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A. N. VoroninUDC 519.51Synergetic methods of data complexation are proposed that make it possible to obtain a maximal amount of available information using a limited number of channels. Instead of reducers of degrees of freedom, a mechanism of discriminators of degrees of freedom is proposed that enables all the channels to take part in the development of a cooperative decision in accordance with their informativeness in a current situation.Topicality of the problem. In the hierarchy of systems theories, synergetics or the science of cooperative processes [1, 2] occupies the upper level. It is an integrated science that allows one to arrive at a holistic understanding of nature, technics, and society on the basis of a unified synergetic conception. In contrast to the general systems theory, synergetics studies cooperative, coherent, and self-consistent processes running in complex systems. Whereas cybernetics develops control methods that force a system to function in a predetermined way to achieve its objective, synergetics organizes a process characterized by self-control and self-organization in accordance with a predetermined objective. In this case, intricate processes are developed not under centralized actions but as result of collective interaction of components. The cooperation of components makes it possible to use reserve capabilities of a system and substantially increases the degree of system effect.Of course, the passage to an integrated conception such as the synergetic one requires new scientific and applied investigations that reflect cooperative (i.e., synergetic) phenomena in corresponding knowledge domains [1] and, hence, the problem considered in this article is topical.Analysis of the state of the problem. Among object domains, biology turns out to be most susceptible to the ideas of synergetics. According to P. K. Anokhin [3], when a biological organism has need of obtaining a definite result, it generates a special functional system to meet this need. The content of the sought-for result (the objective) is formed by the system in the form of some model before the obtaining the result itself. If the result is satisfactory, then the organism passes to the formation of another functional system to obtain another useful result that is the next stage in a universal continuum of objectives. If the result is insufficient, then activating mechanisms are stimulated, new components are actively selected, the degrees of freedom of operating synaptic organizations are changed and, finally, after several trials and errors, a satisfactory result of the process of adaptation is found.A functional system is a genuine cooperation of a set of components aimed at obtaining the predetermined useful result. From this viewpoint, the term "mutual assistance" is more adequate. A component can be added to a system only if it contributes its portion of assistance to the obtaining of the necessary result. After addition to the system, the component immediately eliminates all the degrees of freedom that prevent the o...

A comparative analysis of some aspects inherent in methods of mathematical statistics and synergetic methods of data complexation is carried out. The results obtained are used to increase the efficiency of statistical estimates computed from a small sample and also to determine estimates of characteristics of objects and processes in synergetic systems of data complexation when the number of channels is limited.A direction of investigation in the field of synergetics [1, 2] is the development of methods of data complexation (merging). In contrast to the general theory of systems, synergetics studies cooperative, coherent, and self-consistent processes running in complex systems. Whereas cybernetics develops control methods that provide the achievement of the formulated objective by a system owing to its functioning in a predetermined manner, synergetics organizes a process characterized by self-control and self-organization in accordance with the objective formulated. Here, complicated processes are developed not as a result of centralized actions but owing to the interaction of a collection of components. The cooperation of components makes it possible to use reserve capabilities of a system and to substantially increase the extent of system effect.In complex synergetic systems, information on the same process (an object or an event) is usually transmitted over several channels. The problem lies in determining the channels over which more significant data are transmitted. Depending on this, it is required to combine (integrate) obtained data to develop a cooperative decision on the state of an object. In the traditional method, it is expected that one or several most informative (dominant) channels are selected and that the other channels are truncated. This is realized by means of the mechanism of reducers of degrees of freedom [1]. An advantage of this method is its simplicity but some information contained in data received from the truncated channels drops out of consideration and does not participate in the process of development of a cooperative decision.In synthesizing a synergetic system of data complexation, it makes sense to refuse the conception of a dominant and, instead of reducers of degrees of freedom, to use discriminators of degrees of freedom, i.e., mechanisms that allow all the channels of obtaining data to participate in the process of formation of a decision with the weights corresponding to the degree of their informativeness in the current situation. As a result, all the items of available information will be used properly.The synergetic principle of data complexation has much in common with mathematical statistics [3]. In particular, the synergetic conception of data merging is applied to the estimation of characteristics of processes (objects) from an available data set, and mathematical statistics studies methods for estimation of moments of distribution of random quantities from an available collection of sample units. The commonality of problems of both theories testifies to the topica...

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An approach is proposed to solve a vector optimization problem for complex engineering and economic systems where the information about experimental and statistical data necessary to set up regression models is insufficient (or absent). To solve this problem, multiobjective optimization with nonlinear trade-off scheme is employed.There is often a lack of experimental and statistical data to develop necessary mathematical models for the optimization of complicated engineering and economic systems. The situation is worsened in case of the optimization with respect to several contradictory performance criteria.If there is an acute shortage of experimental data, we propose to obtain the necessary information ("quasiexperimental" data) from experts experienced in the design and maintenance of such complicated systems.The study is based on the example of multiobjective optimization of space engineering objects with respect to a generalized reliability-cost criterion; however, the results can easily be used in other subject areas. By the reliability we will mean the probability of the fact that the key parameters of all the elements of the object are within admissible limits.It is necessary to take into account that the case in hand is designing fundamentally new technological items for which performance indices considerably differ from those developers dealt with earlier or now. One of the particular aspects is the boundedness (or total absence) of experimental and statistical data that would be used to determine mathematical models of reliability and cost.These hardly formalizable conditions involve nonconventional approaches, one of which is considered in the paper. It is natural that in this case we can only mean preliminary calculations and approximate determination of the main tendencies when choosing the factors that influence the reliability and cost of space engineering objects being developed. PROBLEM STATEMENTTo solve the optimization problem, it is necessary to have the following data as the starting point for the mathematical model.