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-T from a proximity relation R based on a max-T composition and produce a T-transitive lower approximation or opening R-T 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-T and R-T. A clustering algorithm based on the proposed T-indistinguishability is thus created. We compare clustering results from three critical t(i)-indistinguishabilities: minimum (t(3)), product (t(2)), and Lukasiewicz (t(1)). A weighted quasiarithmetic mean of a t(1)-transitive closure R-t1 and a t(1)-transitive lower approximation or opening R-t1 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.