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

Abstract

In this paper we propose clustering methods based on weighted quasiarithmetic means of T-transitive fuzzy relations. We first generate a T-transitive closure RT 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 RT 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 Łukasiewicz (t1). A weighted quasiarithmetic mean of a t1-transitive closure [Formula: see text] and a t1-transitive lower approximation or opening [Formula: see text] with the weight [Formula: see text], 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.