• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.635-642
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• 2013

There are many results on the extended operations of two fuzzy numbers based on the Zadeh's extension principle. For the calculation, we have to use existing operations between two ${\alpha}$-cuts. In this paper, we define parametric operations between two ${\alpha}$-cuts which are different from the existing operations. But we have the same results as the extended operations of Zadeh's principle.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.4
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• pp.592-595
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• 2010

The extended algebraic operations are defined by applying the extension principle to normal algebraic operations. And these operations are calculated for some kinds of fuzzy numbers. In this paper, we get exact membership function as a results of calculation of these operations for generalized quadratic fuzzy sets.

• Management Science and Financial Engineering
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• v.7 no.2
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• pp.1-11
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• 2001

Gouveia and Pires (European Journal of Operations Research 112(1999) 134-146) have proposed four extended formulations having precedence variables as extra variables and characterized the projections of three of the four formulations into the natural variable space. In Gouveia and Pires (Discrete Applied Mathematics 112 (2001)), they also have introduced some other extended formulations with the same extra variables and conjectured that the projection of one of the proposed formulations is equivalent to the one proposed by Dantzig, Fulkerson, and Johnson (Operations Research 2(1954) 393-410). In this paper, we provide a unifying framework based on which we give alternative proofs on the projections of three extended formulations and new proofs on those of two formulations appeared in Gouveia and Pires(1999, 2001).

• International Journal of Control, Automation, and Systems
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• v.1 no.4
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• pp.431-443
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• 2003

This paper presents an efficient method to evaluate the performance of an extended stochastic Petri net by simple algebraic operations. The reachability graph is derived from an extended stochastic Petri net, and then converted to a timed stochastic state machine, using a semi-Markov process. The n-th moments of the performance index are derived by algebraic manipulations with each of the n-th moments of transition time and transition probability. For the derivation, three reduction rules are introduced on the transition trajectories in a well-formed regular expression. Efficient computation algorithms are provided to automate the suggested method. The presented method provides a proficient means to derive both the numerical and the symbolic solutions for the performance of an extended stochastic Petri net by simple algebraic manipulations.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.2
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• pp.485-499
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• 2021

Although non-binary low-density parity-check (NB-LDPC) codes have better error-correction capability than that of binary LDPC codes, their decoding complexity is significantly higher. Therefore, it is crucial to reduce the decoding complexity of NB-LDPC while maintaining their error-correction capability to adopt them for various applications. The extended min-sum (EMS) algorithm is widely used for decoding NB-LDPC codes, and it reduces the complexity of check node (CN) operations via message truncation. Herein, we propose a low-cost CN processing method to reduce the complexity of CN operations, which take most of the decoding time. Unlike existing studies on low complexity CN operations, the proposed method employs quick selection algorithm, thereby reducing the hardware complexity and CN operation time. The experimental results show that the proposed selection-based CN operation is more than three times faster and achieves better error-correction performance than the conventional EMS algorithm.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.04a
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• pp.43-43
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• 1995

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1992.04b
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• pp.202-202
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• 1992

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1999.10a
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• pp.169-169
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• 1999

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1991.10a
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• pp.335-335
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• 1991

• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.3
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• pp.1-9
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• 1997

We present an extension of the well-known generalized upper bound (GUB) constraint and consider a linear knapsack problem with both the extended GUB constraints and the simple upper bound (SUB) constraints. An efficient algorithm of order O($n^2log n$) is developed by exploiting structural properties and applying binary search to ordered solution sets, where n is the total number of variables. A numerical example is presented.