Volchkov S. Researching of stability and observation fuzzy discrete systems

Current dissertation work is devoted to decision the problem of dynamic and qualitative research fuzzy discrete systems in the view of theoretical work. The methods and algorithms are proposed for resolving the applied mathematical models of dynamic fuzzy systems. For the fuzzy discrete difference system some approaches are proposed for formalization arithmatical operations with fuzzy discrete sets in the view of two algorithms. These algorithms are used for the description the situation of decision making. The task of more accurate definition models of fuzzy discrete difference systems are formalized in the view of procedure, which calculates the consistency estimation of results of grouping expert poll. For the fuzzy difference system, stablesimialar properties are researched in the cases, when system has and does not have the regular trajectory. For the fuzzy difference system, theorems for stability (asymptotical stability) of solutions by Lyapunov are formulated and proved. For the fuzzy discretedifference system of special view, the procedure of building the function of Lyapunov is proposed. For the fuzzy uncertaing system the task of observation is formulated. The object of observation is considered, which is described by the difference fuzzy uncertaing system. For the observation task theorems about solution's properties are found.