• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.295-302
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• 2021

In this paper, we propose a new iterative algorithm to automatically prove the existence of solutions for a unilateral boundary value problems for second order equations.

• Communications for Statistical Applications and Methods
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• v.19 no.3
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• pp.359-365
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• 2012

The fuzzy set framework has a number of properties that make it suitable to formulize uncertain information in medical diagnosis. This study introduces a fuzzy diagnostic method based on the interval-valued interview chart and the interval-valued intuitionistic fuzzy weighted arithmetic average(IIFWAA) operator. An issue in the use of the IIFWAA operator is to determine the weights. In this study, we propose the occurrence information of symptoms as the weights. An illustrative example is provided to demonstrate its practicality and effectiveness.

• International conference on construction engineering and project management
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• 2011.02a
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• pp.468-473
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• 2011

The goal of a project manager is generally to minimize the cost of the project and also to cope with uncertainty. This paper deals with the problem of project scheduling a set of activities satisfying precedence constraints in order to minimize the sum of the costs associated with the starting times of the activities in the network with imprecise activity durations, represented by means of interval or fuzzy numbers. So far this problem has been completely solved by several authors when the activities durations have crisp values. However, they do not consider the imprecision in activity durations in their models. Here the framework of possibility theory is proposed to solve this problem. In fuzzy arithmetic, usually, the interval calculations are used for the aim of complexity reduction and simplification. Thus the case of interval-valued durations is first addressed, and then extended to fuzzy intervals. A numerical example is used to illustrate the developed concept.

• Computers and Concrete
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• v.2 no.4
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• pp.325-343
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• 2005

Chloride ingress is a common cause of deterioration of reinforced concrete located in coastal zone. Modeling the chloride ingress is an important basis for designing reinforced concrete structures and for assessing the reliability of an existing structure. The modeling is also needed for predicting the deterioration of a reinforced structure. The existing deterministic solution for prediction model of corrosion initiation cannot reflect uncertainties which input variables have. This paper presents an approach to the fuzzy arithmetic based modeling of the chloride-induced corrosion of reinforcement in concrete structures that takes into account the uncertainties in the physical models of chloride penetration into concrete and corrosion of steel reinforcement, as well as the uncertainties in the governing parameters, including concrete diffusivity, concrete cover depth, surface chloride concentration and critical chloride level for corrosion initiation. There are a lot of prediction model for predicting the time of reinforcement corrosion of structures exposed to chloride-induced corrosion environment. In this work, RILEM model formula and Crank's solution of Fick's second law of diffusion is used. The parameters of the models are regarded as fuzzy numbers with proper membership function adapted to statistical data of the governing parameters instead of random variables of probabilistic modeling of Monte Carlo Simulation and the fuzziness of the time to corrosion initiation is determined by the fuzzy arithmetic of interval arithmetic and extension principle. An analysis is implemented by comparing deterministic calculation with fuzzy arithmetic for above two prediction models.

• Proceedings of the Korea Multimedia Society Conference
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• 2003.11b
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• pp.933-936
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• 2003

본 논문은 비트 매트릭스(bit matrix) 확률 모델과 이를 입력으로 사용하는 개량된 이진 산술부호 알고리즘을 제안한다. 비트들로 이루어진 비트 평면에서 3$\times$3 비트 매트릭스를 정의하였다. 그리고 비트 평면을 조사하여 2연속 혹은 3연속 비트 매트릭스들에 대한 확률모델을 구하였다. 본 연구에서는 3 가지의 확률간격(interval)을 가지는 개량된 이진 산술부호기률 사용하였다. 개량된 이진 산술부호 알고리즘의 장점은 구조가 간결하고 또한 부호화가 진행되는 도중에 결과 비트스트림을 생성하는 특징이 있다. 이진 산술부호기는 2연속 혹은 3연속 비트매트릭스를 입력하여 산술부호화를 수행하도록 한다.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.747-755
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• 2020

The mathematical proof for establishing some new inequalities involving arithmetic, geometric, harmonic means for the arguments lying on the paths of triangular wave function (linear) and new parabolic function (curved) over the interval (0, 1) are discussed. The results representing an extension as well as strengthening of Ky Fan Type inequalities.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.263-273
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• 2013

A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation $$\frac{f(x)-F(y)}{x-y}=M(g(x),\;G(y)),\;x{\neq}y$$, where M is a given mean and $f$, F, $g$, G are the unknown functions. Solving this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homographic and square-root functions. A new criterion of the monotonicity of a real function is presented.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.10
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• pp.80-89
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• 1996

This paper proposes a new COA (center of area) defuzzifier that is working in the accurate and fast manner. The proposed COA defuzzifier involves both membership values and the spans of membership functions in clauclating a crisp value. In additon, it avoid division by replacing the COA calculation with the searching of the momentum equilibrium point. The moment equilibrium point is searched in the coarse-to-fine manner such that the moment computing points during the coarse searching are moved in the interval of fuzzy terms until they are reached at two adjacent fuzzy terms searching method accerlates the finding of the moment equilibrium point by O(M) mazimally when compared iwth the equal interval searching method of ruitz. In order to verify the accuracy of the proposed COA defuzzifier, the crisp values obtained form the proposed coarse-to-fine searching are compared with the precise crisp values from the arithmetic calculation. Application to the truck backer-upper control problem of the proposed COA defuzzifier is presented. The control performance is compared with that of the conventional COA defuzzifier in tems of the average tracing distance.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.7
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• pp.1351-1362
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• 1992

Qualitative models in model-based expert system needs modeling paradigm which provides intelligent control of modeling assumptions and extracts robust inferences without quantitative information about the system to be modeled. Qualitative reasoning methodologies has proved the property of the completeness but not the soundness to the corresponding quantitative model. We propose new methodology of qualitative reasoning by introducing the concept of Centroid-Oriented Composite Interval to improve the soundness problem. Arithmetic operations and equivalence classes were composed using this definition. Qualitative simulation results were compared to Kuipers's results and the improvements in the soundness problem is verified.

• Smart Structures and Systems
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• v.14 no.6
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• pp.1131-1150
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• 2014

One of the issues in extending the range of applicable problems of real-time hybrid simulation is the computation speed of the simulator when large-scale computational models with a large number of DOF are used. In this study, functionality of real-time dynamic simulation of MDOF systems is achieved by creating a logic circuit that performs the step-by-step numerical time integration of the equations of motion of the system. The designed logic circuit can be implemented to an FPGA-based system; FPGA (Field Programmable Gate Array) allows large-scale parallel computing by implementing a number of arithmetic operators within the device. The operator splitting method is used as the numerical time integration scheme. The logic circuit consists of blocks of circuits that perform numerical arithmetic operations that appear in the integration scheme, including addition and multiplication of floating-point numbers, registers to store the intermediate data, and data busses connecting these elements to transmit various information including the floating-point numerical data among them. Case study on several types of linear and nonlinear MDOF system models shows that use of resource sharing in logic synthesis is crucial for effective application of FPGA to real-time dynamic simulation of structural response with time step interval of 1 ms.