Ivan A. Dychka, Yevgeniya S. Sulema


Background. The range of hardware for surveillance, monitoring, and measuring is quite wide now. It gives new opportunities for obtaining large amounts of data which describe behaviour of an object (subject, process, phenomenon) of observation. Since observation is a process fulfilling in a course of time as well as usually it is resulted in obtaining multimodal data sets, it is reasonable to represent this time-based multimodal data as a multi-image of an object of observation by employing the apparatus of the Algebraic System of Aggregates.

Objective. The objective of the research is to define ordering operations of the Algebraic System of Aggregates and to present an approach of their application for processing a multi-image of an object of observation.

Methods. The research is based on both the Algebraic System of Aggregates and the concept of multi-image which enable complex representation and processing of multimodal data. There are logical, ordering and arithmetical operations in the Algebraic System of Aggregates. Ordering operations can be used for time-based processing of real objects, subjects, processes data represented as multi-images.

Results. The ordering operations on aggregates are proposed and described. These operations allow to process data of multi-images with respect to time; in particular, they enable reordering of tuples and tuple elements.

Conclusions. The processing of complex data structures of multimodal nature, which are defined, generated, measured, or recorded in terms of time, can be fulfilled based on mathematical apparatus of the Algebraic System of Aggregates, in particular, by using the ordering operations presented in this paper. It can be useful in different areas for data processing of real-world objects (subjects, processes, phenomena), characteristics of which can be measured as multimodal data by multiple sensors and presented as aggregates and multi-images.


Algebraic system of aggregates; Ordering operations; Multimodal data; Multi-image

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M. Grieves and J. Vickers, “Digital twin: Mitigating unpredictable, undesirable emergent behavior in complex systems”, in Transdisciplinary Perspectives on Complex Systems. Springer, 2017. doi: 10.1007/978-3-319-38756-7_4

E.J. Tuegel et al., “Reengineering aircraft structural life prediction using a digital twin”, Int. J. Aerospace Eng., vol. 2011, Article ID 154798, 2011. doi: 10.1155/2011/154798

E. Glaessgen and D. Stargel, “The digital twin paradigm for future NASA and U.S. air force vehicles”, in Proc. 53rd AIAA/ASME/ASCE/AHS/ASC Conf. Structures, Structural Dynamics and Materials, 2012. doi: 10.2514/6.2012-1818

Th.H.-J. Uhlemann et al., “The digital twin: Realizing the cyber-physical production system for industry 4.0”, in Proc. 24th CIRP Conf. Life Cycle Engineering, vol. 61, pp. 335–340, 2017. doi: 10.1016/j.procir.2016.11.152

I. Dychka and Ye. Sulema, “Logical operations in algebraic system of aggregates for multimodal data representation and processing”, in KPI Sci. News, no. 6, pp. 44–52, 2018. doi: 10.20535/1810-0546.2018.6.151546

Ye. Sulema, “ASAMPL: Programming language for mulsemedia data processing based on algebraic system of aggrega­tes”, in Interactive Mobile Communication Technologies and Learning. IMCL 2017. Advances in Intelligent Systems and Computing, vol. 725, M. Auer and T. Tsiatsos, eds. Cham, Switzerland: Springer, 2018, pp. 431–442. doi: 10.1007/978-3-319-75175-7_43

A.I. Maltsev, Algebraic Systems. Moscow, SU: Nauka, 1970, 392 p.

A.A. Fraenkel et al., Foundations of Set Theory. Elsevier, 1973, 415 p.

B.A. Kulik et al., Algebraic Approach to Intellectual Processing of Data and Knowledge. Saint Petersburg, Russia: SPbPU Publ., 2010, 235 p.

A.B. Petrovsky, Space of Sets and Multi-Sets. Moscow, SU: Editorial URSS, 2003, 248 p.

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