Interval-valued fuzzy relation-based clustering with its application to performance evaluation

A similarity relation with its partition tree has been applied in the performance evaluation area for obtaining an agglomerative hierarchical clustering. These fuzzy relation-based methods require a decision maker to perform pair-wise comparisons for the similarity among criteria as forming a fuzzy relation matrix. The approach is developed based on real membership values of fuzzy relations. However, interval-valued memberships may be better than real membership values to represent higher-order imprecision and vagueness for human perception. Thus, in this paper we would like to extend fuzzy relations to interval-valued fuzzy relations and then construct interval-valued similarity relations for performance evaluation. We first give some definitions for these interval-valued types of fuzzy relation, similarity relation and resolution form. We then construct an interval-valued fuzzy similarity relation into a hierarchical structure schema. It is shown that both of procedures and results for the partition tree derived from interval-valued and crisp-valued similarity relation matrices have some corresponding relationships and different merits. To demonstrate the usefulness of the proposed approach, performance evaluations for academic departments of higher education are considered by using actual engineering school data in Taiwan.