# THE LATTICE OF INTUITIONISTIC FUZZY CONGRUENCES

@inproceedings{Hur2006THELO, title={THE LATTICE OF INTUITIONISTIC FUZZY CONGRUENCES}, author={Kul Hur and Su Youn Jang and Informational Statistic and Wanju-kun Chonbuk}, year={2006} }

First, we prove that the set of intuitionistic fuzzy congruences on a semigroup satisfying the particular condition is a modular lattice [Theorem 2.9]. Secondly, we prove that the set of all intuitionistic fuzzy congruences on a regular semigroup contained in (χH, χHc) forms a modular lattice [Proposition 3.5]. And also we show that the set of all intuitionistic fuzzy idempotent separating congruences on a regular semigroup forms a modular lattice[Theorem 3.6]. Moreover, we prove that the…

## 17 Citations

### Fuzzy Congruence on a Product Lattice

- Mathematics, Computer Science
- 2011

It is proved that every fuzzy congruence R on the product L × K of Lattices L and K is of the form R × S where R and S are fuzzy conjoined congruences on L andK respectively.

### Intuitionistic L -Fuzzy congruence on a ring

- 2013

: In this paper we discuss and study some properties of intuitionistic L -fuzzy equivalence relation on a ring. We introduce the concept of intuitionistic L -fuzzy transitive closure of an…

### Characterizations of intuitionistic fuzzy ideals and filters based on lattice operations

- Computer Science
- 2017

This paper characterize the notions of prime intuitionistic fuzzy ideal and filter as interesting kinds and their various characterizations and different properties in terms of the lattice operations and their associated crisp sets.

### Homomorphism of Intuitionistic Fuzzy Groups

- Computer Science
- 2011

In this paper, a relation between the intuitionistic fuzzy set A of X and that of intuitionism fuzzy set f(A) of Y has been obtained with the help of their (α,β) cut sets.

### MORE ON INTUITIONISTIC FUZZY SUBLATTICES AND THEIR IDEALS

- Computer ScienceFacta Universitatis, Series: Mathematics and Informatics
- 2019

Some characterizations and properties of these intuitionistic fuzzy sublattices and ideals with respect to an intuitionism fuzzy t-norm on an adequate lattice are established.

### Isomorphism Theorems on Intuitionistic Fuzzy Abstract Algebras

- Computer Science
- 2021

The concept of abstract algebra on intuitionistic fuzzy sets were introduced and some basic theorems were proved by authors in 2017, and first and third isomorphism theoryms on intuitionist fuzzy abstract algebras are introduced.

### TRANSLATES OF INTUITIONISTIC FUZZY SUBGROUPS

- Computer Science
- 2011

Two operators T+ and T− called the intuitionistic fuzzy translation operator on the intuitionism fuzzy set A are introduced and their properties are investigated and their action on Intuitionistic fuzzy subgroups of a group is studied.

### Linear Diophantine Fuzzy Relations and Their Algebraic Properties with Decision Making

- Computer ScienceSymmetry
- 2021

The main purpose of this paper is to establish a robust fusion of binary relations and LDFSs, and to introduce the concept of linear Diophantine fuzzy relation (LDF-relation) by making the use of reference parameters corresponding to the membership and non-membership fuzzy relations.

### On Intuitionistic Fuzzy Magnified Translation in Rings

- Computer Science
- 2011

This paper defines intuitionistic fuzzy magnified translation of intuitionists fuzzy (normal) subring and ideal of a ring and theorems about Intuitionistic fuzzy rings.

### CHARACTERIZATION OF ( ) βα ,-LOWER LEVEL NORMAL SUBGROUP OF INTUITIONISTIC MULTI-ANTI FUZZY NORMAL SUBGROUP

- Computer Science
- 2018

In this paper, an attempt has been made to study new algebraic nature of ( ) β α , -lower level normal subgroup of intuitionistic multi-anti fuzzy normal subgroup and their properties are discussed.…

## References

SHOWING 1-10 OF 44 REFERENCES

### INTUITIONISTIC FUZZY CONGRUENCES ON A LATTICE

- Computer Science, Mathematics
- 2005

It is proved that the lattice of intuitionistic fuzzy ideals is isomorphic to the lattices of intuitionism fuzzy congruences on a generalized Boolean algebra.

### Lattice of fuzzy congruences in inverse semigroups

- Mathematics, Computer ScienceFuzzy Sets Syst.
- 1997

### INTUITIONISTIC FUZZY NORMAL SUBGROUPS AND INTUITIONISTIC FUZZY COSETS

- Computer Science
- 2004

The concept of an intuitionistic fuzzy coset is introduced and several results are obtained which are analogous of some basic theorems of group theory.

### Intuitionistic Fuzzy Normal Subgroups and Intuitionistic Fuzzy Cosets

- Computer Science, Mathematics
- 2004

The concept of an intuitionistic fuzzy coset is introduced and several results which are analogs of some basic theorems of group theory are obtained.

### THE CATEGORY OF INTUITIONISTIC FUZZY TOPOLOGICAL SPACES

- Computer Science
- 2000

This paper investigates the properties of continuous, open and closed maps in the intuitionistic fuzzy topological spaces, and shows that the category of Chang's fuzzyTopological spaces is a bireflective full subcategory of that of intuitionistic fuzzier spaces.