• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.59-71
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• 1998

In this paper we define a regular relation with respect to a homomorphism in transformation groups and we find the equivalent conditions for the relation to be an equivalence relation.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.235-258
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• 1998

We define a crossing of a link without referring to a specific projection of the link and describe a construction of a non-normalized Alexander polynomial associated to collections of such crossings of oriented links under an equivalence relation, called homology relation. The polynomial is computed from a special Seifert surface of the link. We prove that the polynomial is well-defined for the homology equivalence classes, investigate its relationship with the combinatorially defined Alexander polynomials and study some of its properties.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.181-198
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• 2016

In this work, we suggest a new system of generalized nonlinear regularized nonconvex variational inequalities in a real Hilbert space and establish an equivalence relation between this system and fixed point problems. By using the equivalence relation we suggest a new perturbed projection iterative algorithms with mixed errors for finding a solution set of system of generalized nonlinear regularized nonconvex variational inequalities.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.495-501
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• 2007

In this paper the relative regionally regular relation is defined and it will be given the necessary and sufficient conditions for the relation to be an equivalence relation.

• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.63-69
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• 2013

On any semigroup S, there is an equivalence relation ${\phi}^S$, called the locally equivalence relation, given by a ${\phi}^Sb{\Leftrightarrow}aSa=bSb$ for all $a$, $b{\in}S$. In Theorem 4 [4], Tiefenbach has shown that if ${\phi}^S$ is a band congruence, then $G_a$ := $[a]_{{\phi}^S}{\cap}(aSa)$ is a group. We show in this study that $G_a$ := $[a]_{{\phi}^S}{\cap}(aSa)$ is also a group whenever a is any idempotent element of S. Another main result of this study is to investigate the relationships between $[a]_{{\phi}^S}$ and $aSa$ in terms of semigroup theory, where ${\phi}^S$ may not be a band congruence.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.7-16
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• 2007

First, we investigate fuzzy equivalence relations on a set X in the sense of Youssef and Dib. Second, we discuss fuzzy congruences generated by a given fuzzy relation on a fuzzy groupoid. In particular, we obtain the characterizations of ${\rho}\;o\;{\sigma}{\in}$ FC(S) for any two fuzzy congruences ${\rho}\;and\;{\sigma}$ on a fuzzy groupoid ($S,{\odot}$). Finally, we study the lattice of fuzzy equivalence relations (congruences) on a fuzzy semigroup and give certain lattice theoretic properties.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.2
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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.

• Korean Journal of Mathematics
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• v.27 no.2
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• pp.269-277
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• 2019

Let X be a nonempty set, ${\rho}$ be an equivalence on X, T(X) be the semigroup of all transformations from X into itself, and $T_{\rho}(X)=\{f{\in}T(X)|(x,y){\in}{\rho}{\text{ implies }}((x)f,\;(y)f){\in}{\rho}\}$. In this paper, we investigate some necessary and sufficient conditions for elements in $T_{\rho}(X)$ to be left or right magnifying.

• Honam Mathematical Journal
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• v.42 no.2
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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.