Monotone and interval approximation of qualitative data

Design of quantitative models on the knowledge of qualitative data is discussed. For sequential data the principle of monotone approximation and for nominal data, of nominal approximation are proposed. These approaches are implemented by using the functionals of a specific structure which characterize the quality of approximating the original data by model data. The functional specifies monotone or nominal regression from qualitative data. The characteristic feature of the regression problem is that the model results themselves do not have observed analogs, only the relations on them being observable. For instance, pairwise comparisons such as better-worse, data on the linkage between the processes, information on what ranges the processes belong to can be used. The same approach is applicable when model results have associated observed analogs as in the case of automatic diagnosing from qualitative data.