OVERVIW of the Monograph Gia Sirbiladze, Extremal Fuzzy Dynamic Systems - Theory and Applications, IFSR International Series on Systems Science and Engineering, 28, Springer, 2013, 375 pp

Author: Gia Sirbiladze
Keywords: Extremal Fuzzy Dynamic Systems, Systems Identification, Optimization and Filtration
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The book proposes a new direction in the quantitative fundamental study of weakly structurable dynamic systems (WSDS) and in systems science research in general. Different from other approaches to the investigation of dynamic systems where the source of fuzzy (possibilistic) uncertainty is an expert or an object-expert combination, the book presents the approach where the source of uncertainty is also the time. That is, the time factor also contributed to the uncertainty in dynamic systems, which makes the range of problems to be investigated much wider. The dual approach (extremality) to the study of weakly structurable dynamic systems with respect to fuzzy time is novel and presently has no analogue. The extremality of fuzzy processes makes it possible to describe the fuzzy dynamic system and its prediction in terms of fuzzy “extended current and compressed future” time intervals and thereby to obtain more authentic subjective information from the information source on the expert, his/her knowledge, a state of the investigated WSDS and so on. This is possible because the complement information on the WSDS state in a current fuzzy time interval before the moment t does not in general coincide with information on the WSDS state in a future fuzzy time interval after the moment t, since these both kinds of information overlap each other with respect to the real time moment t. So we construct new type structures in the problems of expert knowledge stream’s formalization, synthesis and analysis. New results are obtained in the theory of extended monotone measures. New Fuzzy-integral models of WSDS’s are constructed with controls taken into account. Methods of identification, filtering, prediction and optimal problems for fuzzy-integral models of extremal fuzzy processes are developed. The trustworthy realizations of possibilistic scenarios are also constructed for future fuzzy-time intervals. These give new possibilities to the researchers of complex dynamic events. The software library, on the other hand, is a novel instrument for engineering of intelligent decision support systems and expert systems.