• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.4
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.4
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• pp.514-519
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• 2005

We define extensional spaces. Moreover, we investigate the relations among T-upper-approximation spaces, T-quasi -equivalence relations and extensional spaces.

• Journal of the Korean Institute of Intelligent Systems
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• v.7 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.685-692
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• 1996

Subshifts of finite type can be classified by various equivalence relations. The most important equivalence relation is undoubtedly strong shift equivalence, i.e., conjugacy. In [W], R. F. Williams introduced shift equivalence which is weaker than conjugacy but still sensitive.

• Journal of Information Technology Services
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• v.9 no.4
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• pp.219-229
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• 2010

The Green's equivalence relations have played a fundamental role in the development of semigroup theory. They are concerned with mutual divisibility of various kinds, and all of them reduce to the universal equivalence in a group. Boolean matrices have been successfully used in various areas, and many researches have been performed on them. Studying Green's relations on a monoid of boolean matrices will reveal important characteristics about boolean matrices, which may be useful in diverse applications. Although there are known algorithms that can compute Green relations, most of them are concerned with finding one equivalence class in a specific Green's relation and only a few algorithms have been appeared quite recently to deal with the problem of finding the whole D or J equivalence relations on the monoid of all $n{\times}n$ Boolean matrices. However, their results are far from satisfaction since their computational complexity is exponential-their computation requires multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices and the size of the monoid of all $n{\times}n$ Boolean matrices grows exponentially as n increases. As an effort to reduce the execution time, this paper shows an isomorphism between the R relation and L relation on the monoid of all $n{\times}n$ Boolean matrices in terms of transposition. introduces theorems based on it discusses an improved algorithm for the J relation computation whose design reflects those theorems and gives its execution results.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.505-511
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• 2007

Recently, the equivalent relations between a symmetric dual problem and a matrix game B(x, y) were given in [6: D.S. Kim and K. Noh, J. Math. Anal. Appl. 298(2004), 1-13]. Using more simpler form of B(x, y) than one in [6], we establish the equivalence relations between a symmetric dual problem and a matrix game, and then give a numerical example illustrating our equivalence results.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.163-181
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• 2005

We study some properties of intuitionistic fuzzy equivalence relations. Also we introduce the concepts of intuitionistic fuzzy transitive closures and level sets of an intuitionistic fuzzy relation and we investigate some of their properties.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.601-610
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• 2018

In the present paper, we construct an ordered regular equivalence relation on an ordered semihyperring by 2-hyperideals such that the corresponding quotient structure is also an ordered semihyperring.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.3
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• pp.425-431
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• 2009

By using the notion of interval-valued fuzzy relations, we forms the poset (IVFR (X), $\leq$) of interval-valued fuzzy relations on a given set X. In particular, we forms the subposet (IVFE (X), $\leq$) of interval-valued fuzzy equivalence relations on a given set X and prove that the poset (IVFE(X), $\leq$) is a complete lattice with the least element and greatest element.