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In this paper a creation of new numerical set-theoretical constructions of Boolean functions with their properties has been presented. The parted conjuncterms and decomposition clones which can be used for realization of different optimization logic synthesis of digital devices and systems have been proposed. Set theoretical operations and procedures with these constructions have been considered. Examples which illustrate simplicity of their practical realization have been presented. Moreover, the paper includes the comparison of new results obtained on the basis of the proposed approach with the results obtained by means of commercial software Quartus II of Altera.