Plenary lecture 3: a fuzzy technologies of weakly structurable systems' modeling and simulation
Gia Sirbiladze · 2009
The Plenary Speech will present the new approach to the study of optimization of weakly structurable fuzzy dynamic systems (Extremal Fuzzy Dynamic System (EFDS)). This approach is based on the six papers published in the Int. Journal of General Systems (by G. Sirbiladze, Modeling of Extremal Fuzzy Dynamic Systems. Parts I-VI: 34,2, 2005, 107-138; 139-167; 169-198; 35, 4, 2006, 435-459; 35, 5, 2006, 529-554; 36,1 2007, 19-58). Different from other approaches where the source of fuzzy uncertainty in dynamic systems is expert, this approach considers time as long as an expert to be the source of fuzzy uncertainty. This notably widens the area of studied problems. All these is connected to the incomplete, imprecise, anomal and extremal processes in nature and society, where connections between the system's objects are of subjective (expert) nature, which is caused by lack of objective information about the evolution of studied system, for example in 1) engineering problems, 2) economics and business of developing countries, 3) management of evacuation processes in catastrophe areas, estimation of disease spreading in epidemical regions; 4) research of complex systems of applied physics, 5) conflictology, sociology, medical diagnosis, etc; One of our purposes is to create scenarios describing possible evolution of EFDS using methods of optimization developed by the framework of expert-possibilistic theory. This includes construction of algorithms of logical-possibilistic simulations of anomal and extremal process analysis. The plenary speech will cover the following topics: introduce the notions of extremal fuzzy time moments and intervals; construction of fuzzy processes with possibilistic uncertainty, the source of which is extremal fuzzy time intervals; the dynamics of EFDS's; questions of the ergodicity of EFDS's; Fuzzy-integral representations of controllable extremal fuzzy processes; Sufficient and necessary conditions for the existence of an extremal fuzzy optimal control processes. A separate consideration will be given to the case where an extremal fuzzy control process acting on the EFDS does not depend on an EFDS state. Applying Bellman's optimality principle and assuming that the gain-loss process exists for the EFDS, a variant of the fuzzy integral representation of an optimal control is given for the EFDS. This variant employs the instrument of extended extremal fuzzy composition measures. An example of constructing of the EFDS optimal control will be presented.