• Journal of Communications and Networks
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• v.14 no.3
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• pp.230-236
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• 2012

Based on the known binary sequence sets and Gray mapping, a new method for constructing quaternary sequence sets is presented and the resulting sequence sets' properties are investigated. As three direct applications of the proposed method, when we choose the binary aperiodic, periodic, and Z-complementary sequence sets as the known binary sequence sets, the resultant quaternary sequence sets are the quaternary aperiodic, periodic, and Z-complementary sequence sets, respectively. In comparison with themethod proposed by Jang et al., the new method can cope with either both the aperiodic and periodic cases or both even and odd lengths of sub-sequences, whereas the former is only fit for the periodic case with even length of sub-sequences. As a consequence, by both our and Jang et al.'s methods, an arbitrary binary aperiodic, periodic, or Z-complementary sequence set can be transformed into a quaternary one no matter its length of sub-sequences is odd or even. Finally, a table on the existing quaternary periodic complementary sequence sets is given as well.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.69-83
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• 2022

We investigate the concept of lacunary statistical convergence and lacunary strongly convergence for sequence of sets in intuitionistic fuzzy metric space (IFMS) and examine their characterization. We obtain some inclusion relation relating to these concepts. Further some necessary and sufficient conditions for equality of the sets of statistical convergence and lacunary statistical convergence for sequence of sets in IFMS have been established. The concept of strong Cesàro summability in IFMS has been defined and some results are established.

• Journal of Communications and Networks
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• v.12 no.4
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• pp.330-333
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• 2010

In this paper, using binary (N, M, L, $\epsilon$) low correlation zone (LCZ) sequence sets, we construct new quaternary LCZ sequence sets with parameters (2N, 2M, L, $2{\epsilon}$). Binary LCZ sequences for the construction should have period $N\;{\equiv}\;3$ mod 4, L|N, and the balance property. The proposed method corresponds to a quaternary extension of the extended construction of binary LCZ sequence sets proposed by Kim, Jang, No, and Chung [1].

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.2 no.3
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• pp.237-241
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• 2002

In this paper, we describe how to represent hand witten decimal digits by a sequence of one to five fuzzy sets. Each fuzzy set represents an arc segment of the digit and is a Cartesian product of four fuzzy sets; the first is fur the arc length of the segment, the second is for the arc direction, the third is fur the arc shape, and the fourth is a crisp number indicating whether it has a junction point and if it has an end point of a stroke. We show that an arbitrary pair of these sequences representing two different digits is mutually disjoint. We also show that various forms of a digit written in different styles can be represented by the same sequence of fuzzy sets and hence the deviations due to different writers can be modeled by using these fuzzy sets.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.757-768
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• 2003

In 1967, as an answer to the question of P. Erdos on a set of integers having distinct subset sums, J. Conway and R. Guy constructed an interesting sequence of sets of integers. They conjectured that these sets have distinct subset sums and that they are close to the best possible with respect to the largest element. About 30 years later (in 1996), T. Bohman could prove that sets from the Conway-Guy sequence actually have distinct subset sums. In this paper, we generalize the concept of subset-sum-distinctness to k-SSD, the k-fold version. The classical subset-sum-distinct sets would be 1-SSD in our definition. We prove that similarly derived sequences as the Conway-Guy sequence are k-SSD.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.345-358
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• 2020

In this paper, we study the concepts of Wijsman lacunary invariant convergence, Wijsman lacunary invariant statistical convergence, Wijsman lacunary ${\mathcal{I}}_2$-invariant convergence (${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$), Wijsman lacunary ${\mathcal{I}}^*_2$-invariant convergence (${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$), Wijsman p-strongly lacunary invariant convergence ([W₂N_σθ]_p) of double sequence of sets and investigate the relationships among Wijsman lacunary invariant convergence, [W₂N_σθ]_p, ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$ and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$. Also, we introduce the concepts of ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence of sets.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.171-189
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• 2005

In this paper, we first establish some characterization of tightness for a sequence of random elements taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in $R^P$. As a result, we give some sufficient conditions for a sequence of fuzzy random sets to converge in distribution.

• Honam Mathematical Journal
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• v.44 no.3
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• pp.461-472
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• 2022

In optimization theory, hypo-convergence is considered as an effective tool by providing the convergence of supremum values under some conditions. This feature makes it different from other types of convergence. Therefore, we have defined the hypo-convergence of a sequence of fuzzy sets due to the increasing interest in fuzzy set theory in recent years. After giving a theoretical framework, we deal with the optimization process by using a sequential characterization of hypo-convergence of sequence of fuzzy sets. Since the maximization process in optimization theory is beyond the presence of hypo-convergence, we give some conditions to satisfy the convergence of supremum values. Furthermore, we show how sequence of fuzzy sets and fuzzy numbers differ in the convergence of the supremum values.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.83-116
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• 2020

Let G be a finite group. By a sequence over G, we mean a finite unordered sequence of terms from G, where repetition is allowed, and we say that it is a product-one sequence if its terms can be ordered such that their product equals the identity element of G. The large Davenport constant D(G) is the maximal length of a minimal product-one sequence, that is, a product-one sequence which cannot be factored into two non-trivial product-one subsequences. We provide explicit characterizations of all minimal product-one sequences of length D(G) over dihedral and dicyclic groups. Based on these characterizations we study the unions of sets of lengths of the monoid of product-one sequences over these groups.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.277-294
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• 2021

In this paper, we introduce the notions of Wijsman regularly invariant convergence types, Wijsman regularly (${\mathcal{I}}_{\sigma}$, ${\mathcal{I}}^{\sigma}_2$)-convergence, Wijsman regularly (${\mathcal{I}}^*_{\sigma}$, ${\mathcal{I}}^{{\sigma}*}_2$)-convergence, Wijsman regularly (${\mathcal{I}}_{\sigma}$, ${\mathcal{I}}^{\sigma}_2$) -Cauchy double sequence and Wijsman regularly (${\mathcal{I}}^*_{\sigma}$, ${\mathcal{I}}^{{\sigma}*}_2$)-Cauchy double sequence of sets. Also, we investigate the relationships among this new notions.