• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.549-562
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• 2015

In this paper we introduce the pointfree version of rough sets. For this we consider a lattice L instead of the power set P(X) of a set X. We study the properties of lower and upper pointfree approximation, precise elements, and their relation with prime elements. Also, we study lower and upper pointfree approximation as a Galois connection, and discuss the relations between partitions and Galois connections.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.653-664
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• 2006

As a generalization of ideals in subtraction algebras, the notion of rough ideals is discussed.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.288-295
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• 1998

This paper proposes a new data classification method based on the tolerant rough set that extends the existing equivalent rough set. Similarity measure between two data is described by a distance function of all constituent attributes and they are defined to be tolerant when their similarity measure exceeds a similarity threshold value. The determination of optimal similarity theshold value is very important for the accurate classification. So, we determine it optimally by using the genetic algorithm (GA), where the goal of evolution is to balance two requirements such that (1) some tolerant objects are required to be included in the same class as many as possible. After finding the optimal similarity threshold value, a tolerant set of each object is obtained and the data set is grounded into the lower and upper approximation set depending on the coincidence of their classes. We propose a two-stage classification method that all data are classified by using the lower approxi ation at the first stage and then the non-classified data at the first stage are classified again by using the rough membership functions obtained from the upper approximation set. We apply the proposed classification method to the handwritten numeral character classification. problem and compare its classification performance and learning time with those of the feed forward neural network's back propagation algorithm.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.11a
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• pp.243-251
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• 2000

In general, Rough Set theory is used for classification, inference, and decision analysis of incomplete data by using approximation space concepts in information system. Information system can include quantitative attribute values which have interval characteristics, or incomplete data such as multiple or unknown(missing) data. These incomplete data cause the inconsistency in information system and decrease the classification ability in system using Rough Sets. In this paper, we present various types of incomplete data which may occur in information system and propose INcomplete information Processing System(INiPS) which converts incomplete information system into complete information system in using Rough Sets.

• Annals of Fuzzy Mathematics and Informatics
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• v.16 no.3
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• pp.337-361
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• 2018

We introduce and study some basic properties of rough $I_{\lambda}$-statistical convergent of weight g (A), where $g:{\mathbb{N}}^3{\rightarrow}[0,\;{\infty})$ is a function statisying $g(m,\;n,\;k){\rightarrow}{\infty}$ and $g(m,\;n,\;k){\not{\rightarrow}}0$ as $m,\;n,\;k{\rightarrow}{\infty}$ and A represent the RH-regular matrix and also prove the Korovkin approximation theorem by using the notion of weighted A-statistical convergence of weight g (A) limits of a triple sequence of Bernstein-Stancu polynomials.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.551-562
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• 2007

This paper concerns a relationship between rough sets, intuitionistic fuzzy sets and ring theory. We consider a ring as a universal set and we assume that the knowledge about objects is restricted by an intuitionistic fuzzy ideal. We apply the notion of intutionistic fuzzy ideal of a ring for definitions of the lower and upper approximations in a ring. Some properties of the lower and upper approximations are investigated.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.3
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• pp.222-230
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• 2014

In this paper, we investigate the properties of join and meet preserving maps in complete residuated lattice using Zhang's the fuzzy complete lattice which is defined by join and meet on fuzzy posets. We define L-upper (resp. L-lower) approximation operators as a generalization of fuzzy rough sets in complete residuated lattices. Moreover, we investigate the relations between L-upper (resp. L-lower) approximation operators and L-fuzzy preorders. We study various L-fuzzy preorders on $L^X$. They are considered as an important mathematical tool for algebraic structure of fuzzy contexts.

• Journal of Biomedical Engineering Research
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• v.32 no.2
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• pp.134-143
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• 2011

The selection of meaningful clinical tests and its reference values from a high-dimensional clinical data with imbalanced class distribution, one class is represented by a large number of examples while the other is represented by only a few, is an important issue for differential diagnosis between similar diseases, but difficult. For this purpose, this study introduces methods based on the concepts of both discernibility matrix and function in rough set theory (RST) with two discretization approaches, equal width and frequency discretization. Here these discretization approaches are used to define the reference values for clinical tests, and the discernibility matrix and function are used to extract a subset of significant clinical tests from the translated nominal attribute values. To show its applicability in the differential diagnosis problem, we have applied it to extract the significant clinical tests and its reference values between normal (N = 351) and abnormal group (N = 101) with either cholecystitis or cholelithiasis disease. In addition, we investigated not only the selected significant clinical tests and the variations of its reference values, but also the average predictive accuracies on four evaluation criteria, i.e., accuracy, sensitivity, specificity, and geometric mean, during l0-fold cross validation. From the experimental results, we confirmed that two discretization approaches based rough set approximation methods with relative frequency give better results than those with absolute frequency, in the evaluation criteria (i.e., average geometric mean). Thus it shows that the prediction model using relative frequency can be used effectively in classification and prediction problems of the clinical data with imbalanced class distribution.

• The Transactions of the Korea Information Processing Society
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• v.5 no.1
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• pp.103-110
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• 1998

In case of traditional Rule-Based Reasoning(RBR) and Case-Based Reasoning(CBR), although knowledge is reasoned either by one of them or by the integration of RBR and CBR, there is a problem that much time should be consumed by numerous rules and cases. In order to improve this time-consuming problem, in this paper, a new type of reasoning technique, which is a kind of integration of reduced RB and CB, is to be introduced. Such a new type of reasoning uses Rough Set, by which we can represent multi-meaning and/or random knowledge easily. In Rough Set, solution is to be obtained by its own complementary rules, using the process of RB and CB into equivalence class by the classification and approximation of Rough Set. and then using reduced RB and CB through the integrated reasoning.

• Journal of Digital Convergence
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• v.11 no.11
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• pp.343-349
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• 2013

Rough set theory comes to derive optimal rules through the effective selection of features from the redundancy of lots of information in data mining using the concept of equivalence relation and approximation space in rough set. The reduction of attributes is one of the most important parts in its applications of rough set. This paper purports to define a information-theoretic measure for determining the most important attribute within the association of attributes using rough entropy. The proposed method generates the effective reduct set and formulates the core of the attribute set through the elimination of the redundant attributes. Subsequently, the control rules are generated with a subset of feature which retain the accuracy of the original features through the reduction.