Strong compatability in data fitting problems with interval data

The data fitting problem is a popular and practically important problem in which a functional dependency between “input” and “output” variables is to be constructed from the given empirical data. Real-life data are almost always inaccurate, and we have to deal with the measurement uncertainty. Traditionally, when processing the measurement results, models of probability theory are used, which are not always adequate to the situations under study. An alternative way to describe data inaccuracy is to use methods of interval analysis, based on specifying interval bounds of the measurement results. Data fitting problems under interval uncertainty are being solved for about half a century. Most studies in this field rely on the concept of compatibility between parameters and measurement data in which any measurement result is a kind of a large point “inflated” to a box (rectangular parallelepiped with facets parallel to the coordinate axes). That the graph of the constructed function passes through such a “point” means a nonempty intersection of the graph with the box. However, in some problems, this natural concept turns out to be unsatisfactory.