• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.331-347
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• 2017

Soft sets are fantastic mathematical tools to handle imprecise and uncertain information in complicated situations. In this paper, we defined the hybrid structure which is the combination of soft set and complex number representation of intuitionistic fuzzy set. We defined basic set theoretic operations such as complement, union, intersection, restricted union, restricted intersection etc. for this hybrid structure. Moreover, we developed this theory to establish some more set theoretic operations like Disjunctive sum, difference, product, conjugate etc.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.59-72
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• 2007

In this paper we find the germ of geometric interpretation of complex number in the Euclid Element and try to show the evolution of geometric interpretation of complex number by through Descarte, Wallis, Vessel. As a result, relations and differences between them are found. They related line with complex number and interpreted complex number geometrically by generalizing the multiplication operation.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.1
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• pp.123-130
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• 2016

In this paper, a high-performance arithmetic unit which can efficiently accelerate a number of algorithms for multimedia application was designed. The 3-stage pipelined arithmetic unit can execute 38 operations for complex and fixed-point data by using efficient configuration for four 16-bit by 16-bit multipliers, new sign extension method for carry-save data, and correction constant scheme to eliminate sign-extension in compression operation of multiple partial multiplication results. The arithmetic unit has about 300-MHz operating frequency and about 37,000 gates on 45nm CMOS technology and its estimated performance is 300 MCOPS(Million Complex Operations Per Second). Because the arithmetic unit has high processing rate and supports a number of operations dedicated to various applications, it can be efficiently applicable to multimedia processors.

• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.489-491
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• 1993

Many optimization problem or multiple attribute, multiple alternative decision making problem may have fuzzy evaluation factors. In this case, fuzzy number operation technique is needed to evaluate and compare object functions which become fuzzy sets. Generally, fuzzy number operations can be defined by extension principle of fuzzy set theory, but it is tedious to do fuzzy number operations by using extension principle when the membership functions are defined by complex functions. Many fast methods which approximate the membership functions such as triangle, trapezoidal, or L-R type functions are proposed. In this paper, a fast fuzzy number operation method is proposed which do not simplify the membership functions of fuzzy numbers.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.377-380
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• 1996

Most manufacturing systems are large and complex. It is natural to divide the control into a hierarchy consisting of a number fo different levels. Each levels is characterized by the length of the planning horizon and the kind of data required for the decision making process. This paper describes an approach for the incorporation of Maintenance times into a hierachical scheduling for a failure prone flexible manufacturing system. The Maintenance should not be performed too often because of the resulting reduction of capacity. The machine failure and preventive maintenance are considered simultaneously.

• Journal for History of Mathematics
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• v.15 no.3
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• pp.17-24
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• 2002

It will be described the discovery of fundamental algebras such as complex numbers and the quaternions. Cardano(1539) was the first to introduce special types of complex numbers such as 5$\pm$$\sqrt{-15}$. Girald called the number a$\pm$$\sqrt{-b}$ solutions impossible. The term imaginary numbers was introduced by Descartes(1629) in “Discours la methode, La geometrie.” Euler knew the geometrical representation of complex numbers by points in a plane. Geometrical definitions of the addition and multiplication of complex numbers conceiving as directed line segments in a plane were given by Gauss in 1831. The expression “complex numbers” seems to be Gauss. Hamilton(1843) defined the complex numbers as paire of real numbers subject to conventional rules of addition and multiplication. Cauchy(1874) interpreted the complex numbers as residue classes of polynomials in R[x] modulo $x^2$＋1. Sophus Lie(1880) introduced commutators [a, b] by the way expressing infinitesimal transformation as differential operations. In this paper, it will be studied general quaternion algebras to finding of algebraic structure in Algebras.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.48 no.4
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• pp.61-68
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• 2011

Event-based service technology integrate service to detect events that occur in real time by analyzing the response. Is the core technology for real-time business and ubiquitous service environment construction. Is required event-based service technology on business processes in real-time business environment that providing rapid response to changing and custom service using a variety of information real-time monitoring and analysis in ubiquitous service environment. Last event-driven business processes can be used as a CEP(Complex Event Processing). The core of CEP technology, the event from multiple event sources analysis of events affecting and the way to handle action, is detect complex event to user. In previous studies, an event occurs that continue to perform without the need for partial operations. so many operations and spend a lot of memory is a problem. To solve these problems, event detection technique is proposed that large streams of data without processing any events, registered to configure a complex event occurs when all events in the application layer, complex event processing. The proposed method, first using a bitmap index to manage the event occurs. The complex events of the last event in response to define a trigger event. The occurrence of an event to display a bitmap index, a composite event occurrence of all event to configure the test through the point at which a trigger event occurs. Is proposed, If any event occurs to perform the operation. The proposed scheme perform operations when all event occurs without events having to perform each of the tests. As a result, avoid unnecessary operations and reducing the number of events to handle the increased efficiency of operations.

• Journal of the military operations research society of Korea
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• v.18 no.2
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• pp.114-125
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• 1992

A policy of periodic replacement with minimal repair at failure is considered for a complex system. Under such a policy the system is replaced at periodic times. iT(i=1,2, $\ldots$), while minimal repair is performed at any intervening system failures. The cost of the j-th minimal repair to the component which fails at age t is g(C(t). $c_j$ (t)), where C(t) is the age-dependent random part, $c_j$(t) is the deterministic part which depends on the age and the number of the minimal repair to the component, and g is a positive nondecreasing continuous function. The cost of replacement is expensive when the number of failures occurring in (0. T) is greater than a threshold level. The problem of determining the optimal replacement period, $T^{\ast}$, which minimizes the total expected cost per unit time over an infinite time horizon is considered. Various special cases are considered.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.9
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• pp.3751-3770
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• 2015

Many sorts of image processing software facilitate image editing and also generate a great number of doctored images. Forensic technology emerges to detect the unintentional or malicious image operations. Most of forensic methods focus on the detection of single operations. However, a series of operations may be used to sequentially manipulate an image, which makes the operation detection problem complex. Forensic investigators always want to know as much exhaustive information about a suspicious image's entire processing history as possible. The detection of the operation chain, consisting of a series of operations, is a significant and challenging problem in the research field of forensics. In this paper, based on the histogram distribution uniformity of a manipulated image, we propose an operation chain detection scheme to identify histogram equalization (HE) followed by the dither-like operation (DLO). Two histogram features and a local spatial feature are utilized to further determine which DLO may have been applied. Both theoretical analysis and experimental results verify the effectiveness of our proposed scheme for both global and local scenarios.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.389-394
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• 1996

The product-user interface for consumer electronic products became complex due to the increased variety of functions corresponding to consumer needs. In this study, three types fo design improvement of the menu interface for a video cassette recorder is studied. Three modifications to an existing menu interface was designed using the semantic, the syntactic and the lexical design factors. A series of the validation experiments was performed to test the effect of the three types of task modifications. The results showed that performance time, number of errors and learning effect were improved for all task modification. It also showed that the performance improvement effect of the semantic factors was 8.8%, that of the syntactic factors was 5.9% and that of the lexical factors was 5.6% respectively. It was found out that the performance improvement effect of the semantic design factors were relatively more significant than the syntactic and the lexical design factors.