Approximation of functions defined in tabular form: Multicriterial approach. II

Computational Mathematics and Mathematical Physics. 2025. Vol. 65. No. 4. P. 689–697.

Nelyubin A. P., Podinovskiy V. V.

This paper continues the development of a new approach to estimating approximation
parameters in which the distance of the approximating function from a given finite set of points is estimated
by a vector criterion whose components are the moduli of the residuals at all points. Using this
vector criterion, a preference relation in terms of distance is defined, and the approximating function
that is not dominated by such a relation is considered the best. Unlike the first paper of the authors
(Computational Mathematics and Mathematical Physics, 2022), which is devoted to parametric
methods, this paper proposes nonparametric methods for several preference relations, including the
Pareto relation and the relation generated by information about the equal importance of criteria. Computational
issues are considered and the relationships between the introduced approximating functions
and classical ones are investigated. Numerical examples are discussed.

Keywords: criteria importance theory, теория важности критериев, аппроксимация функций, approximation of functions, многокритериальный анализ, multicriteria analysis,, непараметрическая аппроксимация, nonparametric approximation

Publication based on the results of: Decision-Making in Socio-Economic, Political and Financial Spheres (2025)