• Ocean Systems Engineering
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• v.9 no.2
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• pp.179-190
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• 2019

This paper deals with the problem of the global stabilization for a class of ocean structure systems. It is well known that, in general, the global asymptotic stability of the ocean structure subsystems does not imply the global asymptotic stability of the composite closed-loop system. The classical fuzzy inference methods cannot work to their full potential in such circumstances because given knowledge does not cover the entire problem domain. However, requirements of fuzzy systems may change over time and therefore, the use of a static rule base may affect the effectiveness of fuzzy rule interpolation due to the absence of the most concurrent (dynamic) rules. Designing a dynamic rule base yet needs additional information. In this paper, we demonstrate this proposed methodology is a flexible and general approach, with no theoretical restriction over the employment of any particular interpolation in performing interpolation nor in the computational mechanisms to implement fitness evaluation and rule promotion.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.358-363
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• 1998

An algorithm for representing the cubic spline interpolation of differentiable functions by a fuzzy system is presented in this paper. The cubic B-spline functions which form a basis for the interpolation function are used as the fuzzy sets for input fuzzification. The ordinal number of the coefficient cKL in the list of the coefficient cij's as sorted in increasing order, is taken to be the output fuzzy set number in the (k, l) th entry of the fuzzy rule table. Spike functions are used for the output fuzzy sets, with cij's as support boundaries after they are sorted. An algorithm to compute the support boundaries explicitly without solving the matrix equation involved is included, along with a few properties of the fuzzy rule matrix for the designed fuzzy system.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.05a
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• pp.86-89
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• 2000

In this paper, we consider a fuzzy system representation for polynomials of two variables. The representation we use is an exact transformation of the corresponding cubic spline interpolation function. We examine some of the properties of their fuzzy rule tables md prove that the rule table is symmetric or antisymmetric depending on whether the polynomial is symmetric or antisymmetric. A few examples are included to verify our proof. These results not only provide some insights on properties of the cubic spline interpolation coefficients but also provide some help in setting up fuzzy rule tables for functions of two variables.

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.295-305
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• 2008

This paper demonstrates how composite-exponential-fitting interpolation rules can be constructed to fit an oscillatory function using not only pointwise values of that function but also of that functions's derivative on a closed and bounded interval of interest. This is done in the framework of exponential-fitting techniques. These rules extend the classical composite cubic Hermite interpolating polynomials in the sense that they become the classical composite polynomials as a parameter tends to zero. Some examples are provided to compare the newly constructed rules with the classical composite cubic Hermite interpolating polynomials (or recently developed interpolation rules).

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.475-485
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• 2007

We construct high-degree interpolation rules using not only pointwise values of a function but also of its derivatives up to the p-th order at equally spaced nodes on a closed and bounded interval of interest by introducing a linear functional from which we produce systems of linear equations. The linear systems will lead to a conclusion that the rules are uniquely determined for the nodes. An example is provided to compare the rules with the classical interpolating polynomials.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.397-407
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• 2006

We construct polynomial-fitting interpolation rules to agree with a function f and its first derivative f' at equally spaced nodes on the interval of interest by introducing a linear functional with which we produce systems of linear equations. We also introduce a matrix whose determinant is not zero. Such a property makes it possible to solve the linear systems and then leads to a conclusion that the rules are uniquely determined for the nodes. An example is investigated to compare the rules with Hermite interpolating polynomials.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.895-898
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• 1993

Instead of Cartesian product for in combining multiple inputs for fuzzy logic controllers, a method using fuzzy relation in inference is proposed. Moreover, fuzzy control rule described by fuzzy relations is derived from given conventional fuzzy control rule by fitting concept. It will be shown through several examples that the proposed technique gives smoother interpolation than conventional ones.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.253-260
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• 2002

In this paper, a good interpolation formulae are applied to the numerical solution of Cauchy integral equations of the first kind with using some Chebyshev quadrature rules. To demonstrate the effectiveness of the Radau-Chebyshev with respect to the olds, [6],[7],[8] and [121, some examples are given.

• Structural Engineering and Mechanics
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• v.43 no.3
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• pp.349-370
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• 2012

Variable-node finite element families, termed (4 + k + l + m + n)-node elements with an arbitrary number of nodes (k, l, m, and n) on each of their edges, are developed based on the generic point interpolation with special bases having slope discontinuities in two-dimensional domains. They retain the linear interpolation between any two neighboring nodes, and passes the standard patch test when subdomain-wise $2{\times}2$ Gauss integration is employed. Their shape functions are automatically generated on the master domain of elements although a certain number of nodes are inserted on their edges. The elements can provide a flexibility to resolve nonmatching mesh problems like mesh connection and adaptive mesh refinement. In the case of adaptive mesh refinement problem, so-called "1-irregular node rule" working as a constraint in performing mesh adaptation is relaxed by adopting the variable-node elements. Through several examples, we show the performance of the variable-node finite elements in terms of accuracy and efficiency.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.8 no.1
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• pp.41-50
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• 1990

The purpose of this thesis lies in proving the practicality of photogrammetry and in promoting photogrammetry in earthwork which plays a major role in civil engineering projects. Analysis of accuracy in the determination of ammount of earthework was done by applying interpolation methods in digital terrain model. As a result of analysis of the data acquisition method, in cross-section method produced acceptable accuracy from Simpson's three-eighths rule and prismoidal rule. In results DTM, we have obtained the fact that earthwork calculation accuracy was increased by applying two or more interpolation methods. Therefore, the method by digital terrain model using aerial photograph has proved to be more efficient.