TO THE FORMALIZATION OF THE ESTIMATES OF THE PHENOMENON STATE

M. E. Salukvadze (), R. Sh. Gogsadze () and N. I. Jibladze ()
Additional contact information
M. E. Salukvadze: A. Eliashvili Institute of Control Systems of the Georgian Academy of Sciences, 34, K. Gamsakhurdia Ave., Tbilisi, 0160, Georgia
R. Sh. Gogsadze: A. Eliashvili Institute of Control Systems of the Georgian Academy of Sciences, 34, K. Gamsakhurdia Ave., Tbilisi, 0160, Georgia
N. I. Jibladze: A. Eliashvili Institute of Control Systems of the Georgian Academy of Sciences, 34, K. Gamsakhurdia Ave., Tbilisi, 0160, Georgia

International Journal of Information Technology & Decision Making (IJITDM), 2007, vol. 06, issue 04, 599-610

Abstract: The questions of the formalization of the estimates of the phenomenon state, which can be used in the decision-making multicriterion problems [Vector-Valued Optimization Problems in Control Theory(Academic Press, New York, 1979)] taking into account the metrics of the space of partial criteria are considered. Any phenomenon is described by some system of characteristic parameters, which values are presented by the coordinates of points in the space of states of the given phenomenon. A notion of the "ideal" state determined by optimal values of each characteristic parameter separately and independently of others is used. Estimate of any state is determined by the distance between that state and the "ideal" one. That permits to choose from a multitude of the given states the best one, to which conforms a minimum distance to the "ideal" state. In the general case of the curved space the distances are measured by geodesic lines drawn by using a metric tensor of the given space. The metric tensor components themselves are determined by the solution of the differential equations set up from the condition of minimization of a certain functional.

Keywords: Metrics; tensor; geodesic; distance; curvature; invariance (search for similar items in EconPapers)
Date: 2007
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219622007002708
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijitdm:v:06:y:2007:i:04:n:s0219622007002708

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219622007002708

Access Statistics for this article

International Journal of Information Technology & Decision Making (IJITDM) is currently edited by Yong Shi

More articles in International Journal of Information Technology & Decision Making (IJITDM) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().