• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.37-40
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• 2003

We introduce the category IRel (H) consisting of intuitionistic fuzzy relational spaces on sets and we study structures of the category IRel (H) in the viewpoint of the topological universe introduced by L.D.Nel. Thus we show that IRel (H) satisfies all the conditions of a topological universe over Set except the terminal separator property and IRel (H) is cartesian closed over Set.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.3
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• pp.389-394
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• 2005

The purpose of this paper is to introduce the notions of L-fuzzy topological towers by using a completely distributive lattic L and show that the category L-FPrTR of L-fuzzy pretopoplogical tower spaces and the category L-FPsTR of L-fuzzy pseudotopological tower spaces are extensional topological constructs. And we show that L-FPsTR is the cartesian closed topological extension of L-FPrTR. Hence we show that L-FPsTR is a topological universe.

• Honam Mathematical Journal
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• v.32 no.2
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• pp.333-362
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• 2010

We define H*H-fuzzy set and form a new category Set(H*H) consisting of H*H-fuzzy sets and morphisms between them. First, we study it in the sense of topological universe and obtain an exponential objects of Set(H*H). Second, we investigate some relationships among the categories Set(H*H), Set(H) and ISet(H).

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.2
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• pp.134-141
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• 2010

We introduce the category IVSet(H) of interval-valued H-fuzzy sets and show that IVSet(H) satisfies all the conditions of a topological universe except the terminal separator property. And we study some relations among IVSet (H), ISet (H) and Set (H).

• The Pure and Applied Mathematics
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• v.12 no.1
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• pp.33-45
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• 2005

We introduce the category ISet(H) of intuitionistic H-fuzzy sets and show that ISet(H) satisfies all the conditions of a topological universe except the terminal separator property. And we study the relation between Set(H) and ISet(H).

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.33-36
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• 2003

We introduce the subcategory IRel$\_$R/ (H) of IRel (H) consisting of intuitionistic H-fuzzy reflexive relational spaces on sets and we study structures of IRel$\_$R/ (H) in a viewpoint of the topological universe introduce by L.D.Nel. We show that IRel$\_$R/ (H) is a topological universe over Set. Moreover, we show that exponential objects in IRel$\_$R/ (H) are quite different from those in IRel (H) constructed in [7].

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.29-32
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• 2003

We introduce the subcategories IRe $l_{PR}$ (H), IRe $l_{PO}$ (H) and IRe $l_{E}$(H) of IRe $l_{R}$(H) and study their structures in a viewpoint of the topological universe introduced by L.D.Nel. In particular, the category IRe $l_{R}$(H)(resp. IRe $l_{P}$(H) and IRe $l_{E}$(H)) is a topological universe eve, Set. Moreover, we show that IRe $l_{E}$(H) has exponential objects.ial objects.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.1
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• pp.73-81
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• 2010

We introduce the new category VSet(H) consisting of H-fuzzy spaces and H-fuzzy mappings between them satisfying a certain condition, and investigate VSet(H) in the sense of a topological universe. Moreover, we show that VSet(H) is Cartesian closed over Set.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1341-1356
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• 2018

The author devotes this paper to defining a new class of generalized soft open sets, namely soft somewhere dense sets and to investigating its main features. With the help of examples, we illustrate the relationships between soft somewhere dense sets and some celebrated generalizations of soft open sets, and point out that the soft somewhere dense subsets of a soft hyperconnected space coincide with the non-null soft ${\beta}$-open sets. Also, we give an equivalent condition for the soft csdense sets and verify that every soft set is soft somewhere dense or soft cs-dense. We show that a collection of all soft somewhere dense subsets of a strongly soft hyperconnected space forms a soft filter on the universe set, and this collection with a non-null soft set form a soft topology on the universe set as well. Moreover, we derive some important results such as the property of being a soft somewhere dense set is a soft topological property and the finite product of soft somewhere dense sets is soft somewhere dense. In the end, we point out that the number of soft somewhere dense subsets of infinite soft topological space is infinite, and we present some results which associate soft somewhere dense sets with some soft topological concepts such as soft compact spaces and soft subspaces.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.2
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• pp.53.2-53.2
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• 2019

The genus of the matter density eld, as traced by galaxies, contains information regarding the nature of dark energy and the fraction of dark matter in the Universe. In particular, this topological measure is a statistic that provides a clean measurement of the shape of the linear matter power spectrum. As the genus is a topological quantity, it is insensitive to galaxy bias and gravitational collapse. Furthermore, as it traces the linear matter power spectrum, it is a conserved quantity with redshift. Hence the genus amplitude is a standard population that can be used to test the distance-redshift relation. In this talk, I present measurements of the genus extracted from the SDSS DR7 LRGs in the local Universe, and also slices of the BOSS DR12 data at higher redshift. I show how these combined measurements can be used to place cosmological parameter constraints on m, wde.