• International Journal of Fuzzy Logic and Intelligent Systems
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• v.15 no.3
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• pp.208-215
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• 2015

Since upper and lower approximations could be induced from the rough set structures, rough sets are considered as approximations. The concept of fuzzy rough sets was proposed by replacing crisp binary relations with fuzzy relations by Dubois and Prade. In this paper, we introduce and investigate some properties of intuitionistic fuzzy rough approximation operators and intuitionistic fuzzy relations by means of topology.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.34 no.2
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• pp.30-34
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• 2011

Variable precision rough set models have been successfully applied to problems whose domains are discrete values. However, there are many situations where discrete data is not available. When it comes to the problems with interval values, no variable precision rough set model has been proposed. In this paper, we propose a variable precision rough set model for interval values in which classification errors are allowed in determining if two intervals are same. To build the model, we define equivalence class, upper approximation, lower approximation, and boundary region. Then, we check if each of 11 characteristics on approximation that works in Pawlak's rough set model is valid for the proposed model or not.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.81-89
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• 2021

In this paper, we introduce the notions of a distance function, Alexandrov topology and ⊖-upper (⊕-lower) approximation operator based on complete co-residuated lattices. Under various relations, we define (⊕, ⊖)-fuzzy rough set on complete co-residuated lattices. Moreover, we study their properties and give their examples.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.5
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• pp.441-447
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• 2001

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 tole 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.

• The Journal of the Acoustical Society of Korea
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• v.28 no.3
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• pp.174-186
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• 2009

When we apply a propagation model to the ocean with boundaries, we can calculate reflected wave using reflection coefficient suggested by Rayleigh assuming the boundaries are flat. But boundaries in ocean such as sea surface and sea bottom have an irregular rough surface. To calculate the reflection loss for an irregular boundary, it is needed to compute the coherent reflection coefficient based on an experimental formula or scattering theory. In this article, we derive the coherent reflection coefficients for a fluid-fluid interface using perturbation theory, Kirchhoff approximation and small-slope approximation respectively. Based on each formula, we can calculate coherent reflection coefficients for a rough sea surface or sea bottom, and then compare them to the Rayleigh reflection coefficient to analyze the reflection loss for a random rough surface. In general, the coherent reflection coefficient based on small-slope approximation has a wide valid region. Comparing it with the coherent reflection coefficients derived from the Kirchhoff approximation and perturbation theory, we discuss a valid region of them.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.1
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• pp.45-52
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• 1995

A new Kirchhoff approximation(KA) method was proposed for microwave scttering from randomly rough surfaces. Using the spectral representation of delta function and its sifting theorem, a new KA was formulated directly without any further approximation, and this formulated was used to compute exact backscttering coefficients. The validity of the KA was verified by a numerical method, and this new KA technique was used to evaluate the existing approximated KkA methods; i.t., the zeroth-order and the first-order approximated physical optics(PO) models. It was shown that the first-order approximated PO model has small error than the zeroth-order approximated PO model at low incidence angles and the opposite happens at higher incidence angles. This new KA model can be used to compute exact scattering coefficients in the validity regions of KA and to evaluate other theoretical and numerical models for scattering from randomly rough surfaces.

• Korean Journal of Mathematics
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• v.25 no.1
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• pp.71-85
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• 2017

This paper introduces a novel extension of soft rough fuzzy set so-called modified soft rough fuzzy set model in which new lower and upper approximation operators are presented together their related properties that are also investigated. Eventually it is shown that these new models of approximations are finer than previous ones developed by using soft rough fuzzy sets.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1996.10a
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• pp.337-339
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• 1996

In this paper, we construct rough relational database model using approximation concepts of rough set. Also, we analyze the relation between objects, attributes and attribute values and, propose the method that can generate flexible retrieval results.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.1
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• pp.57-65
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• 2014

In this paper, we investigate the properties of L-lower approximation operators as a generalization of fuzzy rough set in complete residuated lattices. We study relations lower (upper, join meet, meet join) approximation operators and Alexandrov L-topologies. Moreover, we give their examples as approximation operators induced by various L-fuzzy relations.

• Journal of the Korea Society of Computer and Information
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• v.1 no.1
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• pp.183-188
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• 1996

Fuzzy sets Introduced by Zadeh is a concept which can process, and reson a vague Information using membership functions. The notion of rough sets introduced by Pawlak is based on the ability to classify. reduce. and perform approximation reasoning for the Indiscernible data.A comparison between fuzzy sets and rough sets has been given In Pawlak where it is shown that these concepts are different and can't combine each other. The purpose of this paper Is to Introduce and define the notion of fuzzy-rough sets which joins the membership function of fuzzy sets to the rough sets.