Abstract.The relationship between the properties of difunctionality and ternary relations for information factorization problems is analyzed. The conditions where arbitrary n-ary relations induce multialgebraic systems with common carrier in the form of Cartesian cube are found. Multigroup axiomatics is considered. The conditions of the existence of groups on equivalence classes are formulated and proved. The examples of multigroups producing and the cases where common carrier does not exist are provided. Figs: 4. Refs: 19 titles.

Keywords: granulation calculus, multialgebraic system, ternary relation, difunctionality, multigroup, quotient set.