Transitive Fuzzy Similarity Multigraph-Based Model for Alternative Clustering in Multi-criteria Group Decision-Making Problems

Graph node clustering methods, which aim to partition graph vertices into several disjoint groups of data with similar features, are usually fulfilled based on topological structural similarity of nodes, such as connectivity between vertices or neighborhood similarity of them. However, the attribute-based clustering is recently challenging to data clustering. The present paper contributes to considering a novel data clustering algorithm, called FBC-Cluster, based on fuzzy multigraphs in terms of both structural and attribute similarities. In the proposed algorithm, attribute similarity is achieved through in-polar fuzzy T-equivalences among alternatives (objects) and structural similarity is defined based on a new similarity measurement, called behavioral similarity index, using closed neighborhood in the attributed clusters. The output of the proposed clustering algorithm includes two main categories, namely certain and possible clusters, based on threshold level beta given on the behavioral similarity index. A numerical example is discussed to demonstrate the performance of the designed clustering algorithm. The quality of resultant clusters is also evaluated through density and entropy functions.