Shlyakhov V. Multialgebraic systems in factorization process models

A research object is processes of functioning of the sensory systems. Thesis is dedicated to development, justification and all-around study of methods and models for factorization of arbitrary physical nature data. Complex of this methods and models provides an instrumental mathematical mechanism for adequate modeling of intellectual information perception processes. The concept of multialgebraic systems was introduced and necessary and sufficient properties were derived, fulfilling these properties induces basic multialgebraic systems: multirelations and multioperations. The isomorphism conditions of multialgebraic systems were discovered, this allows to distinguish fundamentally different systems, both in case of carrier distinction and main relations and operations distinction. On the set of partitions of an arbitrary measurable set we introduce the functional that takes into account not only the measure of sets similarity, but also the measure of their differences. It is proven that this functional is a metric; created analogy with entropic metric; obtained probabilistic and integral interpretations of metric properties. Investigated geometrical properties of set of partitions as a metric space object. Built specifically multialgebrac system in the form of a linear space and the conditions for the existence of metric predicates for evaluating the curvature of the metric properties of space, induced by a homeomorphism that is present in models of sensory systems. Performed experimental analysis of metric and predicative factorization problems.. Degree of introduction: were drawn on research results in NII of information technologies of the Kherson state university (act from 3.12.2008); in the institute of "Ukrndispecstal'" (act from 28.11.2007); in the Kharkov military university (act from 20.12.2000); there is "Mercury" in AKB (certificate from 13.05.2008); in an educational process at preparation of specialists, master's degrees on speciality "informatics" on the department of informatics of the Kharkov national university of radio electronics (act from 22.12.2009). Sphere of the use - in organizations, which are engaged in the problems of development of models and methods of treatment of faktorizational information of arbitrary physical; in establishments, which are engaged in developments in industry of information technologies, finances, transport; in an educational process at preparation of specialists in industries of informatics, applied mathematics and intellectual treatment of information.