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Mathematics - Applications | Extremal Fuzzy Dynamic Systems - Theory and Applications

Extremal Fuzzy Dynamic Systems

Theory and Applications

Sirbiladze, Gia

2013, XXII, 402 p.

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  • ​Presents a new approach for fuzzy modeling of dynamic processes in the systems sciences research ​
  • Systematica​lly organizes the topic by covering theory first and applications later
  • Introduces a software library which is used to demonstrate the applications

In this book the author presents a new approach to the study of weakly structurable dynamic systems. It differs from other approaches by considering time as a source of fuzzy uncertainty in dynamic systems. It begins with a thorough introduction, where the general research domain, the problems, and ways of their solutions are discussed. The book then progresses systematically by first covering the theoretical aspects before tackling the applications. In the application section, a software library is described, which contains discrete EFDS identification methods elaborated during fundamental research of the book.

Extremal Fuzzy Dynamic Systems will be of interest to theoreticians interested in modeling fuzzy processes, to researchers who use fuzzy statistics, as well as practitioners from different disciplines whose research interests include abnormal, extreme and monotone processes in nature and society. Graduate students could also find this book useful.

Content Level » Research

Keywords » Dynamic Systems Theory - Extremal Fuzzy Processes - Extremal Fuzzy Software - Fuzzy Measures - Fuzzy Statistics

Related subjects » Analysis - Applications - Artificial Intelligence - Operations Research & Decision Theory - Theoretical Computer Science

Table of contents 

Fuzzy Measures and Fuzzy Statistics: Its Probability Representations.- Extended Extremal Fuzzy Measures.- Extended Extremal Fuzzy Measures on Compositional Product of Measurable Spaces.- Modeling of Extremal and Controllable Extremal Fuzzy Processes.- Identification of  Fuzzy-Integral Models of Extremal fuzzy Processes.- Optimization of Continuous Controllable Extremal Fuzzy Processes and the Choice of Decisions.- Problems of States Estimation (Filtration) of Extremal Fuzzy Processes. - Conclusions on the Parts I-VII.- Algorithms and software for Discrete Possibilistic EFDS.- Application  of the Discrete Possibilistic Model  of the EFDS in the Evaluation of  Expert Knowledge Streams.- Application: Forecasting of  Increasing Financial Risks (Credit Risks) of Georgia-based Organization (LTD-“Fractal”) by the Discrete Possibilistic EFDS’s Finite Model.-  General Conclusions.- Bibliography.​

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