Clustering Methods Based on Weighted Quasi-Arithmetic Means of T-Transitive Fuzzy Relations

In this paper we propose clustering methods based on weighted quasiarithmetic means of T -transitive fuzzy relations. We first generate a T -transitive closure R from a proximity relation R based on a max-T composition and produce a T -transitive lower approximation or opening RT from the proximity relation R through the residuation operator. We then aggregate a new T -indistinguishability fuzzy relation by using a weighted quasiarithmetic mean of R and RT . A clustering algorithm based on the proposed T -indistinguishability is thus created. We compare clustering results from three critical ti-indistinguishabilities: minimum (t3), product (t2), and Lukasiewicz (t1). A weighted quasiarithmetic mean of a t1-transitive closure R t1 and a t1-transitive lower approximation or opening Rt1 with the weight p = 0.5, demonstrates the superiority and usefulness of clustering begun by using a proximity relation R based on the proposed clustering algorithm. The algorithm is then applied to the practical evaluation of the performance of higher education in Taiwan.