Publishing house Radiotekhnika

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Theoretical Foundations for Decision Making

G.I. Andreev,  P.A. Sozinov,  V.A. Tikhomirov

Decision theory represents the set of concepts and systematic methods allowing the preparation procedure for alternate solutions to be organized, the decidability of these solutions in unique situations with high level of uncertainty is evaluated on the base of critical analysis. The necessity to make decisions in situation of uncertainty occurs in all fields of engineering, economics and social sciences. The success of the decision depends on the methods, which the deciding person owns. At the present time there is rather a big amount of works, devoted to the issues of methods and models of decision-making improvement. The instrumental methodical complex developed in them, beginning from set-theoretical methods and ending with the models of cognitive computer graphics, allows successfully solving the important social and technical problems.
At the common background of such researches there is a small number of works in which the decision-making process would be the object of researches and study. At the historic background in the monograph the content and subject tasks are revealed, the main concepts and terms are introduced; on the base of the given classification the tie of decision theory with other disciplines is established. The distinctive feature of the offered monograph is conditioned that fact that it relates to the category of the multipurpose books. The book can be used as a reference book, tutorial and scientific-methodical manual. This book contains very detailed stated and submitted for consideration main theses of decision theory; issues of decision methodology, realized in generalized methods of decision- making organization; the detailed concept of information probabilistic approach to mathematical model forming of accepted decisions efficiency evaluation.
Studying the mathematical fundamentals of decision theory the authors represented the concept of the mathematical structure as the theoretic base of model construction in decision theory and set-theoretical concept. It is demonstrated, that the set forming procedure for choice options is connected with the main theses of classical approach. In this book methodological bases of optimum decision for practical tasks of decision theory are given, external fundamentals of probability theory are revealed (not remarkable for theoretically strict stating of the own fundamentals, demonstrating the power of mathematical abstraction) and the main concepts of this theory, elementary mathematical models of collisions are considered.
The represented materials, connected with certainty value of the results ob-tained, and also the problem of confirmation and denial of scientific theses and decision theory deserve particular attention. The key part of the reliable knowledge determining problem is considered, the main theses and principles of validity of the judgements establishing and the bases of validation of scientific hypotheses and models for alternate solution forming are formulated.
The analysis of the main concept theses of methodology of strategic management made by the authors is aimed at construction of information -probabilistic method and mathematical model building for strategic decisions evaluations for systems of any physical content. The model is based on the following principles of: general theory of topological spaces constant functions; fuzzy set theory; Bayesian approach; models and some theses of mathematical statistics, connected with test construction for validation of statistically simple hypothesis and principles of information theory with its average entropy-information evaluations. The process of these evaluations determination not only provides the difficult preference determination in set of alternatives, but also makes the ground for conducting the analysis of the process of strategic decisions making.

М: Publisher «Radiotekhnika», 2017 y. – 648 pages: , pict.

ISBN 978-5-93108-154-0
Format: 60x90/16, Binding, cover


_________________ ГЛАВА 1________________

Научные основы  теории принятия решений

1.1.  Собственные основания теории принятия решений

1.2.  Внешние основания теории принятия решений

1.3.  Базисная модель принятия решений

1.4.  Концепция математической структуры  как теоретическая основа построения моделей  теории принятия решений


_________________ ГЛАВА 2_________________

Математические основы  теории принятия решений

2.1.  Теоретико-множественная концепция

2.2.  Элементы функционального анализа

2.3.  Элементы линейной алгебры

2.4.  Алгебра матриц, специальные виды матриц


_________________ ГЛАВА 3_________________

Методы теории принятия решений  в условиях определенности

3.1.  Методы поиска экстремумов функций

3.2.  Многомерная минимизация.  Методы математического программирования

3.3.  Методы нелинейного программирования

3.4.  Методы случайного поиска


_________________ ГЛАВА 4_________________

Модели и методы теории вероятностей и математической статистики

4.1.  Основные понятия теории вероятностей

4.2.  Формирование моделей теории вероятностей

4.3.  Теоретические основы  математической статистики

4.4.  Аналитическое исследование  вероятностных моделей


_________________ ГЛАВА 5_________________

Методы, основанные на использовании  интуиции и опыта специалистов

5.1.  Экспертные методы в теории принятия решений

5.2.  Общие положения и основные свойства  методов экспертных оценок

5.3.  Особенности методов экспертных оценок  

5.4.  Построение групповых решений  на основе нечетких отношений предпочтения


_________________ ГЛАВА 6_________________

Подтверждение и опровержение  достоверности принимаемых решений

6.1.  Определение достоверности оценок результатов  принимаемых решений

6.2.  Концептуальная модель оценки результатов  принимаемых решений  

6.3.. Процесс принятия решений по процедуре  идентификации модели

6.4.  Достоверность и обоснованность  полученных результатов принимаемых решений


_________________ ГЛАВА 7_________________

Информационно-вероятностная концепция  теории принятия решений  в ситуации стратегического прогноза

7.1.  Информационно-вероятностный подход

7.2.  Информационно-вероятностный метод  стратегической оценки принимаемых решений

7.3.  Программная реализация информационной модели  принимаемых решений

7.4.  Концепция оценки систем  различной физической природы  на основе средних  энтропийно-информационных показателей



 Science series «Decision Making in Management»

G.I. Andreev,  P.A. Sozinov,  V.A. Tikhomirov

Theoretical Foundations for Decision Making

Научная школа  «Теория принятия решений в управлении развитием  сложных технических систем» 

June 24, 2020
May 29, 2020

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