# Analysis of Data Presented by Multisets Using a Linguistic Approach +
## 5 Experimental Research  
The proposed linguistic approach to the analysis of data presented by multisets was applied to the analysis of competitive projects (CPs). The problems of clustering, classification and ordering of CPs, represented by multisets, were considered based on the results of a group expert assessment performed by 7 experts for the group of 16 CPs on 4 features (\(s=16\), \(q=4\), \(e=7\)). When performing a group expert assessment, each expert assessed the CP according to 4 features:* \(P_{1}\)--'social and economic importance';
* \(P_{2}\)--'competitiveness';
* \(P_{3}\)--'financial level of the applicant';
* \(P_{4}\)--'relevance and novelty',  
setting interval assessments on the linguistic scale at \(L=3\). A herewith, each expert, according to any feature, could determine his own interval values of assessments, significantly different from the interval values of assessments of other experts according to the same feature. Figure 2 shows the results of a group expert assessment of 16 CPs based on four features. In each subfigure, the assessments of the experts are located from bottom to top, starting with the 1 st and ending with the 7 th. The column number determines the CP number. The line number determines the number of the feature to be evaluated. In addition, each expert assigned the proposal to one of two classes: 'Accept the CP for implementation' and 'Reject the CP'. The total membership of the CP in the class was determined based on the data of individual CPs classifications according to the rule of the simple majority of votes. The problem of clustering the CPs was solved in order to identify the optimal number of clusters hidden in the group of 16 CPs. In addition, the search was carried out for CPs, which can be considered according to the results of the group expert assessment as noise. Such CPs require additional analysis and should be removed from the group so as not to distort the real division of CPs into clusters (and, in the future, into classes described by GDRCs). The solution to the clustering problem was obtained for various variants of assessments strategies. A herewith, the FCM algorithm was applied. This algorithm allows objects to belong to several clusters at the same time, but with different degrees of belonging (on the assumption that the transition from belonging to a cluster to non-belonging is smooth, and not abrupt). In particular, a study of clustering results was carried out for three assessment variants: for purely risky, neutral, and purely conservative assessment strategies. It should be noted that with different variants of assessment, due to the use of interval values of features, multisets containing a different number of elements will correspond to competitive projects, since different number of gradations will correspond to the same features for different variants of assessment. In the example under consideration, each feature with a purely conservative, neutral, and purely risky assessment strategy corresponds to 19, 11, and 5 gradations; therefore, the total number of elements in the corresponding multisets will be equal to 76, 44, and 20. Table 1 shows examples of scales for each feature for purely conservative, neutral, and purely risky assessment strategies. When forming the assessment scale for each feature, first, for each expert, the current value of the assessment by the feature was calculated for the selected value of the index \(\delta\) responsible for the choice of the assessment strategy, and then the unique values of the assessments for the analyzed feature were identified, after ordering them in ascending order, the assessment scale was formed by the feature.