• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.901-914
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• 2013

Kwon and Bae gave an interpolation for a continuous form of H$\ddot{o}$lder's inequality for a real-valued bounded measurable function on a product of measure spaces. It is given some generalizations of their result.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.489-496
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• 2007

Let g be a continuous function on an interval I which is not constant on any subinterval of I, and let ${\mu}$ be a Borel measure on I. In this paper we give a necessary and sufficient conditions guaranteeing, for the strongly measurable function f on I with values in a Banach space X, the existence of a continuous primitive function F on I with respect to g.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.317-334
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• 1997

The existence of an operator-valued function space integral as an operator on $L_p(R) (1 \leq p \leq 2)$ was established for certain functionals which involved the Labesgue measure [1,2,6,7]. Johnson and Lapidus showed the existence of the integral as an operator on $L_2(R)$ for certain functionals which involved any Borel measures [5]. J. S. Chang and Johnson proved the existence of the integral as an operator from L_1(R)$ to $C_0(R)$ for certain functionals involving some Borel measures [3]. K. S. Chang and K. S. Ryu showed the existence of the integral as an operator from $L_p(R) to L_p'(R)$ for certain functionals involving some Borel measures [4].

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.7
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• pp.3128-3149
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• 2018

A number of effective methods for multiple-attribute group decision making (MAGDM) with interval-valued intuitionistic fuzzy numbers (IVIFNs) have been proposed in recent years. However, the different methods frequently yield different, even sometimes contradictory, results for the same problem. In this paper a novel criterion to determine the advantages and disadvantages of different methods is proposed. First, the decision-making process is divided into three parts: translation of experts' preferences, aggregation of experts' opinions, and comparison of the alternatives. Experts' preferences aggregation is considered the core step, and the quality of the collective matrix is considered the most important evaluation index for the aggregation methods. Then, methods to calculate the similarity measure, correlation, correlation coefficient, and energy of the intuitionistic fuzzy matrices are proposed, which are employed to evaluate the collective matrix. Thus, the optimal method can be selected by comparing the collective matrices when all the methods yield different results. Finally, a novel approach for aggregating experts' preferences with IVIFN is presented. In this approach, experts' preferences are mapped as points into two-dimensional planes, with the plant growth simulation algorithm (PGSA) being employed to calculate the optimal rally points, which are inversely mapped to IVIFNs to establish the collective matrix. In the study, four different methods are used to address one example problem to illustrate the feasibility and effectiveness of the proposed approach.

• Journal of the Korea Management Engineers Society
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• v.23 no.4
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• pp.87-103
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• 2018

This paper introduces the method to develop two main types of the fuzzy OEE (Overall Equipment Effectiveness) models via triangular membership function for measuring uncertainty. The fuzzy OEE includes model type 1 and model type 2. The model type 1 is used when the theoretical machine speed only reflects the time loss whereas model type 2 is used when the actual machine speed reflects both time and speed loss. Model type 2 has shown to perform a lower availability rate and a higher performance rate compared to model type 1. In addition, the fuzzy UPH (Unit Per Hour) which is derived from using the fuzzy OEE is presented to satisfy demand uncertainty. The fuzzy UPH can easily measure the fuzzy tact time and cycle time by reciprocating itself. Finally, this study demonstrates the fuzzy OEE models using IVIFS (Interval-Valued Intuitionistic Fuzzy Set) based on the characterization via membership function, non-membership function and hesitant function. For the purpose of analyzing the fuzzy system OEE, the OEE for each machine of plant structure is considered triangular interval-valued intuitionistic fuzzy number. Regardless of plant structure, the validity degree of fuzzy membership function of system OEE decreases when the number of machine with worst value of the validity degree increases. Corresponding examples are presented in this paper for practitioner to understand the applicability and practicability of the proposed fuzzy OEE methods.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.413-431
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• 2012

Let $C^r[0,t]$ be the function space of the vector-valued continuous paths $x:[0,t]{\rightarrow}\mathbb{R}^r$ and define $X_t:C^r[0,t]{\rightarrow}\mathbb{R}^{(n+1)r}$ and $Y_t:C^r[0,t]{\rightarrow}\mathbb{R}^{nr}$ by $X_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}),\;x(t_n))$ and $Y_t(x)=(x(t_0),\;x(t_1),\;{\cdots},\;x(t_{n-1}))$, respectively, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n=t$. In the present paper, using two simple formulas for the conditional expectations over $C^r[0,t]$ with the conditioning functions $X_t$ and $Y_t$, we establish evaluation formulas for the analogue of the conditional analytic Fourier-Feynman transform for the function of the form $${\exp}\{{\int_o}^t{\theta}(s,\;x(s))\;d{\eta}(s)\}{\psi}(x(t)),\;x{\in}C^r[0,t]$$ where ${\eta}$ is a complex Borel measure on [0, t] and both ${\theta}(s,{\cdot})$ and ${\psi}$ are the Fourier-Stieltjes transforms of the complex Borel measures on $\mathbb{R}^r$.

• Honam Mathematical Journal
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• v.8 no.1
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• pp.1-19
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• 1986

We show that a (possibly unbounded) linear operator, T, is scalar on the real line (spectral operator of scalar type, with real spectrum) if and only if (iT) generates a uniformly bounded semigroup and $(1-iT)(1+iT)^{-1}$ is scalar on the unit circle. T is scalar on [0, $\infty$) if and only if T generates a uniformly bounded semigroup and $(1+T)^{-1}$ is scalar on [0,1). By analogy with these results, we define $C^0$-scalar, on the real line, or [0. $\infty$), for an unbounded operator. We show that a generator of a positive-definite group is $C^0$-scalar on the real line. and a generator of a completely monotone semigroup is $C^0$-scalar on [0, $\infty$). We give sufficient conditions for a closed operator, T, to generate a positive-definite group: the sequence < $\phi(T^{n}x)$ > $_{n=0}^{\infty}$ must equal the moments of a positive measure on the real line, for sufficiently many positive $\phi$ in $X^{*}$, x in X. If the measures are supported on [0, $\infty$), then T generates a completely monotone semigroup. On a reflexive Banach lattice, these conditions are also necessary, and are equivalent to T being scalar, with positive projection-valued measure. T generates a completely monotone semigroup if and only if T is positive and m-dispersive and generates a bounded holomorphic semigroup.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.809-823
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• 2020

Let C[0, T] denote the space of continuous, real-valued functions on the interval [0, T] and let C₀[0, T] be the space of functions x in C[0, T] with x(0) = 0. In this paper, we introduce a Banach algebra ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ on C[0, T] and its equivalent space ${\bar{\mathcal{F}}}({\mathcal{H}}) $, a space of transforms of equivalence classes of measures, which generalizes Fresnel class 𝓕(𝓗), where 𝓗 is an appropriate real separable Hilbert space of functions on [0, T]. We also investigate their properties and derive an isomorphism between ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ and ${\bar{\mathcal{F}}}({\mathcal{H}}) $. When C[0, T] is replaced by C₀[0, T], ${\bar{\mathcal{F}}}({\mathcal{H}}) $ and ${\bar{\mathcal{S}}}_{{\alpha},{\beta};{\varphi}}$ reduce to 𝓕(𝓗) and Cameron-Storvick's Banach algebra 𝓢, respectively, which is the space of generalized Fourier-Stieltjes transforms of the complex-valued, finite Borel measures on L²[0, T].

• Journal of the Korea Academia-Industrial cooperation Society
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• v.4 no.2
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• pp.81-86
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• 2003

There are many studies to measure and compare Korean foot length or foot shape. However, to make high-valued shoe product, it is not easy to find the research results about the shoe's products that include the customer requirements, price, and color. The purpose of this study is to investigate the customer's requirements for men's shoe product using the survey method, to analysis customer's needs, and to supply information to make the shoe that they want.

• Transactions of Materials Processing
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• v.16 no.2 s.92
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• pp.101-106
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• 2007

Uniaxial displacement controlled tests were performed on annealed Type 304 stainless steel at room temperature. A servo-controlled testing machine and strain measurement on the gage length were employed to measure the response to a given input. The test results exhibit that the flow stress increases nonlinearly with the strain rate and the relaxed stress at the end of the relaxation periods depends strongly on the strain rate preceding the relaxation test. The rate-dependent inelastic deformation behavior is simulated using a new unified viscoplasticity model that has the rate-dependent format of nonlinear kinematic hardening rule, which plays a key role in modeling the rate dependence of relaxation behavior. The model does not employ yield or loading/unloading criteria and consists of a flow law and the evolution laws of two tensor and one scalar-valued state variables.