• International Journal of Fuzzy Logic and Intelligent Systems
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• 제8권4호
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• pp.276-283
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• 2008

We investigate the images and preimages of intuitionistic fuzzy G-equivalence relations and G-congruences under product mappings.

• 한국지능시스템학회논문지
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• 제7권2호
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• pp.106-109
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• 1997

In this paper we define the t-fuzzy equivalence relation on a set and we prove some properties in connection with t-fuzzy relations.

• 호남수학학술지
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• 제42권2호
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• pp.219-234
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• 2020

The fundamental relation on a fuzzy hyperring is defined as the smallest equivalence relation, such that the quotient would be the ring, that is not commutative necessarily. In this paper, we introduce a new fuzzy strongly regular equivalence on fuzzy hyperrings, where the ring is commutative with respect to both sum and product. With considering this relation on fuzzy hyperring, the set of the quotient is a commutative ring. Also, we introduce fundamental functor between the category of fuzzy hyperrings and category of commutative rings and some related properties. Eventually, we introduce α-part in fuzzy hyperring and determine some necessary and sufficient conditions so that the relation α is transitive.

• Journal of applied mathematics & informatics
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• 제42권4호
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• pp.801-818
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• 2024

The purpose of this paper is to introduce the concept of (∈, ∈ ∨q)-fuzzy congruence relation over ring and discuss some properties of the (∈, ∈ ∨q)-fuzzy congruence relation. We also establish a brief relation between (∈, ∈ ∨q)-fuzzy ideal and (∈, ∈ ∨q)-fuzzy congruence relation. The image and preimage of (∈, ∈ ∨q)-fuzzy congruence are also studied under the so called semibalanced map.

• Korean Journal of Mathematics
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• 제18권4호
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• pp.343-356
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• 2010

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, discuss some of its basic properties, and characterize the G-fuzzy congruence generated by a fuzzy relation on a semigroup. We also give certain lattice theoretic properties of G-fuzzy congruences on semigroups.

• Korean Journal of Mathematics
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• 제22권4호
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• pp.683-691
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• 2014

We redefine a fuzzy congruence, discuss some properties of the fuzzy congruences, find the fuzzy congruence generated by a fuzzy relation on a semigroup, and give some lattice theoretic properties of the fuzzy congruences on semigroups.

• 디지털융복합연구
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• 제19권10호
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• pp.377-382
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• 2021

X와 Y사이의 퍼지 관계를 곱집합 X × Y의 퍼지 부분집합으로 Zadeh에 의해 처음으로 소개된 이후 퍼지집합에 대한 개념은 자연과학 및 컴퓨터과학에서 많은 연구성과가 이루어져 왔다. 그 결과 Muralli와 Nemitz는 동치관계 및 함수와 관련하여 퍼지관계를 연구하였고, Ounalli와 Jaoua는 중요한 수학적 도구로서 퍼지 다이펑션날 관계를 정의하여 소프트디자인과 데이터베이스 이론에서 중요한 역할을 하는 것으로 증명되었으며, 또한 프로그램 표식과 프로그램 정확도를 정의하는데 유용한 것으로 밝혀졌다. 본 논문에서는 한 집합 위에 퍼지 디터미니스틱 관계를 정의하여 퍼지 디터미니스틱 관계를 레벨 부분집합으로 특성화 하였고, 퍼지 디터미니스틱 관계와 관련하여 일부 성질을 증명하였다. 특히, 퍼지 디터미니스틱 관계와 퍼지 함수가 동치임을, 퍼지 함수가 퍼지 다이펑션날 관계가 동치임을 증명하였다.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.205-213
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• 2000

In this paper we introduce the concept of a fuzzy strongly regular relation on a sumihypergroup, and prove a few results concerning this concept.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권1호
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• pp.30-35
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• 2009

We investigate the properties of fuzzy relations, metrics and $\bigodot$-equivalence relation on a stsc quantale lattice L and a commutative cqm-lattice. In particular, pseudo-(quasi-) metrics induce $\bigodot$-(quasi)-equivalence relations.

• 한국지능시스템학회논문지
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• 제19권2호
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• pp.291-296
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• 2009

We investigate the properties of fuzzy relations and $\bigodot$-equivalence relation on a stsc quantale lattice L and a commutative cqm-lattice. In particular, we find $\bigodot$-equivalence relations induced by fuzzy relations.