Properties of tolerance relations and tolerance classes are studied. Tolerance classes are demonstrated to form carrier set coverings. The conditions are proved under which tolerance and equivalence classes coincide.

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The relationship between the properties of difunctionality and ternary relations is analyzed as applied to information factorization problems. Conditions are found under which arbitrary n-ary relations induce multialgebraic systems with a common carrier in the form of a Cartesian cube. Multigroup axiomatics is considered. Conditions of existence of groups over equivalence classes are formulated and proved. Examples of producing multigroups and cases when a common carrier is absent are given.

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Image processing for the efficient retrieval should perform the ability of data granulation and interpretation. In this paper the properties of metric on nested partitions which allow to analyze objects represented at different levels of granularity and abstraction is considered. It also ensures a retrieval of image parts corresponding to the searched objects i.e. provides a search criterion for background independent objects.