Soft measurements of qualitative integral indicators for monitoring quantitative dataset

Abstract

In many areas, the criteria for the adoption of certain decisions are not quantitative, but qualitative assessments of some crucial criteria. This applies, in particular, to the integral assessment of the health status of patients, or the assessment of the ecological state of the environment, etc. Therefore, an integral qualitative assessment of an object, based on the known numerical states of its individual elements, is an urgent non-trivial task.Currently, there are methods for calculating the quantitative integral assessment, which is a kind of “code” for the qualitative assessment. A direct verbal evaluation is obtained, as a rule, by ranking the possible numerical values of the resulting integral code, and assigning to each given interval a certain qualitative definition. However, well-known methods for constructing analytical computational integrated assessment are not effective.As an alternative, the authors of the article propose an approach consisting in a comprehensive assessment of the state of objects based on the allocation of “similar” groups, and analysis of the basic general properties of objects in the group. Such problems can be solved by cluster analysis methods. Cluster analysis allows you to group (decompose) data that has the property of “similarity” in a given sense and to separate them from “dissimilar” data. By analyzing data in groups, experts can give a high-quality interpretation of homogeneous data in a cluster.However, when analyzing the obtained groupings by domain experts, a situation often arises when the data in some groups have a sufficient degree of homogeneity in order to give them a qualitative assessment, and in others the mathematical method of clustering does not allow to separate heterogeneous data from each other, and experts cannot give rating.So the idea to apply step-by-step clusterization when in each step it is decided whether every cluster has a sufficient degree of homogeneity or not. If not, all non-homogeneous clusters should be further decomposed into two or more clusters. It remained to decide which clustering method to choose for the data decomposition. To address this problem, reconnaissance experiments were conducted. As a result, the Kohonen Self-Organizing Map (SOM-cards) method has been proved to be the best.The proposed algorithm for multilevel clustering was called the Cascade Neural Network Filtering Data. Its effectiveness was confirmed by numerical experiments.