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