Kagramanyan O. Models of information factorization on the basis of multigroups

The thesis is devoted to developing of methods and models of a generalization (roughening) or a concretization (detailing) of data within the limits of multialgebraic systems. The task of information granulation models synthesis is solved in the conditions of group properties fulfillment for quotient sets. Criteria of formation of the uniform carrier for the ternary relations induced by arbitrary n-arity relation are obtained, the group axiomatics in ternary relation notation is formulated, boundary conditions of factorization procedures are established. Necessary and sufficient conditions, at which fulfillment for arbitrary relation on the source data a multigroup is induced on classes of equivalences, and an usage of multigroup provides possibilities of the analysis of reversibility of functionalities on quotient sets and creates premises for search of the reasonable compromise between excessive and insufficient factorization of sets, are found. The metric defined on partitions of any nature measurable sets is introduced, ground and studied. Experimental researches confirmed efficiency of the proposed methods and models. Methods of double factorization of video (in time and in field of view) are taken as a principle of partitions exploration of video frames which, in turn, are represented by partitions on which there exist a group relationship.