Authors: A. A. Bosov, V. M. Ilman, N. V. Khalipova
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Purpose. The development of complicated techniques of production and management processes, information systems, computer science, applied objects of systems theory and others requires improvement of mathematical methods, new approaches for researches of application systems. And the variety and diversity of subject systems makes necessary the development of a model that generalizes the classical sets and their development – sets of sets. Multiple objects unlike sets are constructed by multiple structures and represented by the structure and content. The aim of the work is the analysis of multiple structures, generating multiple objects, the further development of operations on these objects in application systems. Methodology. To achieve the objectives of the researches, the structure of multiple objects represents as constructive trio, consisting of media, signatures and axiomatic. Multiple object is determined by the structure and content, as well as represented by hybrid superposition, composed of sets, multi-sets, ordered sets (lists) and heterogeneous sets (sequences, corteges). Findings. In this paper we study the properties and characteristics of the components of hybrid multiple objects of complex systems, proposed assessments of their complexity, shown the rules of internal and external operations on objects of implementation. We introduce the relation of arbitrary order over multiple objects, we define the description of functions and display on objects of multiple structures. Originality.In this paper we consider the development of multiple structures, generating multiple objects.Practical value. The transition from the abstract to the subject of multiple structures requires the transformation of the system and multiple objects. Transformation involves three successive stages: specification (binding to the domain), interpretation (multiple sites) and particularization (goals). The proposed describe systems approach based on hybrid sets can be used in many application systems for structural and content analysis. An example of the use the hybrid sets for logistics systems modeling is shown.