LAST FORTYFIVE YEARS
22.00.00 Sociological sciences
DescriptionSociology is one of the most important social sciences. Mathematical and primarily statistical methods are effective intellectual tools of sociologists. Let us analyze the work of the author of this article on the development of statistical methods to meet the challenges of sociology. Then we give the review of development of statistical methods in Russian sociology for 45 years (1970-2015). The basic scientific events of these years, first of all, were formation of applied statistics and its basis - statistics of the non-numerical data (in sociology of 70-90% of variables have non-numerical nature). Over the last 30 years, the Russian sociology has been growing rapidly in all quantitative parameters. Clearly, the depth of investigation gives the use of advanced scientific apparatus - methodology and methods of data collection and analysis, mathematical models. In our view, a fundamental breakthrough was made in our country in the 1970s. It was then in the arsenal of Russian sociologists appeared measurement theory and fuzzy sets, mathematical methods of classification and multidimensional scaling, nonparametric statistics and statistics of non-numeric data. In subsequent decades it has been a natural development of scientific apparatus. The same mathematical and statistical methods and models can be successfully applied in various fields of science and practice. Statistical methods and models are very effective in sociological, socio-economic, managerial, technical and feasibility studies, medicine, history, in almost any industry and application areas of knowledge. Within this field, the main event of the last thirty five years - is becoming a scientific and practical discipline "Applied Statistics", dedicated to the development and application of statistical methods and models. An analysis of the dynamics of applied statistics leads to the conclusion that in the XXI century the statistics of non-numerical data is becoming a central area of applied statistics, as it contains the most common approaches and results
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MATHEMATICAL THEORY OF RATINGS
01.00.00 Physical-mathematical sciences
DescriptionWhen developing management solutions with the aim of joint consideration and comparison of various factors, partial removal of uncertainty is widely used ratings. In the theory of decisionmaking in almost the same sense, we use the terms "composite index" or "integrated indicator". The article is devoted to the mathematical theory of ratings as tools for studying socio-economic systems. We considered, primarily, linear ratings which is a linear function from a single (private) indicators (factors, criteria), constructed using the coefficients of importance (weightiness, importance). The study discusses the factors affecting the magnitude of the ratings. Three groups of causes affect the value of a line ranking: the ways of measurement of individual indicators, the choice of the set of indicators; the values of the coefficients of importance. We considered binary ratings when the rating takes two values. To compare the proposed rankings we use a new indicator of the quality of diagnostics and prognostic power. Significantly, in many managerial situations, significant differences between objects are identified using any rating. According to the fundamental results of stability theory, the same source data should be processed in several ways. Matching findings, obtained using multiple methods, likely reflect the properties of reality. The difference is the result of a subjective selection method. When using the results of the comparison of objects according to several indicators (criteria ratings), including in dynamics, very useful is the selection of the Pareto set. We discuss the examples of the application of the decision theory, expert evaluations and rankings when developing complex technical systems