FUZZY CLUSTERING BASED ON INTUITIONISTIC FUZZY RELATIONS

2004 ◽  
Vol 12 (04) ◽  
pp. 513-529 ◽  
Author(s):  
WEN-LIANG HUNG ◽  
JINN-SHING LEE ◽  
CHENG-DER FUH
Keyword(s):  
Fuzzy Clustering ◽  
Missing Values ◽  
Clustering Algorithm ◽  
Fuzzy Relation ◽  
Similarity Relation ◽  
Fuzzy Relations ◽  
Intuitionistic Fuzzy ◽  
Step Procedure ◽  
Proximity Relation ◽  
Relation Matrix

It is well known that an intuitionistic fuzzy relation is a generalization of a fuzzy relation. In fact there are situations where intuitionistic fuzzy relations are more appropriate. This paper discusses the fuzzy clustering based on intuitionistic fuzzy relations. On the basis of max -t & min -s compositions, we discuss an n-step procedure which is an extension of Yang and Shih's [17] n-step procedure. A similarity-relation matrix is obtained by beginning with a proximity-relation matrix using the proposed n-step procedure. Then we propose a clustering algorithm for the similarity-relation matrix. Numerical comparisons of three critical max -t & min -s compositions: max -t1 & min -s1, max -t2 & min -s2 and max -t3 & min -s3, are made. The results show that max -t1 & min -s1 compositions has better performance. Sometimes, data may be missed with an incomplete proximity-relation matrix. Imputation is a general and flexible method for handling missing-data problem. In this paper we also discuss a simple form of imputation is to estimate missing values by max -t & min -s compositions.

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.

scholarly journals Intuitionistic fuzzy relations compatible with the group Zn

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
E. G. Emam
Keyword(s):  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Fundamental Properties ◽  
Intuitionistic Fuzzy

AbstractIn this paper, we define the compatibility of finite intuitionistic fuzzy relations with the group Zn and prove some of their fundamental properties. We show that some compositions of Zn-compatible intuitionistic fuzzy relations are also Zn-compatible intuitionistic fuzzy relation. Also, from any given finite intuitionistic fuzzy relation ρ, we can construct two intuitionistic fuzzy relations denoted by ρL and ρU which are compatible with Zn. We have also provided some examples to clarify the notions and results.

PERTURBATION OF INTUITIONISTIC FUZZY RELATIONS

2001 ◽  
Vol 09 (01) ◽  
pp. 81-103 ◽  
Author(s):  
H. BUSTINCE ◽  
P. BURILLO
Keyword(s):  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Intuitionistic Fuzzy ◽  
Do So

In this paper we present a way of perturbing reflexive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relations afterward obtaining the perturbation of another reflexive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relation. To do so we study the main properties of an operator that allows us to go from an intuitionistic fuzzy set to another also intuitionistic fuzzy set, we then apply this operator to intuitionistic fuzzy relations with different properties and we study the conditions there must be for the new intuitionistic fuzzy relation to maintain the original properties.

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