Issue 1 (195), article 4


Kibern. vyčisl. teh., 2018, Issue 1 (195), pp.

MILIAVSKYI Yu.L., Senior Lecturer,
Department of the Mathematical Methods of System Analysis

National Technical University of Ukraine “I. Sikorsky Kyiv Polytechnic Institute”
37 Peremohy av., Kyiv, 03056, Ukraine


Introduction. Cognitive map is a popular way of modeling complex multivariate systems. Usually weights coefficients of edges connecting the cognitive map nodes are suggested by experts. But such a method is always inaccurate. In case when nodes coordinates are measured, there is the possibility for mathematical identification of these coefficients. However, the issue is that often not all nodes coordinates of a cognitive map are measured, but only a few of them. In this case the problem of identification is much more complicated.
The purpose of the article is to research and develop a method for identifying weights of cognitive map nodes in case when number of nodes is known, but not all of them are measured.
Results. Identification method based on 4SID method is suggested. It allows finding some realization of the system equivalent to the original cognitive map in its outputs, with the control observation matrices remaining unchanged.Invariants of the original and identified systems are analyzed. Practical example of identifying a cognitive map of an IT company is considered. It is shown what the accuracy of the suggested method depends on and under which conditions it is applicable.
Conclusions. As demonstrated in the research, the proposed method of identifying cognitive maps achieves almost full coincidence of measured coordinates between the original and the identified systems, although the incidence matrices themselves may not be equal. Invariants of the system, specifically eigenvalues, are identified with sufficient precision if the problem is well-conditioned, i.e. with sufficient number of measurable coordinates, sufficient number of measurement periods and low level of measurement noise. If these conditions are not fulfilled, the identification results become incorrect.

Keywords: cognitive map, identification, 4SID method, unmeasurable coordinates.

Download full text!


  1. Roberts F. Discrete Mathematical Models with Applications to Social, Biological, and Environmental Problems. Englewood Cliffs: Prentice-Hall, 1976. 559p.
  2. V. Gubarev, V. Romanenko, Y. Milyavsky. Identification in cognitive maps in the impulse process mode with full information.Problems of control and informatics. 2018.
    № 4. P. 30–43 (in Russian).
  3. Verhagen M., Dewilde P., Subspace model identification. Part I: the output-error state space model identification class of algorithms. Int. J. Control. 1992,. №56. P. 1187–1210.
  4. V. Romanenko, Y. Milyavsky, M. Polyakov, Y. Letser, G. Shevchenko. Research of scenarios of IT company development based on decision-making in cognitive maps impulse process control mode. Proceedings of 1st international scientific and practical
    forum “Science and business”
    . (29-30 of June, 2015, Dnipropetrovsk), Dnipropetrovsk, 2015. P. 233–237.2015. P. 233–237.

Recieved 27.11.2018