• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.1
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• pp.126-134
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• 2012

By using the concept of intuitionistic interval-valued fuzzy sets, we introduce the notion of intuitionistic interval-valued fuzzy topology. And we study some fundamental properties of intuitionistic interval-valued fuzzy topological spaces: First, we obtain analogues[see Theorem 3.11 and 3.12] of neighborhood systems in ordinary topological spaces. Second, we obtain the result[see Theorem 4.9] corresponding to "the 14-set Theorem" in ordinary topological spaces. Finally, we give the initial structure on intuitionistic interval-valued fuzzy topologies[see Theorem 5.9].

• Journal of Internet Computing and Services
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• v.24 no.1
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• pp.27-37
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• 2023

In this paper, we define a new Lucas-Padoovan sequence using the Padovan sequence, and a new topological interconnection network is constructed using it. Coding nonnegative integers using subsequences of the Lucas-Padovan sequence, and using this to construct a new Lucas-Padovan cubes to deal with topological properties.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.199-215
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• 2014

Owing to the development of the notion of normal adjacency of a digital product [9], product properties of digital topological properties were studied efficiently. To equivalently represent a normal adjacency of a digital product, the present paper proposes an S-compatible adjacency of a digital product. This approach can be helpful to understand a normal adjacency of a digital product. Finally, using an S-compatible adjacency of a digital product, we can study product properties of digital topological properties, which improves the presentations of the normal adjacency of a digital product in [9] and [5, 6].

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.641-648
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• 2003

In this paper, we characterize the compact sets full-invariant properties, dual invariant properties and quasi full invariant properties in a class of infinite matrix algebras.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.711-738
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• 2010

We list two kinds of gradation of openness and we study in the sense of the followings: (i) We give the definition of IVGO of fuzzy sets and obtain some basic results. (ii) We give the definition of interval-valued gradation of clopeness and obtain some properties. (iii) We give the definition of a subspace of an interval-valued smooth topological space and obtain some properties. (iv) We investigate some properties of gradation preserving (in short, IVGP) mappings.

• Journal of the Korean Mathematical Society
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• v.17 no.2
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• pp.169-173
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• 1981

• Kyungpook Mathematical Journal
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• v.25 no.1
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• pp.29-34
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• 1985

• Kyungpook Mathematical Journal
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• v.33 no.1
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• pp.75-86
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• 1993

• Bulletin of the Korean Chemical Society
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• v.35 no.5
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• pp.1413-1416
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• 2014

A novel topological index (TG Index) has been introduced. The graphical matrix representation of the TG index includes the use of directed subgraphs for the first time in graph theory literature. The application of the TG index on certain properties of polyenes yielded very well correlation data.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.2
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• pp.187-191
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• 2002

In this paper, we introduce the notion of smooth neighborhoods in smooth topological spaces and investigate some of their properties. In particular, we can obtain some smooth topologies from a smooth neighborhood system.