A Multicriteria Method for Identification and Forecasting
- 3 Downloads
A multicriteria approach to identify and forecast mathematical models is considered. The need for such an approach arises, in particular, when it is necessary to take into account errors that cannot be reduced to one function and in the absence of specific information about the data interference class. The paper deals with a multicriteria version of the identification sets method based on approximating and visualizing the graph of the vector function of identification errors and its projections onto the space of identification parameters. The nearness function is introduced that describes the proximity of a criterion point to the set of nonimprovable (Pareto efficient) solutions of the identification problem. The efficient criteria set (Pareto frontier), the sets of efficient and subefficient parameters, and the corresponding forecast trajectory tubes are studied. To construct these objects, methods for approximating implicitly specified sets are used, in particular, methods for approximating the Edgeworth–Pareto hull and the deep holes method. The technique and examples for two criteria of identification quality are considered in detail.
Keywordsparameter identification forecasting robustness multicriteria decision making efficient set Pareto frontier Edgeworth–Pareto hull efficient and subefficient solutions methods for approximating implicitly specified sets identification sets method interactive decision maps
Unable to display preview. Download preview PDF.
- 6.G. K. Kamenev, Method for Analyzing Uncertainty in Model Parameter Identification (Vychisl. Tsentr RAN, Moscow, 2010) [in Russian].Google Scholar
- 8.V. A. Bushenkov, O. L. Chernykh, G. K. Kamenev, and A. V. Lotov, “Multidimensional images given by mappings: construction and visualization,” Pattern Recognit. Image Anal. 5, 35–56 (1995).Google Scholar
- 12.M. Yu. Andreev, V. P. Vrzheshch, N. P. Pilnik, I. G. Pospelov, M. A. Khokhlov, A. A. Zhukova, and S. A. Radionov, “Intertemporal general equilibrium model of the Russian economy based on national accounts deaggregation,” in Proceedings of the Seminar of I. G. Petrovskii (Mosk. Gos. Univ., Moscow, 2013), pp. 43–145; J. Math. Sci. (N.Y.) 197, 175–236 (2014).MathSciNetMATHGoogle Scholar