# Analysis of Data Presented by Multisets Using a Linguistic Approach +
###### Abstract  
The problem of the analysis of datasets formed by the results of group expert assessment of objects by a certain set of features is considered. Such datasets may contain mismatched, including conflicting values of object evaluations by the analyzed features. In addition, the values of the assessments for the features can be not only point, but also interval due to the incompleteness and inaccuracy of the experts' knowledge. Taking into account all the results of group expert assessment of objects for a certain set of features, estimated pointwise, can be carried out using the multiset toolkit. To process interval values of assessments, it is proposed to use a linguistic approach which involves the use of a linguistic scale in order to describe various strategies for evaluating objects: conservative, neutral and risky, and implement various decision-making strategies in the problems of clustering, classification, and ordering of objects. The linguistic approach to working with objects assessed by a group of experts with setting interval values of assessments has been successfully applied to the analysis of the dataset presented by competitive projects. A herewith, for the dataset under consideration, using various assessment strategies, solutions of clustering, classification, and ordering problems were obtained with the study of the influence of the chosen assessment strategy on the results of solving the corresponding problem. multiset; linguistic approach; interval assessments; group expert assessment; clustering; classification; ordering +
Footnote †: This paper is an extended version of our paper published in the proceedings of the 9-th International Workshop on Mathematical Models and their Applications (IWMMA 2020) (Krasnoyarsk, Russia, 16-18 November 2020). For most data analysis algorithms it is important that the values of the features of objects (the values of assessments of objects by features) are represented by numerical values, i.e., were converted to a scale of intervals or ratios. Often, you can only define the intervals to which the characteristic values of the objects belong. Such situations, for example, are possible when the values of the features of objects are determined by the results of a group expert assessment or from several sources of information. In the case of expert assessment of objects quite often even highly qualified specialists (experts) are able to determine only intervals for evaluating objects according to the evaluated features, since they find it difficult to set unambiguous clear assessments on any point scale. Currently, there are various approaches to solving the problems of clustering, classification and ordering of various objects according to a number of features based on the data of group expert assessment, but they cannot be recognized as universal. There is an obvious need for the development of mathematical tools that allow making informed and adequate decisions using data, including using subjective qualitative data presented in the form of interval assessments [15; 16]. The assessments for features in a group expert assessment set on a certain point scale can often be significantly different and even contradictory. Data analysis is even more problematic if experts give interval assessments rather than point (point) ones. Approaches to the analysis of such data imply, for example, discarding extreme assessments (minimum and maximum) for each feature, averaging assessments for each feature, and agreeing assessments for each feature using the Delphi method. Obviously, when any of these approaches are applied, part of the initial information about the assessments of objects by features is lost. One of the promising approaches to taking into account all, including contradictory assessments by features in group expert assessment, is an approach that implements the use of tools from the theory of multisets [17; 18; 19].