• 제목/요약/키워드: Set functions

검색결과 1,681건 처리시간 0.031초

On fuzzy number-valued Choquet integrals

  • 장이채;김태균
    • 한국전산응용수학회:학술대회논문집
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    • 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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    • pp.7-7
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    • 2003
  • We studied closed set-valued Choquet integrals in two papers(1997, 2000) and convergence theorems under some sufficient conditions in two papers(2003), for examples : (i) convergence theorems for monotone convergent sequences of Choquet integrably bounded closed set-valued functions, (ii) covergence theorems for the upper limit and the lower limit of a sequence of Choquet integrably bounded closed set-valued functions. In this presentation, we consider fuzzy number-valued functions and define Choquet integrals of fuzzy number-valued functions. But these concepts of fuzzy number-valued Choquet inetgrals are all based on the corresponding results of interval-valued Choquet integrals. We also discuss their properties which are positively homogeneous and monotonicity of fuzzy number-valued Choquet integrals. Furthermore, we will prove convergence theorems for fuzzy number-valued Choquet integrals. They will be used in the following applications : (1) Subjectively probability and expectation utility without additivity associated with fuzzy events as in Choquet integrable fuzzy number-valued functions, (2) Capacity measure which are presented by comonotonically additive fuzzy number-valued functionals, and (3) Ambiguity measure related with fuzzy number-valued fuzzy inference.

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확장 B-spline 기저 함수를 이용한 레벨셋 기반의 형상 최적 설계 (Level Set based Shape Optimization using Extended B-spline Bases)

  • 김민근;조선호
    • 한국전산구조공학회:학술대회논문집
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    • 한국전산구조공학회 2008년도 정기 학술대회
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    • pp.391-396
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    • 2008
  • A level set based topological shape optimization using extended B-spline basis functions is developed for steady state heat conduction problems. The only inside of complicated domain is identified by the level set functions and taken into account in computation. The solution of Hamilton-Jacobi equation leads to an optimal shape according to the normal velocity field determined from the sensitivity analysis, minimizing a thermal compliance while satisfying a volume constraint. To obtain exact shape sensitivity, the precise normal and curvature of geometry need to be determined using the level set and B-spline basis functions. The nucleation of holes is possible whenever and wherever necessary during the optimization using a topological derivative concept.

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Non-linear distributed parameter system estimation using two dimension Haar functions

  • Park Joon-Hoon;Sidhu T.S.
    • Journal of information and communication convergence engineering
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    • 제2권3호
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    • pp.187-192
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    • 2004
  • A method using two dimension Haar functions approximation for solving the problem of a partial differential equation and estimating the parameters of a non-linear distributed parameter system (DPS) is presented. The applications of orthogonal functions, including Haar functions, and their transforms have been given much attention in system control and communication engineering field since 1970's. The Haar functions set forms a complete set of orthogonal rectangular functions similar in several respects to the Walsh functions. The algorithm adopted in this paper is that of estimating the parameters of non-linear DPS by converting and transforming a partial differential equation into a simple algebraic equation. Two dimension Haar functions approximation method is introduced newly to represent and solve a partial differential equation. The proposed method is supported by numerical examples for demonstration the fast, convenient capabilities of the method.

DUAL ALGORITHM FOR $GL_1$ ISOTONIC OPTIMIZATION WITH WEIGHTS ON A PARTIALLY ORDERED SET

  • Chung, Seiyoung
    • 대한수학회보
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    • 제28권2호
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    • pp.243-254
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    • 1991
  • For a given function f.mem.F and a set of functions J.subeq.F, the problem of isotonic optimization is to determine an element in the set nearest to f in some sense. Specifically, let X be a partially ordered finite set with a partial order << and, let F"=F(X) be the linear space of all bounded real valued functions on X. A function g.mem.F is said to be an isotonic function if g(x).leq.g(y) whenever x,y.mem.X and x << y.<< y.

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보편적인 기저함수를 이용한 개인의 머리전달함수 모델링 (Modeling of individual head-related impulse responses using a set of general basis functions)

  • 황성목;박영진;박윤식
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2007년도 추계학술대회논문집
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    • pp.1430-1436
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    • 2007
  • A principal components analysis (PCA) of the median head-related impulse responses (HRIRs) in the CIPIC HRTF database reveals that the individual HRIRs can be adequately reconstructed by a linear combination of 12 orthonormal basis functions. These basis functions can be used generally to model arbitrary HRIRs, which are not included in the process to obtain the basis functions. To clarify whether these basis functions can be used to model other set of arbitrary HRIRs, an numerical error analysis for modeling and a series of subjective listening tests were carried out using the measured and modeled HRIRs. The results showed that the set of individual HRIRs, which were measured in our lab using different measurement conditions, techniques, and source positions, can be well modeled with reasonable accuracy. Furthermore, all subjects reported not only the accurate vertical perception but also the front-back discrimination with the modeled HRIRs based on 12 basis functions. However, as less basis functions were used for HRIR modeling, the modeling accuracy and localization performance deteriorated.

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ON OPTIMALITY AND DUALITY FOR GENERALIZED NONDIFFERENTIABLE FRACTIONAL OPTIMIZATION PROBLEMS

  • Kim, Moon-Hee;Kim, Gwi-Soo
    • 대한수학회논문집
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    • 제25권1호
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    • pp.139-147
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    • 2010
  • A generalized nondifferentiable fractional optimization problem (GFP), which consists of a maximum objective function defined by finite fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions, is considered. Recently, Kim et al. [Journal of Optimization Theory and Applications 129 (2006), no. 1, 131-146] proved optimality theorems and duality theorems for a nondifferentiable multiobjective fractional programming problem (MFP), which consists of a vector-valued function whose components are fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions. In fact if $\overline{x}$ is a solution of (GFP), then $\overline{x}$ is a weakly efficient solution of (MFP), but the converse may not be true. So, it seems to be not trivial that we apply the approach of Kim et al. to (GFP). However, modifying their approach, we obtain optimality conditions and duality results for (GFP).

SOME NEW CLASSES OF ZERO-DIFFERENCE BALANCED FUNCTIONS AND RELATED CONSTANT COMPOSITION CODES

  • Sankhadip, Roy
    • 대한수학회보
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    • 제59권6호
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    • pp.1327-1337
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    • 2022
  • Zero-difference balanced (ZDB) functions can be applied to many areas like optimal constant composition codes, optimal frequency hopping sequences etc. Moreover, it has been shown that the image set of some ZDB functions is a regular partial difference set, and hence provides strongly regular graphs. Besides, perfect nonlinear functions are zero-difference balanced functions. However, the converse is not true in general. In this paper, we use the decomposition of cyclotomic polynomials into irreducible factors over 𝔽p, where p is an odd prime to generalize some recent results on ZDB functions. Also we extend a result introduced by Claude et al. [3] regarding zero-difference-p-balanced functions over 𝔽pn. Eventually, we use these results to construct some optimal constant composition codes.

V노치 또는 예리한 균열을 가지는 Mindlin 직사각형 평판의 휨 진동해석 (Flexural Vibration Analysis of Mindlin Rectangular Plates Having V-notches or Sharp Cracks)

  • Kim, Joo-Woo;Jung, Eui-Young;Kim, Seung-Hyun
    • 한국전산구조공학회:학술대회논문집
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    • 한국전산구조공학회 2003년도 봄 학술발표회 논문집
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    • pp.35-42
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    • 2003
  • This paper provides the first known flexural vibration data for thick (Mindlin) rectangular plates having V-notches. The V-notch has bending moment and shear force singularities at its sharp corner due to the transverse vibratory bending motion. Based upon Mindlin plate theory, in which transverse shear deformation and rotary inertia effects are considered, the Ritz procedure is employed with a hybrid set of admissible functions assumed for the rotational and transverse vibratory displacements. This set includes: (1) a mathematically complete set of admissible algebraic-trigonometric polynomials which guarantee convergence to exact frequencies as sufficient terms are retained; and (2) an admissible set of Mindlin corner functions which account for the bending moment and shear force singularities at the sharp corner of the V-notch. Extensive convergence studies demonstrate the necessity of adding the Mindlin corner functions to achieve accurate frequencies for rectangular plates having sharp V-notches.

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AN AVERAGE OF SURFACES AS FUNCTIONS IN THE TWO-PARAMETER WIENER SPACE FOR A PROBABILISTIC 3D SHAPE MODEL

  • Kim, Jeong-Gyoo
    • 대한수학회보
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    • 제57권3호
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    • pp.751-762
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    • 2020
  • We define the average of a set of continuous functions of two variables (surfaces) using the structure of the two-parameter Wiener space that constitutes a probability space. The average of a sample set in the two-parameter Wiener space is defined employing the two-parameter Wiener process, which provides the concept of distribution over the two-parameter Wiener space. The average defined in our work, called an average function, also turns out to be a continuous function which is very desirable. It is proved that the average function also lies within the range of the sample set. The average function can be applied to model 3D shapes, which are regarded as their boundaries (surfaces), and serve as the average shape of them.

보편적인 기저함수를 이용한 중앙면상의 머리전달함수 모델링 (Modeling of Median-plane Head-related Impulse Responses Using a Set of General Basis Functions)

  • 황성목;박영진;박윤식
    • 한국소음진동공학회논문집
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    • 제18권4호
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    • pp.448-457
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    • 2008
  • A principal components analysis (PCA) of the median-plane head-related impulse responses (HRIRs) in the CIPIC HRTF database reveals that the individual HRIRs in the median plane can be adequately reconstructed by a linear combination of 12 orthonormal basis functions. These basis functions can be used to model arbitrary median-plane HRIRs, which are not included in the process to obtain the basis functions. Memory size can be reduced up to 5-fold depending on the number of HRIRs to be modeled. To clarify whether these basis functions can be used to model other set of arbitrary median plane HRIRs, a numerical error analysis for modeling and a series of subjective listening tests were carried out using the measured and modeled HRIRs. The results showed that the set of individual HRIRs in the median plane, which were measured in our lab using different measurement conditions, techniques, and source positions, can be modeled with reasonable accuracy. All subjects, involved in the subjective listening test, reported not only the accurate vertical perception but also the front-back discrimination with the modeled HRIRs based on 12 basis functions.