• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.2
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• pp.141-147
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• 2007

We consider a GI/M/1 queue with vacations such that the server works with different rate rather than completely stops working during a vacation period. We derive the transform of the joint distribution of the length of a busy period, the number of customers served during the busy period, and the length of the subsequent idle period.

• 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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.2
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• pp.428-431
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• 2007

A floating-point number system is used to represent a wide range of real numbers using finite number of bits. The standard the IEEE adopted in 1987 divides the range of real numbers into intervals of [$2^E,2^{E+1}$), where E is an Integer represented with finite bits, and defines equally spaced equal counts of discrete numbers in each interval. Since the numbers are defined discretely, not only the number representation itself includes errors but in floating-point arithmetic some strange behaviors are observed which cannot be agreed with the real world arithmetic. In this paper errors with floating-point number representation, those with arithmetic operations, and those due to order of arithmetic operations are analyzed theoretically with help of and verification with the results of some MATLAB program executions.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.10a
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• pp.27-30
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• 1996

Determination of input variables for artificial neural network (ANN) depends entirely on the judgement of a modeller. As the number of input variables increases, the training time for the resulting ANN increases exponentially. Moreover, larger number of input variables does not guarantee better performance. In this research, we employ Genetic Algorithm for selecting proper input variables that yield the best performance in training the resulting ANN.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.513-520
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• 2005

We calculate the normal fuzzy probability for trigonometric fuzzy numbers defined by trigonometric functions. And we study the normal probability for some operations of two trigonometric fuzzy numbers. Furthermore, we calculate the normal fuzzy probability for some fuzzy numbers generated by operations.

• Journal of the military operations research society of Korea
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• v.6 no.1
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• pp.119-124
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• 1980

An efficient algorithm which can be employed in obtaining the minimal cut sets of a fault tree containing repeated events is introduced. A sample fault tree illustrates this algorithm. Efficiency of an algorithm is defined as the ratio of the number of minimal cut sets to the number of cut sets determined by the algorithm. An efficiency of the proposed algorithm is compared with those of two existing algorithms : Fussell and Vesely's algorithm and Bengiamin et al. 's algorithm. The proposed algorithm is shown to be more efficient than the existing two algorithms.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.97-115
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• 2008

In high school mathematics class, to subtract a number b from a, we add the additive inverse of b to a and to divide a number a by a non-zero number b, we multiply a by the multiplicative inverse of b, which is the formal approach for operations of real numbers. This article aims to give a connection between the intuitive models in middle school mathematics class and the formal approach in high school for teaching operations of negative integers. First, we highlight the teaching methods(Hwang et al, 2008), by which subtraction of integers is denoted by addition of integers. From this methods and activities applying the counting model, we give new teaching methods for the rule that the product of negative integers is positive. The teaching methods with horizontal mathematization(Treffers, 1986; Freudenthal, 1991) of operations of integers, which is based on consistently applying the intuitive model(number line model, counting model), will remove the gap, which is exist in both teachers and students of middle and high school mathematics class. The above discussion is based on students' cognition that the number system in middle and high school and abstracted number system in abstract algebra course is formed by a conceptual structure.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.2
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• pp.217-228
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• 1994

This paper presents a new integer formulation (Type III ALB) for a single model assembly line balancing problem. The objective of the formulation is to minimize the total idle time, which is defined as the product of the number of work stations and the cycle times minus the total work content. This formulation considers currently existing Type I (minimizing the number of work stations for a given cycle time) and type II (minimizing the cycle time for a given number of work stations) formulations as its special cases and provides the global minimum solutions of the cycle time and the number of work stations. This information would be of great value to line designers involved in designing new assembly lines and rebalancing old lines under flexible conditions. Solution methods based on combination of Type I and Type II approaches are also suggested and compared.

• Journal of the Korean Operations Research and Management Science Society
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• v.31 no.1
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• pp.1-13
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• 2006

In this paper we consider a design problem of a cyclic queueing network with two stages, each with a local buffer of limited capacity. Based on the theory of reversibility and product-form solution, we derive the throughput function of the network as a key performance measure to maximize. Two cases are considered. In case each stage consists of a single server, an optimal allocation policy of a given buffer capacity and work load between stages as well as the optimal number of customers is identified by exploiting the properties of the throughput function. In case each stage consists of multiple servers, the optimal policy developed for the single server case doesn't hold any more and an algorithm is developed to allocate with a small number of computations a given number of servers, buffer capacity as well as total work load and the total number of customers. The differences of the optimal policies between two cases and the implications of the results are also discussed. The results can be applied to support the design of certain manufacturing and computer/communication systems.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.629-638
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• 2005

In this paper, we consider two issues in collaborative filtering, which are closely related with the number of ratings of a user. First issue is the relationship between the number of ratings of a user and the performance of collaborative filtering. The relationship is investigated with two datasets, EachMovie and Movielens datasets. The number of ratings of a user is critical when the number of ratings is small, but after the number is over a certain threshold, its influence on recommendation performance becomes smaller. We also provide an explanation on the relationship between the number of ratings of a user and the performance in terms of neighborhood formations in collaborative filtering. The second issue is how to select an initial product list for new users for gaining user responses. We suggest and analyze 14 selection strategies which include popularity, favorite, clustering, genre, and entropy methods. Popularity methods are adequate for getting higher number of ratings from users, and favorite methods are good for higher average preference ratings of users.