• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1995.11a
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• pp.51-58
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• 1995

The importance of the risk analysis tool has been recognized and its use also has been emphasized by a number of researchers recently The methodology were examined but neither algorithms nor practical applications have been implemented or practiced in Korea. In this paper, the architecture of the Buddy System, one of the automated risk assessment tools. is analyzed in depth to provide the algorithmic understanding and to promote the development of the risk analysis methodology. The Buddy System mainly uses three main factors of vulnerability, threat and countermeasures as a nucleus of the qualatative analysis with the modified loss expectancy value. These factors are identified and assessed by the separation of duties between the end user and security analyst. The Buddy System uses five axioms as its bases of assessment algorithm and the assessed vulnerability level is strictly within these axioms. Since the In-place countermeasures reduce the vulnerability level up to a certain level. the security analyst may use "what if " model to examine the impact of additional countermeasures by proposing each to reduce the vulnerability level further to within the acceptable range. The emphasis on the qualitative approach on vulnerability leveling is very well balanced with the quantitative analysis that the system performance is prominent.prominent.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.387-399
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• 2014

We show that in quasi-topological spaces, separation axiom $T_2$ is equivalent to ${\alpha}-T_2$, $T_0$ is equivalent to semi - $T_0$, and semi - $T_{\frac{1}{2}}$ is equivalent to semi - $T_D$. Also, we give characterizations for ${\alpha}-T_1$, semi - $T_1$ and semi - $T_{\frac{1}{2}}$ generalized topological spaces.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.773-791
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• 2017

In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory on topological spaces under appropriate separation axioms. First, we discuss fundamental properties of attractors such as maximality and stability and establish some existence results. Then, we give a converse Lyapunov theorem. Finally, the Morse decomposition of attractors is also addressed.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.11a
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• pp.59-62
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• 2000

In this paper we introduce the notion of fuzzy ${\gamma}$-open sets by using an operation ${\gamma}$ on fuzzy topological space (X, $\tau$) and investigate the related fuzzy topological properties of the associated fuzzy topology $\tau$$\_$${\gamma}$/ and $\tau$. And ${\gamma}$-T$\_$i/(i=0,1,2) separation axioms are defined in fuzzy topological spaces and the validity of some results analogous to those in fuzzy T$\_$i/ spaces due to Ganguly and Saha [2] are examined.

• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.155-164
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• 2007

It is the objective of this paper to study further the notion of ${\Lambda}_s$-semi-${\theta}$-closed sets which is defined as the intersection of a ${\theta}$-${\Lambda}_s$-set and a semi-${\theta}$-closed set. Moreover, introduce some low separation axioms using the above notions. Also we present and study the notions of ${\Lambda}_s$-continuous functions, ${\Lambda}_s$-compact spaces and ${\Lambda}_s$-connected spaces.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.583-588
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• 2018

In this manuscript, we show that the equality relations of the two assertions (ix) and (x) of [Theorem 2.11, p.p.224] in [3] do not hold in general, by giving a concrete example. Also, we illustrate that Example 6.3, Example 6.7, Example 6.11, Example 6.15 and Example 6.20 do not satisfy a soft semi $T_0$-space, a soft semi $T_1$-space, a soft semi $T_2$-space, a soft semi $T_3$-space and a soft semi $T_4$-space, respectively. Moreover, we point out that the three results obtained in [3] which related to soft subspaces are false, by presenting two examples. Finally, we construct an example to illuminate that Theorem 6.18 and Remark 6.21 made in [3] are not valid in general.

• Journal of the Korean Institute of Intelligent Systems
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• v.2 no.1
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• pp.3-16
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• 1992

In this paper, we establish the conceptes of compactifications of a L-fuzzy topological space and a order relation in these compactifications. This order is a preorder. The existemce problem and the uniqueness problem of the largest compactifications are closely related to the mapping extension problem. We give out the largest compactifications and show the non-uniqueness of the largest compactifications in the preorder for a kind of spaces. Moreover, under some natural assumptions of separation axioms, we prove that the preorder is just a partial order, thus it ensures the uniqueness of the largest compactification. In addition. the related discussion involves the special properties of fuzzy product space, the latter seems to be independent interesting.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.457-475
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• 2010

In this paper, we have use a fuzzy bitopological space (X, $\tau_1$, $\tau_2$) to create a family $\tau_{ij}^s$ which is a supra fuzzy topology on X. Also, we introduce and study the concepts of r-($\tau_i$, $\tau_j$)-generalized fuzzy regular closed, r-($\tau_i$, $\tau_j$)-generalized fuzzy strongly semi-closed and r-($\tau_i$, $\tau_j$)-generalized fuzzy regular strongly semi-closed sets in fuzzy bitopological space in the sense of $\check{S}$ostak. Also, these classes of fuzzy subsets are applied for constructing several type of fuzzy closed mapping and some type of fuzzy separation axioms called fuzzy binormal, fuzzy mildly binormal and fuzzy almost pairwise normal.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.85-98
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• 2022

The purpose of this paper is to introduce the notion of Fermatean fuzzy topological space by motivating from the notion of intuitionistic fuzzy topological space, and define Fermatean fuzzy continuity of a function defined between Fermatean fuzzy topological spaces. For this purpose, we define the notions of image and the pre-image of a Fermatean fuzzy subset with respect to a function and we investigate some basic properties of these notions. We also construct the coarsest Fermatean fuzzy topology on a non-empty set X which makes a given function f from X into Y a Fermatean fuzzy continuous where Y is a Fermatean fuzzy topological space. Finally, we introduce the concept of Fermatean fuzzy points and study some types of separation axioms in Fermatean fuzzy topological space.

• Bulletin of the Korean Mathematical Society
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• v.22 no.1
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• pp.17-22
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• 1985

B.M. Munshi and D.S. Bassan defined and developed the concept of super continuity in [5]. The concept has been investigated further by I. L. Reilly and M. K. Vamanamurthy in [6] where super continuity is characterized in terms of the semi-regularization topology. Super continuity is related to the concepts of .delta.-continuity and strong .theta.-continuity developed by T. Noiri in [7]. The purpose of this note is to derive relationships between super continuity and other strong continuity conditions and to develop additional properties of super continuous functions. Super continuity implies continuity, but the converse implication is false [5]. Super continuity is strictly between strong .theta.-continuity and .delta.-continuity and strictly between complete continuity and .delta.-continuity. The symbols X and Y will denote topological spaces with no separation axioms assumed unless explicity stated. The closure and interior of a subset U of a space X will be denoted by Cl(U) and Int(U) respectively and U is said to be regular open (resp. regular closed) if U=Int[Cl(U) (resp. U=Cl(Int(U)]. If necessary, a subscript will be added to denote the space in which the closure or interior is taken.