• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.43-56
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• 1997

In this paper, we introduce a new class of ${\delta}$-frames and study its properties. To do so, we introduce ${\delta}$-filters, almost Lindel$\ddot{o}$f frames and Lindel$\ddot{o}$f frames. First, we show that a complete chain or a complete Boolean algebra is a ${\delta}$-frame. Next, we show that a ${\delta}$-frame L is almost Lindel$\ddot{o}$f iff for any ${\delta}$-filter F in L, ${\vee}\{x^*\;:\;x{\in}F\}{\neq}e$. Last, we show that every regular Lindelof ${\delta}$-frame is normal and a Lindel$\ddot{o}$f ${\delta}$-frame is preserved under a ${\delta}$-isomorphism which is dense and codense.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.569-585
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• 2021

In this paper, we introduce the concept of relative co-fuzzy annihilator filters in distributive lattices. We give a set of equivalent conditions for a co-fuzzy annihilator to be a fuzzy filter and we characterize distributive lattices with the help of co-fuzzy annihilator filters. Furthermore, using the concept of relative co-fuzzy annihilators, we prove that the class of fuzzy filters of distributive lattices forms a Heyting algebra. We also study co-fuzzy annihilator filters. It is proved that the set of all co-fuzzy annihilator filters forms a complete Boolean algebra.

• Proceedings of the KIEE Conference
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• 1979.08a
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• pp.69-72
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• 1979

This paper deals with the computer method of finding the minimal sum of products for a switching function by using the MASK method derived from the characteristics of the Boolean algebra. The experiments with the program which is dissimilar to the previous computer programs show that the algorithm presented will be more efficient.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.121-135
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• 1999

This paper studies the problem of inverting minimal path sets to obtain minimal cut sets for complex system. We describe efficiency of inversion algorithm by the use of boolean algebra and we develop inclusion-exclusion algorithm and pivotal decomposition algorithm for reliability calculation of complex system. Several examples are illustrated and the computation speeds between the two algorithms are undertaken.

• 전기의세계
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• v.28 no.11
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• pp.37-44
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• 1979

This paper deals with the computer program of finding the minimal sum-of-products for a switching function by using the MASK method derived from the characteristics of the Boolean algebra. The approach differs from the previous procedures in that all the prime implicants are determined only by the bit operation and the minimal sum-of-products are obtained by the modified Petrick method in this work. The important features are the relatively small amount of the run time and the less memory capacity to solve a problem, as compared to the previous computer programs.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.5 no.1
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• pp.49-53
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• 1980

Since Zadeh had published the fuzzy set theory at 1965, it has been applied to many fields such as realizability of communication nets, automatic control, learning systems, switching circuits. In this paper, the method of applying a fuzzy logic to a pattern classification is studied and the difference of fuzzy logic from Boolean algebra is discussed. Classfication experiment is carried out 16 persons' photos of three families by fourty male and female observers and recognition rate 94% is obtained.

• Proceedings of the Korea Contents Association Conference
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• 2003.05a
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• pp.406-410
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• 2003

B. M. Schein([1]) considered systems of the form (${\Phi}$; ${\circ}$,-), where ${\Phi}$ is a set of functions closed under the composition "${\circ}$" of functions and the set theoretic subtraction "-". In this structure, (${\Phi}$; ${\circ}$) is a function semigroup and (${\Phi}$;-) is a subtraction algebra in the sense of [1]. He proved that every subtraction semigroup is isomorphic to a difference semigroup of invertible functions. Also this structure is closely related to the mathematical logic, Boolean algebra, Bck-algera, etc. In this paper, we define the near subtraction semigroup as a generalization of the subtraction semigroup, and define the notions of strong for it, and then we will search the general properties of this structure, the properties of ideals, and the application of it.

• Journal of the Korea Society of Computer and Information
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• v.15 no.11
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• pp.215-224
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• 2010

Most chronic diseases are complex diseases which are caused by interactions of several genes. Studies on finding SNPs and gene-gene interactions involved in the development of complex diseases can contribute to prevention and treatment of the diseases. Previous studies mostly concentrate on finding only the set of SNPs involved. In this study we suggest a way to see how these SNPs interact using boolean expressions. The proposed method consists of two stages. In the first stage we find the set of SNPs involved in the development of diseases using mutual information based on entropy. In the second stage we find the highest accuracy boolean expression that consists of the SNP set obtained in the first stage. We experimented with clinical data to demonstrate the effectiveness of the proposed method. We also compared the differences between our method and the previous results on the SNP associations studies.

• Journal of The Korean Association of Information Education
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• v.13 no.3
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• pp.341-349
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• 2009

In this paper, we proposed an Electric Circuit manipulation method to identify easily results of Digital Logic Circuits. Using this method for computer science educations, we can feasibly instruct and understand principles of a Digital Logic Circuit which is a basis of real Digital systems. Furthermore, we developed an PBL-based education program for Digital Logic Circuit concept and Boolean Algebra concept by applying the proposed Electric Circuit manipulation method and by explaining real life Digital Instrument examples. The experimental results are analyzed in views of the problem-solving ability and suitability of allocating degrees of difficulties to the developed Digital Logic Circuit problems.

• Korean Journal of Computational Design and Engineering
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• v.10 no.6
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• pp.432-443
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• 2005

Recent three-dimensional feature-based CAD systems based on solid or non-manifold modelling functionality have been widely used for product design in manufacturing companies. When product models associated with features are used in various downstream applications such as analysis, however, simplified and abstracted models at various levels of detail (LODs) are frequently more desirable and useful than the full detailed model. To provide multi-resolution models, the features need to be rearranged according to a criterion that measures the significance of the feature. However, if the features are rearranged, the resulting shape is possibly different from the original because union and subtraction Boolean operations are not commutative. To solve this problem, in this paper, the new concept of the effective zone of a feature is defined and identified using Boolean algebra. By introducing the effective zone, an arbitrary rearrangement of features becomes possible and arbitrary LOD criteria may be selected to suit various applications. Besides, because the effective zone of a feature is independent of the data structure of the model, the multi-resolution modelling algorithm based on the effective zone can be implemented on any 3D CAD system based on conventional solid representations as well as non-manifold topological (NMT) representations.