Similarity assessment of multiparameter objects whose parameters are described in different metrological scales

The purpose of this article is to develop principles for assessing the similarity between multiparameter objects whose states are described by disparate characteristics. The parameters of many objects are described using different metrological scales (names, ranks, intervals, ratios). These parameters may be described by different units of measurement and have different levels of importance for the degree of similarity between pairs of objects. When comparing the parameters of a test object, there may be various permissible deviations, either upward or downward, relative to the reference object. Furthermore, there may be other conditions under which a test object can be considered similar to the reference object. An analysis of metrics for determining closeness between objects, as well as similarity measures, diversity measures, and inclusion measures, revealed that these theoretical principles have limitations when determining similarity between multiparameter objects. To address these limitations, we propose theoretical principles based on the formation of conditions that allow for recognizing objects as similar for each parameter, as well as additional conditions. Recognition of similarity for specific parameters between a test object and a reference object is accomplished by defining a range of permissible values. If the parameter of the compared object falls within the acceptable range, a decision is generated as one; if it does not, a decision is generated as zero. As a result, a sequence consisting of zeros and ones is formed for the compared object. The elements of the sequence are then summed, taking into account the weighting coefficient of each parameter. The values of the weighting coefficients are distributed so that their sum equals one. As a result, the closer the sum of the sequence elements is to one, the greater the similarity between the objects is considered. To assess the feasibility of the proposed provisions, a sample of values describing the condition of forest areas was used. The results demonstrate the formation of subgroups of objects whose parameters fall within acceptable value ranges and satisfy an additional condition relative to the reference object. The proposed provisions open up opportunities for the further development of information systems for analyzing the condition of complex objects.