Clustering Z-information based on a system of fuzzy reference requirements

Abstract

The paper develops a clustering model of multi-criteria object evaluations, taking into account the reliability of the results obtained. Clustering is based on a system of fuzzy reference requirements about the importance of the evaluated characteristics of objects for each of the clusters. Object evaluations are formalized on the basis of linguistic Z-numbers, both fuzzy numbers of which are the values of linguistic variables. Information for each object and each cluster is presented as a set of pairs (according to the number of characteristics) consisting of a fuzzy number (importance of a characteristic for the corresponding cluster) and a Z-number (an evaluation of the object within this characteristic and its reliability). Using this information, fuzzy ratings are determined for each object in accordance with fuzzy reference requirements for each cluster. Fuzzy ratings of objects, defined as fuzzy numbers, reflect the compliance of multi-criteria ratings of objects with fuzzy reference requirements. The comparative analysis of fuzzy ratings of all objects within one cluster proposed in the paper makes it possible to identify the best representative (or best representatives) of the cluster under consideration and determine the degree of belonging of the remaining objects to this cluster. The analysis is carried out for all clusters. A numerical example is given, which shows the effectiveness of the developed method under Z-information.