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.

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.

A Survey of Atanassov’s Intuitionistic Fuzzy Relations

2016 ◽  
pp. 65-78 ◽  
Author(s):  
Humberto Bustince ◽  
Edurne Barrenechea ◽  
Miguel Pagola ◽  
Javier Fernandez ◽  
Raul Orduna ◽  
...  
Keyword(s):  
Fuzzy Relations ◽  
Intuitionistic Fuzzy

scholarly journals Bipolar Fuzzy Relations

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1044 ◽  
Author(s):  
Jeong-Gon Lee ◽  
Kul Hur
Keyword(s):  
Equivalence Class ◽  
Level Set ◽  
Equivalence Relation ◽  
Level Sets ◽  
Equivalence Classes ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Transitive Relation ◽  
Fuzzy Partition

We introduce the concepts of a bipolar fuzzy reflexive, symmetric, and transitive relation. We study bipolar fuzzy analogues of many results concerning relationships between ordinary reflexive, symmetric, and transitive relations. Next, we define the concepts of a bipolar fuzzy equivalence class and a bipolar fuzzy partition, and we prove that the set of all bipolar fuzzy equivalence classes is a bipolar fuzzy partition and that the bipolar fuzzy equivalence relation is induced by a bipolar fuzzy partition. Finally, we define an ( a , b ) -level set of a bipolar fuzzy relation and investigate some relationships between bipolar fuzzy relations and their ( a , b ) -level sets.

scholarly journals On rough sets induced by fuzzy relations approach in semigroups

2018 ◽  
Vol 16 (1) ◽  
pp. 1634-1650
Author(s):  
Rukchart Prasertpong ◽  
Manoj Siripitukdet
Keyword(s):  
Prime Ideal ◽  
Rough Set ◽  
Rough Sets ◽  
Sufficient Conditions ◽  
Unit Interval ◽  
Fuzzy Relation ◽  
Prime Ideals ◽  
Fuzzy Relations ◽  
Completely Prime Ideal

AbstractIn this paper, we introduce a rough set in a universal set based on cores of successor classes with respect to level in a closed unit interval under a fuzzy relation, and some interesting properties are investigated. Based on this point, we propose a rough completely prime ideal in a semigroup structure under a compatible preorder fuzzy relation, including the rough semigroup and rough ideal. Then we provide sufficient conditions for them. Finally, the relationships between rough completely prime ideals (rough semigroups and rough ideals) and their homomorphic images are verified.

FUZZY RELATION CALCULUS IN THE COMPRESSION AND DECOMPRESSION OF FUZZY RELATIONS

2002 ◽  
Vol 02 (04) ◽  
pp. 617-631 ◽  
Author(s):  
VINCENZO LOIA ◽  
WITOLD PEDRYCZ ◽  
SALVATORE SESSA
Keyword(s):  
Lossy Compression ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Triangular Norm ◽  
Fuzzy Matrix ◽  
Fuzzy Relation Equations

We firstly review some fundamentals of fuzzy relation calculus and, by recalling some known results, we improve the mathematical contents of our previous papers by using the properties of a triangular norm over [0,1]. We make wide use of the theory of fuzzy relation equations for getting lossy compression and decompression of images interpreted as two-argument fuzzy matrices.The same scope is achieved by decomposing a fuzzy matrix using the concept of Schein rank. We illustrate two algorithms with a few examples.

scholarly journals IntuitionisticH-fuzzy relations

2005 ◽  
Vol 2005 (17) ◽  
pp. 2723-2734 ◽  
Author(s):  
Kul Hur ◽  
Su Youn Jang ◽  
Hee Won Kang
Keyword(s):  
Fuzzy Relations ◽  
Intuitionistic Fuzzy ◽  
Cartesian Closed

We introduce the categoryIRel(H)consisting of intuitionistic fuzzy relational spaces on sets and we study structures of the categoryIRel(H)in the viewpoint of the topological universe introduced by Nel. Thus we show thatIRel(H)satisfies all the conditions of a topological universe overSetexcept the terminal separator property andIRel(H)is cartesian closed overSet.

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