• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.471-486
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• 2014

This study introduces a new type of symbolic data, a candle chart-valued time series. We aggregate four stock indices (i.e., open, close, highest and lowest) as a one data point to summarize a huge amount of data. In other words, we consider a candle chart, which is constructed by open, close, highest and lowest stock indices, as a type of symbolic data for a long period. The proposed candle chart-valued time series effectively summarize and visualize a huge data set of stock indices to easily understand a change in stock indices. We also propose novel approaches for the candle chart-valued time series modeling based on a combination of two midpoints and two half ranges between the highest and the lowest indices, and between the open and the close indices. Furthermore, we propose three types of sum of square for estimation of the candle chart valued-time series model. The proposed methods take into account of information from not only ordinary data, but also from interval of object, and thus can effectively perform for time series modeling (e.g., forecasting future stock index). To evaluate the proposed methods, we describe real data analysis consisting of the stock market indices of five major Asian countries'. We can see thorough the results that the proposed approaches outperform for forecasting future stock indices compared with classical data analysis.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.37-48
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• 2010

In this paper we use a generalized Brownian motion process to defined an analytic operator-valued generalized Feynman integral. We then obtain explicit formulas for the analytic operatorvalued generalized Feynman integrals for functionals of the form $$F(x)=f\({\int}^T_0{\alpha}_1(t)dx(t),{\cdots},{\int}_0^T{\alpha}_n(t)dx(t)\)$$, where x is a continuous function on [0, T] and {${\alpha}_1,{\cdots},{\alpha}_n$} is an orthonormal set of functions from ($L^2_{a,b}[0,T]$, ${\parallel}{\cdot}{\parallel}_{a,b}$).

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.27-40
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• 2016

We define the notion of a residuated lattice valued function on a set as Jun and Song have done in BCK-algebras. We also investigate related properties of residuated lattice valued function. We establish the codes generated by residuated lattice valued function and conversely we give residuated lattice valued function and residuated lattice obtained by the giving binary block-code.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.4
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• pp.323-326
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• 2002

In this paper, we consider Choquet integrals of interval number-valued functions(simply, interval number-valued Choquet integrals). Then, we prove convergence theorem for interval number-valued Choquet integrals with respect to an autocontinuous fuzzy measure.

• Journal of the Korean Institute of Telematics and Electronics
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• v.20 no.5
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• pp.1-7
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• 1983

Generally, multiple-valued logic algebra is based on the number system of modulo-M. In this paper, characters a, b, c‥… each of them represents the independent state, are regarded as the elements of the symbolic multiple-valued logic. By using the set theory, the symbolic multiple - valued logic and their functions are defined. And Varation for the symbolic logic function due to the variation of a variable and their properties are suggested and analized. With these variations, the MacLaurin's and Taylor's Series expansions of the symbolic logic functions are proposed and proved.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.66-70
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• 2007

Note that Choquet integral is a generalized concept of Lebesgue integral, because two definitions of Choquet integral and Lebesgue integral are equal if a fuzzy measure is a classical measure. In this paper, we consider interval-valued Choquet integrals with respect to fuzzy measures(see [4,5,6,7]). Using these Choquet integrals, we define a mappings on the classes of Choquet integrable functions and give an example of a mapping defined by interval-valued Choquet integrals. And we will investigate some relations between m-convex mappings ${\phi}$ on the class of Choquet integrable functions and m-convex mappings $T_{\phi}$, defined by the class of closed set-valued Choquet integrals with respect to fuzzy measures.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1281-1284
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• 1993

By the exponential representation form (EF) for fuzzy logic, any fuzzy value a (in fuzzy valued logic or fuzzy linguistic valued logic) can be represented as Bc, where B is called the truth base and C the confidence exponent. This paper will propose the basic concepts of this form and discuss its interesting properties. By using a different truth base, the exponential form can be used to represent the positive and the negative logic in fuzzy valued logic as well as in fuzzy linguistic valued logic. Some Simple application examples of EF for approximate reasoning are also illustrated in this paper.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.11a
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• pp.49-52
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• 2000

• Journal of the Korean Mathematical Society
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• v.29 no.2
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• pp.341-350
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• 1992

• East Asian mathematical journal
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• v.17 no.2
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• pp.297-301
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• 2001