• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.10a
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• pp.331-337
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• 1997

In this paper we will discuss a type of inductive learning called learning from examples, whose task is to induce general descriptions of concepts from specific instances of these concepts. In many real life situations however new instances can be added to the set of instances. It is first proposed within the framework of rough set theory, for such cases, an algorithm to find minimal set of rules for decision tables without recalculation for overall set of instances. The method of learning presented here is based on a rough set concept proposed by Pawlak[2]. It is shown an algorithm to fund minimal set of rules using reduct change theorems giving criteria for minimum recalculation and an illustrative example.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.1
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• pp.11-20
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• 1995

A new graph problem is formulated to limit the maximum path length of a general directed graph when a minimal set of vertices together with their incident edges are removed from the graph. An optimal algorithm and a heuristic algorithm are proposed and the proposed heuristic algorithm is shown to be effective through experiments using a collection of graphs obtained from large sequential circuits. The heuristic algorithm is based on a feedback vertex set algorithm based on graph reduction.

• Kyungpook Mathematical Journal
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• v.27 no.1
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• pp.27-33
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• 1987

Minimal s-Urysohn and minimal s-regular spaces are studied. An s-Urysohn (respectively, s-regular) space (X, $\mathfrak{T}$) is said to be minimal s-Urysohn (respectively, minimal s-regular) if for no topology $\mathfrak{T}^{\prime}$ on X which is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) is s-Urysohn (respectively s-regular). Several characterizations and other related properties of these classes of spaces have been obtained. The present paper is a study of minimal P-spaces where P refers to the property of being an s-Urysohn space or an s-regular space. A P-space (X, $\mathfrak{T}$) is said to be minimal P if for no topology $\mathfrak{T}^{\prime}$ on X such that $\mathfrak{T}^{\prime}$ is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) has the property P. A space X is said to be s-Urysohn [2] if for any two distinct points x and y of X there exist semi-open set U and V containing x and y respectively such that $clU{\bigcap}clV={\phi}$, where clU denotes the closure of U. A space X is said to be s-regular [6] if for any point x and a closed set F not containing x there exist disjoint semi-open sets U and V such that $x{\in}U$ and $F{\subseteq}V$. Throughout the paper the spaces are assumed to be Hausdorff.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.308-313
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• 1998

In this paper we will discuss a type of inductive learning called learning from examples, whose task is to induce general description of concepts from specific instances of these concepts. In many real life situations, however, new instances can be added to the set of instances. It is first proposed within the framework of rough set theory, for such cases, an algorithm to find minimal set of rules for decision tables without recalculation for overcall set of instances. The method of learning presented here is base don a rough set concept proposed by Pawlak[2][11]. It is shown an algorithm to find minimal set of rules using reduct change theorems giving criteria for minimum recalculation with an illustrative example. Finally, the proposed learning algorithm is applied to fuzzy system to learn sampled I/O data.

• Korean Journal of Mathematics
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• v.21 no.2
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• pp.181-187
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• 2013

In this paper we give some results on homomorphisms of pointed minimal sets. In particular, we investigate some characterizations on quasi-Ellis groups.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.4
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• pp.358-364
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• 1999

The auxiliary transformers or start-up/stand-by transformer(s) are installed against the start-up and shut-down of generator and emergency status in fossil power plant. The on-site power supply configuration using these transformers must be determined, considering configuration requirements, site characteristics, reliability and availability severely because it is remarkably important for safety and ecfonomy of plant. The auxiliary or start-up/stand-by power supply configuration has been determined considering only safety requirements and construction cost until now in Korea. This paper presents general theorems for the reliability estimation and proposes 2-unit based 4 alternatives for the start-up power supply stystem of 500㎿ standardized fossil power plant. The reliability and unavailability of equipment, system and configuration are determined using minimal cut-set methodology. The optimized plan of 4 alternatives is determined based on this ultimate reliability and unavailability.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.293-311
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• 2018

We study the homotopical minimal periods for maps on infra-solvmanifolds of type (R) using the density of the homotopical minimal period set in the natural numbers. This extends the result of [10] from flat manifolds to infra-solvmanifolds of type (R). We give some examples of maps on infra-solvmanifolds of dimension three for which the corresponding density is positive.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1055-1062
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• 2014

Let $O_n$ and $PO_n$ denote the order-preserving transformation and the partial order-preserving transformation semigroups on the set $X_n=\{1,{\ldots},n\}$, respectively. Then the strictly partial order-preserving transformation semigroup $SPO_n$ on the set $X_n$, under its natural order, is defined by $SPO_n=PO_n{\setminus}O_n$. In this paper we find necessary and sufficient conditions for any subset of SPO(n, r) to be a (minimal) generating set of SPO(n, r) for $2{\leq}r{\leq}n-1$.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.689-701
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• 2021

The purpose of this paper is to optimize the number of source places required for the unique representation of the destination using the tools of graph theory. A subset S of vertices of a graph G is called a rational resolving set of G if for each pair u, v ∈ V - S, there is a vertex s ∈ S such that d(u/s) ≠ d(v/s), where d(x/s) denotes the mean of the distances from the vertex s to all those y ∈ N[x]. A rational resolving set is called minimal rational resolving set if no proper subset of it is a rational resolving set. In this paper we study varieties of minimal rational resolving sets defined on the basis of its complements and compute the minimum and maximum cardinality of such sets, respectively called as lower and upper rational metric dimensions for power of a path P_n analysing various possibilities.

• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.263-271
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• 2012

We introduce the concept of fuzzy $r$-minimal ${\beta}$-open set on a fuzzy minimal space and basic some properties. We also introduce the concept of fuzzy $r-M$ ${\beta}$-continuous mapping which is a generalization of fuzzy $r-M$ continuous mapping and fuzzy $r-M$ semicontinuous mapping, and investigate characterization for the continuity.