• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1993년도 Fifth International Fuzzy Systems Association World Congress 93
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• pp.777-780
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• 1993

Three optical fuzzy calculating modules, MAX/MIN, NOT/THROUGH, and SUP/THROUGH operating modules, are proposed. The MAX/MIN operating on inputted 2 membership functions. The NOT/THROUGH operating module calculates the complement of the membership function. The SUP/THROUGH operating module outputs an image representing the supremum (least upper bound) of the membership function. The THROUGH operation passes the image of the inputted membership function from the entrance to the exit. This paper demonstrates that these modules can output the image into which the modules transform inputted images on the basis of operation on fuzzy logic.

• 대한수학회논문집
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• 제34권4호
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• pp.1329-1334
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• 2019

We define the concept of a generator for a ${\mathbb{Z}}^k$-action T and show that T is expansive if and only it has a generator. Further, we prove several properties of a ${\mathbb{Z}}^k$-action including that the least upper bound of the set of expansive constants is not an expansive constant.

• 대한수학회보
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• 제55권5호
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• pp.1523-1528
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• 2018

For $r{\geq}2$, let ${\mathcal{H}}$ be an r-uniform hypergraph with n vertices and m hyperedges. Let R be a random vertex set obtained by choosing each vertex of ${\mathcal{H}}$ independently with probability p. Let ${\mathcal{H}}[R]$ be the subhypergraph of ${\mathcal{H}}$ induced on R. We obtain an upper bound on the matching number ${\nu}({\mathcal{H}}[R])$ and a lower bound on the independence number ${\alpha}({\mathcal{H}}[R])$ of ${\mathcal{H}}[R]$. First, we show that if $mp^r{\geq}{\log}\;n$, then ${\nu}(H[R]){\leq}2e^{\ell}mp^r$ with probability at least $1-1/n^{\ell}$ for each positive integer ${\ell}$. It is best possible up to a constant factor depending only on ${\ell}$ if $m{\leq}n/r$. Next, we show that if $mp^r{\geq}{\log}\;n$, then ${\alpha}({\mathcal{H}}[R]){\geq}np-{\sqrt{3{\ell}np\;{\log}\;n}-2re^{\ell}mp^r$ with probability at least $1-3/n^{\ell}$.

• ETRI Journal
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• 제21권4호
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• pp.9-22
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• 1999

This paper considers a problem of configuring both physical backbone and logical virtual path (VP) networks in a reconfigurable asynchronous transfer mode (ATM) network where links are subject to failures. The objective is to determine jointly the VP assignment, the capacity assignment of physical links and the bandwidth allocation of VPs, and the routing assignment of traffic demand at least cost. The network cost includes backbone link capacity expansion cost and penalty cost for not satisfying the maximum throughput of the traffic due to link failures or insufficient link capacities. The problem is formulated as a zero-one non-linear mixed integer programming problem, for which an effective solution procedure is developed by using a Lagrangean relaxation technique for finding a lower bound and a heuristic method exploited for improving the upper bound of any intermediate solution. The solution procedure is tested for its effectiveness with various numerical examples.

• 한국정보시스템학회:학술대회논문집
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• 한국정보시스템학회 2005년도 추계학술대회 발표 논문집
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• pp.326-333
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• 2005

The purpose of this paper is to provide a decision support method to a rational buyer, who wants to pay the least price for the product with the highest quality and service. We suggest a minimum efficiency game model and DEA game model to valuate many vendors whose qualifies of outputs are measured by percentage. Our results gave a decision maker (buyer) the upper bound and lower bound of the true efficiency score of a decision making unit (vendor) with respect to the benchmark (target) set by the buyer. As a result, a buyer can choose the best vendor in terms of his/her preference.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제28권1호
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• pp.22-32
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• 2024

In this paper we present a method of conic section approximation by hexic Bézier curves. The hexic Bézier approximants are G³ Hermite interpolations of conic sections. We show that there exists at least one hexic Bézier approximant for each weight of the conic section The hexic Bézier approximant depends one parameter and it can be obtained by solving a quartic polynomial, which is solvable algebraically. We present the explicit upper bound of the Hausdorff distance between the conic section and the hexic Bézier approximant. We also prove that our approximation method has the maximal order of approximation. The numerical examples for conic section approximation by hexic Bézier curves are given and illustrate our assertions.

• 한국음향학회지
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• 제23권7호
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• pp.540-547
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• 2004

칼만/위너 필터에 근거한 음성향상 알고리즘은 잡음의 선험적 지식을 요구하고, 음성신호와 추정신호의 오차분산을 최소화하는데 중점을 두고 있어, 잡음에 대한 통계적 추정에 오류가 있을 경우 결과에 악영향을 미칠 수 있다. 그러나 H/sub ∞/필터는 잡음에 대한 어떠한 가정이나 선험적 지식을 요구하지 않으며, 최소상계 (Least Upper Bound)를 적용하여 추정된 모든 신호들로부터 최소에러 신호를 갖는 최상의 추정신호를 찾아내므로 칼만/위너 필터보다 잡음의 변화에 강인하다. 본 논문에서는 학습 신호로부터 은닉 마코프 모델의 파라미터를 추정한 후, 오염된 신호를 고정된 개수의 H/sub ∞/필터를 통과시켜 각 출력에 가중된 합으로 향상된 음성 신호를 구하는 다중 H/sub ∞/필터에 의한 강인한 음성향상 방법을 제안한다. 제안된 방법의 성능 평가를 위하여 음성 향상 시간과 신호 대 잡음비를 비교한 결과, 기존의 방법에 비해 계산량은 다소 증가하지만 신호 대 잡음비는 약 1∼2dB 향상 되었다.

• 산업경영시스템학회지
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• 제38권3호
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• pp.169-180
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• 2015

Recently, scheduling problems with position-dependent processing times have received considerable attention in the literature, where the processing times of jobs are dependent on the processing sequences. However, they did not consider cases in which each processed job has different learning or aging ratios. This means that the actual processing time for a job can be determined not only by the processing sequence, but also by the learning/aging ratio, which can reflect the degree of processing difficulties in subsequent jobs. Motivated by these remarks, in this paper, we consider a two-agent single-machine scheduling problem with linear job-dependent position-based learning effects, where two agents compete to use a common single machine and each job has a different learning ratio. Specifically, we take into account two different objective functions for two agents: one agent minimizes the total weighted completion time, and the other restricts the makespan to less than an upper bound. After formally defining the problem by developing a mixed integer non-linear programming formulation, we devise a branch-and-bound (B&B) algorithm to give optimal solutions by developing four dominance properties based on a pairwise interchange comparison and four properties regarding the feasibility of a considered sequence. We suggest a lower bound to speed up the search procedure in the B&B algorithm by fathoming any non-prominent nodes. As this problem is at least NP-hard, we suggest efficient genetic algorithms using different methods to generate the initial population and two crossover operations. Computational results show that the proposed algorithms are efficient to obtain near-optimal solutions.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.421-426
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• 2007

The problem of vertex labeling with a condition at distance two in a graph, is a variation of Hale's channel assignment problem, which was first explored by Griggs and Yeh. For positive integer $p{\geq}q$, the ${\lambda}_{p,q}$-number of graph G, denoted ${\lambda}(G;p,q)$, is the smallest span among all integer labellings of V(G) such that vertices at distance two receive labels which differ by at least q and adjacent vertices receive labels which differ by at least p. Van den Heuvel and McGuinness have proved that ${\lambda}(G;p,q){\leq}(4q-2){\Delta}+10p+38q-24$ for any planar graph G with maximum degree ${\Delta}$. In this paper, we studied the upper bound of ${\lambda}_{p,q}$-number of some planar graphs. It is proved that ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+2(2p-1)$ if G is an outerplanar graph and ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+6p-4q-1$ if G is a Halin graph.

• Geomechanics and Engineering
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• 제10권1호
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• pp.59-76
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• 2016

The non-linear Hoek-Brown failure criterion has been widely accepted and applied to evaluate the stability of rock slopes under plane-strain conditions. This paper presents a kinematic approach of limit analysis to assessing the static and seismic stability of three-dimensional (3D) rock slopes using the generalized Hoek-Brown failure criterion. A tangential technique is employed to obtain the equivalent Mohr-Coulomb strength parameters of rock material from the generalized Hoek-Brown criterion. The least upper bounds to the stability number are obtained in an optimization procedure and presented in the form of graphs and tables for a wide range of parameters. The calculated results demonstrate the influences of 3D geometrical constraint, non-linear strength parameters and seismic acceleration on the stability number and equivalent strength parameters. The presented upper-bound solutions can be used for preliminary assessment on the 3D rock slope stability in design and assessing other solutions from the developing methods in the stability analysis of 3D rock slopes.