Tereshchenko E. The investigation of the classification problems in indefinite conditions and the elaboration of the solution algorithms at graph model for them

The double-level modeling for special classification problem has been constructed in the dissertation. This problem has special criteria vector for the estimation of the solution and for non-full and non-exact data conditions. The graph model of this classification problem as vector optimization problem of a covering the graph G by stars with interval weights of edges, has been developed at the upper level of the modeling. The properties of this problem have been studied. Two groups of the approximate polynomial algorithms have been elaborated and proved. The sufficient conditions of the statistically effective algorithms at the first group and asymptotically exact algorithms at the second group have been proved. The Boolean model of the different types of data has been elaborated at the lower level of the modeling. It allows finding weights of edges of the graph G, finding conformity to natural laws of the class as Boolean function. The method of build for fuzzy class in the form d-expansion of the class with belong function in the matrix-form have been constructed.