• Journal of the Korean Society for information Management
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• v.12 no.1
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• pp.87-97
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• 1995

Boolean retrieval systems have been most widely used in the area of information retrieval due to easy implementation and efficient retrieval. Conventional Boolean retrieval systems. however, cannot rank retrieved documents in decreasing order of query-document similarities because they cannot compute similarity coefficients between queries and documents. Extended Boolean models such as fuzzy set. Waller-Kraft, Paice, P-Norm and Infinite-One have been developed to provide the document ranking facility. In extended Boolean models, the formulas evaluating Boolean operators AND and OR are an important component to affect the quality of document ranking. In this paper we present mathematical properties of the formulas, and analyse their effect on retrieval effectiveness. Our analyses show that P-Norm is the most suitable for achieving high retrieval effectiveness.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1525-1532
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• 2011

The $m{\times}n$ Boolean matrix A is said to be of Boolean rank r if there exist $m{\times}r$ Boolean matrix B and $r{\times}n$ Boolean matrix C such that A = BC and r is the smallest positive integer that such a factorization exists. We consider the the sets of matrix ordered pairs which satisfy extremal properties with respect to Boolean rank inequalities of matrices over nonbinary Boolean algebra. We characterize linear operators that preserve these sets of matrix ordered pairs as the form of $T(X)=PXP^T$ with some permutation matrix P.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.77-86
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• 2006

We consider the set of commuting pairs of matrices and their preservers over binary Boolean algebra, chain semiring and general Boolean algebra. We characterize those linear operators that preserve the set of commuting pairs of matrices over a general Boolean algebra and a chain semiring.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.169-178
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• 2007

We consider the set of $n{\times}n$ idempotent matrices and we characterize the linear operators that preserve idempotent matrices over Boolean algebras. We also obtain characterizations of linear operators that preserve idempotent matrices over a chain semiring, the nonnegative integers and the nonnegative reals.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.507-521
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• 2019

For any $m{\times}n$ nonbinary Boolean matrix A, its spanning column rank is the minimum number of the columns of A that spans its column space. We have a characterization of spanning column rank-1 nonbinary Boolean matrices. We investigate the linear operators that preserve the spanning column ranks of matrices over the nonbinary Boolean algebra. That is, for a linear operator T on $m{\times}n$ nonbinary Boolean matrices, it preserves all spanning column ranks if and only if there exist an invertible nonbinary Boolean matrix P of order m and a permutation matrix Q of order n such that T(A) = PAQ for all $m{\times}n$ nonbinary Boolean matrix A. We also obtain other characterizations of the (spanning) column rank preserver.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.113-123
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• 2014

The term rank of a matrix A over a semiring $\mathcal{S}$ is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we characterize linear operators that preserve the sets of matrix ordered pairs which satisfy extremal properties with respect to term rank inequalities of matrices over nonbinary Boolean semirings.

• Korean Journal of Computational Design and Engineering
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• v.5 no.4
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• pp.293-300
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• 2000

The non-manifold geometric modeling technique is to improve design process and to Integrate design, analysis, and manufacturing by handling mixture of wireframe model, surface model, and solid model in a single data structure. For the non-manifold geometric modeling, Euler operators and other high level modeling methods are necessary. Boolean operation is one of the representative modeling method for the non-manifold geometric modeling. This thesis studies Boolean operations of non-manifold model with the data structure of selective storage. The data structure of selective storage is improved non-manifold data structure in that existing non-manifold data structures using ordered topological representation method always store non-manifold information even if edges and vortices are in the manifold situation. To implement Boolean operations for non-manifold model, intersection algorithm for topological cells of three different dimensions, merging and selection algorithm for three dimensional model, and Open Inventor(tm), a 3D toolkit from SGI, are used.

• Journal of KIISE:Software and Applications
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• v.26 no.10
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• pp.1219-1229
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• 1999

일반적으로 AND, OR, NOT과 같은 연산자를 사용하는 불리언 질의는 사용자의 검색의도를 정확하게 표현할 수 있기 때문에 검색 전문가들은 불리언 질의를 사용하여 높은 검색성능을 얻는다고 알려져 있지만, 일반 사용자는 자신이 원하는 정보를 불리언 형태로 표현하는데 익숙하지 않다. 본 논문에서는 검색성능의 향상과 사용자 편의성을 동시에 만족하기 위하여 사용자의 자연어 질의를 확장 불리언 질의로 자동 변환하는 방법론을 제안한다. 먼저 자연어 질의를 범주문법에 기반한 구문분석을 수행하여 구문트리를 생성하고 연산자 및 키워드 정보를 추출하여 구문트리를 간략화한다. 다음으로 간략화된 구문트리로부터 명사구를 합성하고 키워드들에 대한 가중치를 부여한 후 불리언 질의를 생성하여 검색을 수행한다. 또한 구문분석의 오류로 인한 검색성능 저하를 최소화하기 위하여 상위 N개 구문트리에 대해 각각 불리언 질의를 생성하여 검색하는 N-BEST average 방법을 제안하였다. 정보검색 실험용 데이타 모음인 KTSET2.0으로 실험한 결과 제안된 방법은 수동으로 추출한 불리언 질의보다 8% 더 우수한 성능을 보였고, 기존의 벡터공간 모델에 기반한 자연어질의 시스템에 비해 23% 성능향상을 보였다. Abstract There have been a considerable evidence that trained users can achieve a good search effectiveness through a boolean query because a structural boolean query containing operators such as AND, OR, and NOT can make a more accurate representation of user's information need. However, it is not easy for ordinary users to construct a boolean query using appropriate boolean operators. In this paper, we propose a boolean query formulation method that automatically transforms a user's natural language query into a extended boolean query for both effectiveness and user convenience. First, a user's natural language query is syntactically analyzed using KCCG(Korean Combinatory Categorial Grammar) parser and resulting syntactic trees are structurally simplified using a tree-simplifying mechanism in order to catch the logical relationships between keywords. Next, in a simplified tree, plausible noun phrases are identified and added into the same tree as new additional keywords. Finally, a simplified syntactic tree is automatically converted into a boolean query using some mapping rules and linguistic heuristics. We also propose an N-BEST average method that uses top N syntactic trees to compensate for bad effects of single incorrect top syntactic tree. In experiments using KTSET2.0, we showed that a proposed method outperformed a traditional vector space model by 23%, and surprisingly manually constructed boolean queries by 8%.

• Korean Journal of Computational Design and Engineering
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• v.11 no.4
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• pp.235-245
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• 2006

This paper proposes a CSG-based representation scheme for heterogeneous objects including multi-material objects and Functionally Graded Materials (FGMs). In particular, this scheme focuses on the construction of complicated heterogeneous objects guaranteeing desired material continuities at all the interfaces. In order to create various types of heterogeneous primitives, we first describe methods for specifying material composition functions such as geometry-independent, geometry-dependent functions. Constructive Material Composition (CMC) and corresponding heterogeneous Boolean Operators (e.g. material union, difference, intersection. and partition) are then proposed to illustrate how material continuities are dealt with. Finally, we describe the model hierarchy and data structure for computer representation. Even though the proposed scheme alone is sufficient for modeling all sorts of heterogeneous objects, the proposed scheme adopts a hybrid representation between CSG and decomposition. That is because hybrid representation can avoid the unnecessary growth of binary trees.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.251-268
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• 2020

In this paper, we estimate the degree of approximation by means of the complete modulus of continuity, the partial modulus of continuity, the Lipschitz-type class and Petree's K-functional for the bivariate Szász-Kantorovich operators based on Brenke-type polynomials. Later, we construct Generalized Boolean Sum operators associated with combinations of the Szász-Kantorovich operators based on Brenke-type polynomials. In addition, we obtain the rate of convergence for the GBS operators with the help of the mixed modulus of continuity and the Lipschitz class of the Bögel continuous functions.