A New Algorithm to Compute Low T-Transitive Approximation of a Fuzzy Relation Preserving Symmetry. Comparisons with the T-Transitive Closure

2005 ◽  
pp. 576-586 ◽  
Author(s):  
Luis Garmendia ◽  
Adela Salvador
Keyword(s):  
Transitive Closure ◽  
Fuzzy Relation ◽  
Transitive Approximation

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

2015 ◽  
Vol 23 (05) ◽  
pp. 715-733
Author(s):  
Miin-Shen Yang ◽  
Ching-Nan Wang
Keyword(s):  
Clustering Algorithm ◽  
Transitive Closure ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Clustering Methods ◽  
Arithmetic Means ◽  
Lower Approximation ◽  
Practical Evaluation ◽  
Quasiarithmetic Means ◽  
Proximity Relation

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.

THE LENGTH AND BETWEENNESS RELATIONS OF INDISTINGUISHABILITY OPERATORS

1999 ◽  
Vol 07 (03) ◽  
pp. 203-212 ◽  
Author(s):  
D. BOIXADER ◽  
J. JACAS ◽  
J. RECASENS
Keyword(s):  
Representation Theorem ◽  
Transitive Closure ◽  
Fuzzy Relation ◽  
Betweenness Relations

The most common ways used to generate indistinguishability operators, namely as transitive closure of reflexive and symmetric fuzzy relation, via the Representation Theorem and as decomposable relations, are related for archimedean t-norms introducing the notion of length of indistinguishability operators.

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