• Journal for History of Mathematics
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• v.22 no.4
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• pp.115-128
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• 2009

In this paper, we modify the axiom of infinity of von Neumann's axioms modified by Pinter([5]), and then discuss an existence of an unknowable class in the system and a relationship between the unknowable class and the axiom of choice.

• International Journal of Aerospace System Engineering
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• v.2 no.2
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• pp.73-78
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• 2015

According to the characteristic of carrier-based aircraft, the method of solving safe set during arresting landing is discussed in this paper based on optimal control and invariant set theory. The safe sets of carrier aircraft are evaluated in different states on the characteristic of longitudinal augmented system by using the level set method. Then, the influence on the boundary of safe set under various factors is analyzed. At last, the maneuverability envelope protection is established based on the corresponding theory, and the validity of the system is verified through simulation. The results demonstrate preliminarily that: compared with mass and thrust, the elevator is the greatest influence factor for the boundary of safe set; the dynamic trajectory of carrier-based aircraft can be located at the interior of safe set effectively with the maneuverability envelope protection.

• Annals of Fuzzy Mathematics and Informatics
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• v.16 no.3
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• pp.261-284
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• 2018

In this paper, we recall the definition of soft set, fuzzy soft set, hesitant fuzzy set and hesitant fuzzy soft set and some of their examples. We define the concept of hesitant fuzzy soft multiset which combines hesitant fuzzy soft set and soft multiset theory. We also define basic terms in hesitant fuzzy soft multiset with relevant examples. Some basic operations such as restricted intersection, extended intersection, union, restricted union, AND-product and OR-product and their properties are given, supported with illustrative examples. We finally establish some important results, including De Morgan's inclusions and laws.

• Journal of Information Processing Systems
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• v.12 no.1
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• pp.109-128
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• 2016

This paper presents a new combined forecasting method that is guided by the soft set theory (CFBSS) to predict business failures with different sample sizes. The proposed method combines both qualitative analysis and quantitative analysis to improve forecasting performance. We considered an expert system (ES), logistic regression (LR), and support vector machine (SVM) as forecasting components whose weights are determined by the receiver operating characteristic (ROC) curve. The proposed procedure was applied to real data sets from Chinese listed firms. For performance comparison, single ES, LR, and SVM methods, the combined forecasting method based on equal weights (CFBEWs), the combined forecasting method based on neural networks (CFBNNs), and the combined forecasting method based on rough sets and the D-S theory (CFBRSDS) were also included in the empirical experiment. CFBSS obtains the highest forecasting accuracy and the second-best forecasting stability. The empirical results demonstrate the superior forecasting performance of our method in terms of accuracy and stability.

• Journal of Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.1-8
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• 2023

This study is on a Boolean B or Boolean lattice L in abstract algebra with closed binary operation *, complement and distributive properties. Both Binary operations and logic properties dominate this set. A lattice sheds light on binary operations and other algebraic structures. In particular, the construction of the elements of this L set from idempotent elements, our definition of k-order idempotent has led to the expanded definition of the definition of the lattice theory. In addition, a lattice offers clever solutions to vital problems in life with the concept of logic. The restriction on a lattice is clearly also limit such applications. The flexibility of logical theories adds even more vitality to practices. This is the main theme of the study. Therefore, the properties of the set elements resulting from the binary operation force the logic theory. According to the new definition given, some properties, lemmas and theorems of the lattice theory are examined. Examples of different situations are given.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.1
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• pp.46-51
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• 2007

In this paper, we propose a new data clustering method using local probability and hypothesis theory. To cluster the test data set we analyze the local area of the test data set using local probability distribution and decide the candidate class of the data set using mean standard deviation and variance etc. To decide each class of the test data, statistical hypothesis theory is applied to the decided candidate class of the test data set. For evaluating, the proposed classification method is compared to the conventional fuzzy c-mean method, k-means algorithm and Discriminator analysis algorithm. The simulation results show more accuracy than results of fuzzy c-mean method, k-means algorithm and Discriminator analysis algorithm.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.2
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• pp.82-88
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• 1999

In this paper, we propose a new structure optimization method of multilayer neural networks which begin and carry out learning from a bigger network. This method redundant links and neurons according to the rough set theory. In order to find redundant links, we analyze the variations of all weights and output errors in every step of the learning process, and then make the decision table from their variation of weights and output errors. We can find the redundant links from the initial structure by analyzing the decision table using the rough set theory. This enables us to build a structure as compact as possible, and also enables mapping between input and output. We show the validity and effectiveness of the proposed algorithm by applying it to the XOR problem.

• Proceedings of the KIEE Conference
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• 2002.11c
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• pp.333-336
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• 2002

In many cases, fuzzy modeling has a defect that the design procedure cannot be theoretically justified. To overcome this difficulty, we suggest a new design method for fuzzy model by combining genetic algorithm(GA) and mush set theory. GA, which has the advantages is optimization, and rule base. However, it is some what time consuming, so are introduce rough set theory to the rule reduction procedure. As a result, the decrease of learning time and the considerable rate of rule reduction is achieved without loss of useful information. The preposed algorithm is composed of three stages; First stage is quasi-optimization of fuzzy model using GA(coarse tuning). Next the obtained rule base is reduced by rough set concept(rule reduction). Finally we perform re-optimization of the membership functions by GA(fine tuning). To check the effectiveness of the suggested algorithm, examples for time series prediction are examined.

• Proceedings of the KIEE Conference
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• 1998.07g
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• pp.2222-2224
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• 1998

This paper presents a 3D feature extraction method using rough set theory. Using the stereo cameras, we obtain the raw images and then perform several processes including gradient computation and image matching process. Decision rule constructed via rough set theory determines whether a ceratin point in the image is 3D edge or not. We propose a method finding rules for 3D edge extraction using rough set.

• The Korean Journal of Community Living Science
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• v.15 no.4
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• pp.45-60
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• 2004

The purpose of this study was to set related variables for leadership measurement in the leader of a community organization as an effort to Community development constantly. Therefore, in this study, first, various theories on leadership were reviewed. Second, approaches and variable relationships were reviewed by leadership theory study. Third, leadership measurement variables were set based on Bass's Transformational theory, one of new trend theory, to measure the leadership of the community organization leader. As a follow up, clear and scientific analysis, through empirical analysis, based on the variables set in this study will be made to measure leadership of a community organization after creating investigation tools based on the variables set in this study A literature study was mainly used. 'Human Behavior' by Dr Han-geom Lee, 'Leadership Theory' by Eung-seop Shin, many other related books, articles of the Human Relation Organization Association, and theses and Bass's writings. Major findings of this study, through the literature study, were as follows. As conventional leadership theories, characteristics theory, behavior theory and situational leadership theory were proposed. First, characteristics theory searches the characteristics of an effective leader. It proposes that effective leaders and ineffective leaders have different characteristics, respectively. Therefore, it proposes to study the leader's characteristics. However, there is not a flexed definition for leader's characteristics. Scholars make different definition on leader's characteristics, and they are very subjective. Thus it cannot be a valid theory. Second, behavior theory describes how the leader behaves to his fellows. It studies leader's behavior focusing on what type and what combination is the most effective in all situations. However, it has weakness in that it focuses on a leader's behavior only, and ignores the situational features. Third, situational theory describes the relationship between leadership type and situation. It suggests that there is not a single leadership style that can suit all situations. It emphasizes the relationship between leadership type and situation. Although situational theory considers more variables than characteristics theory or behavior theory, it also sees situations as static and flxed. Although Fiedler's theory tried to comply with situations, he did not analyze interactions between a leader and his fellows.