Vyacheslav V Kolbin – författare
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This monograph defines the notion of a “system” by reference to those systems which exhibit goal-oriented behavior and utilize the notion of decision making and controls. Such systems allow for phenomenological description and fix the nature of causal transformations of input effects into output quantities. The study of consequences of the fact that the systems possess some properties constitutes the content of systems optimization methodology which goes beyond the scope of descriptive classification of systems.Chapter 1 deals with philosophical problems of systems methodology. An attempt is made to systematize and analyze the problems of scientific methodology as applied to systems modeling methodology which is viewed as the most general concept utilized in modern science.Chapter 2 focuses on problems of qualitative analysis in natural and social sciences. Attention is drawn to problems of measurement theory and quantitative analysis of systems.Approaches and methods of systems analysis and synthesis form the central portion of the book. Much study is given to the methods of systems decomposition, an integration using both discrete and continuous descriptions of objects, processes, and phenomena. Examples of complex goal-oriented systems are also provided.The remaining part of the book is largely centered around the methodology of multiobjective systems optimization.
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This monograph deals with theoretical fundamentals and numerical methods of optimizing nondetermined models of systems. The main body of this work is devoted to investigation and optimization of system models under incomplete information. Much consideration is given to one-, two- and multistage problems of stochastic programming, solution methods and problems of solution stability. Optimization problems with fuzzy variables and optimization problems in function spaces are investigated. Examples are given for implementation of specific models of optimization under incomplete information.The book is based on lectures delivered by the author since 1965 for undergraduates and postgraduates at St. Petersburg (Leningrad) State University.
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The problem of selection of alternatives or the problem of decision making in the modern world has become the most important class of problems constantly faced by business people, researchers, doctors and engineers.The fields that are almost entirely focused on conflicts, where applied mathematics is successfully used, are law, military science, many branches of economics, sociology, political science, and psychology. There are good grounds to believe that medicine and some branches of biology and ethics can also be included in this list. Modern applied mathematics can produce solutions to many tens of classes of conflicts differing by the composition and structure of the participants, specific features of the set of their objectives or interests, and various characteristics of the set of their actions, strategies, behaviors, controls, and decisions as applied to various principles of selection or notions of decision optimization.The current issues of social and economic systems involve the necessity to coordinate and jointly optimize various lines of development and activities of modern society. For this reason, the decision problems arising in investigation of such systems are versatile, which shows up not only in the multiplicity of participants, their interests and complexity of reciprocal effects, but also in the laborious development of social utility criteria for a variety of indices and versatile objectives. The efficient decision methods for such complex systems can be developed only the basis of specially developed mathematical tools.