Cluster analysis based on fuzzy equivalence relation

In this paper, a cluster analysis method based on fuzzy equivalence relation is proposed. At first, the distance formula between two trapezoidal fuzzy numbers is used to aggregate subjects' linguistic assessments about attributes ratings to obtain the compatibility relation. Then a fuzzy equivalence relation based on the fuzzy compatibility relation can be constructed. Finally, using a cluster validity index to determine the best number of clusters and taking suitable λ-cut value, the clustering analysis can be effectively implemented. By utilizing this clustering analysis, the subjects' fuzzy assessments with various rating attitudes can be taken into account in the aggregation process to assure more convincing and accurate cluster analysis.