Idealization of j-approximation spaces

The current work concentrates on generating different topologies by using the concept of the ideal. These topologies are used to make more thorough studies on generalized rough set theory. The rough set theory was first proposed by Pawlak in 1982. Its core concept is upper and lower approximations. The principal goal of the rough set theory is reducing the vagueness of a concept to uncertainty areas at their borders by increasing the lower approximation and decreasing the upper approximation. For the mentioned goal, different methods based on ideals are proposed to achieve this aim. These methods are more accurate than the previous methods. Hence it is very interesting in rough set context for removing the vagueness (uncertainty).

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Seleksi Fitur Pada Klasifikasi Multi-label Menggunakan Proportional Feature Rough Selector

JATISI (Jurnal Teknik Informatika dan Sistem Informasi) ◽

10.35957/jatisi.v8i4.1259 ◽

2021 ◽

Vol 8 (4) ◽

pp. 2084-2094

Author(s):

Vilat Sasax Mandala Putra Paryoko

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Set Theory ◽

Boundary Region ◽

Lower Approximation ◽

Upper Approximation ◽

Tv Shows

Proportional Feature Rough Selector (PFRS) merupakan sebuah metode seleksi fitur yang dikembangkan berdasarkan Rough Set Theory (RST). Pengembangan ini dilakukan dengan merinci pembagian wilayah dalam set data menjadi beberapa bagian penting yaitu lower approximation, upper approximation dan boundary region. PFRS memanfaatkan boundary region untuk menemukan wilayah yang lebih kecil yaitu Member Section (MS) dan Non-Member Section (NMS). Namun PFRS masih hanya digunakan dalam seleksi fitur pada klasifikasi biner dengan tipe data teks. PFRS ini juga dikembangkan tanpa memperhatikan hubungan antar fitur, sehingga PFRS memiliki potensi untuk ditingkatkan dengan mempertimbangkan korelasi antar fitur dalam set data. Untuk itu, penelitian ini bertujuan untuk melakukan penyesuaian PFRS untuk bisa diterapkan pada klasifikasi multi-label dengan data campuran yakni data teks dan data bukan teks serta mempertimbangkan korelasi antar fitur untuk meningkatkan performa klasifikasi multi-label. Pengujian dilakukan pada set data publik yaitu 515k Hotel Reviews dan Netflix TV Shows. Set data ini diuji dengan menggunakan empat metode klasifikasi yaitu DT, KNN, NB dan SVM. Penelitian ini membandingkan penerapan seleksi fitur PFRS pada data multi-label dengan pengembangan PFRS yaitu dengan mempertimbangkan korelasi. Hasil penelitian menunjukkan bahwa penggunaan PFRS berhasil meningkatkan performa klasifikasi. Dengan mempertimbangkan korelasi, PFRS menghasilkan peningkatan akurasi hingga 23,76%. Pengembangan PFRS juga menunjukkan peningkatan kecepatan yang signifikan pada semua metode klasifikasi sehingga pengembangan PFRS dengan mempertimbangkan korelasi mampu memberikan kontribusi dalam meningkatkan performa klasifikasi.

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δβ-I APPROXIMATION SPACES

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi1702163r ◽

2017 ◽

pp. 163

Author(s):

A. E. Radwan ◽

Rodyna A. Hosny ◽

A. M. Abd El-latif

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Set Theory ◽

Approximation Spaces ◽

Upper Approximation ◽

Basic Properties

In this paper, we generalize rough set theory by introducing concepts of δβ-I lower and δβ-I -upper approximation for any ideal I on X which depends on the concept δβ-I -open sets. Some of their basic properties with the help of examples are investigated and the interrelation between them are obtained. Also, the connections between the rough approximations de_ned in [2] and our new approximations are studied.

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Rough Hyperfilters in Po-LA-Semihypergroups

Discrete Dynamics in Nature and Society ◽

10.1155/2019/8326124 ◽

2019 ◽

Vol 2019 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Ferdaous Bouaziz ◽

Naveed Yaqoob

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Set Theory ◽

Lower Approximation ◽

Upper Approximation

This paper concerns the study of hyperfilters of ordered LA-semihypergroups, and presents some examples in this respect. Furthermore, we study the combination of rough set theory and hyperfilters of an ordered LA-semihypergroup. We define the concept of rough hyperfilters and provide useful examples on it. A rough hyperfilter is a novel extension of hyperfilter of an ordered LA-semihypergroup. We prove that the lower approximation of a left (resp., right, bi) hyperfilter of an ordered LA-semihypergroup becomes left (resp., right, bi) hyperfilter of an ordered LA-semihypergroup. Similarly we prove it for upper approximation.

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Implementation of Lower and Upper Approximation features of rough set theory on FPGA

10.1109/icccnt51525.2021.9579822 ◽

2021 ◽

Author(s):

Shubham Tonde ◽

Vanita Agarwal

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Set Theory ◽

Upper Approximation

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Topologies of Approximation Spaces of Rough Set Theory

Advances in Soft Computing - Interval / Probabilistic Uncertainty and Non-Classical Logics ◽

10.1007/978-3-540-77664-2_14 ◽

2008 ◽

pp. 176-186 ◽

Cited By ~ 1

Author(s):

Milan Vlach

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Set Theory ◽

Approximation Spaces

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Covering-Based Rough Sets on Eulerian Matroids

Journal of Applied Mathematics ◽

10.1155/2013/254797 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 8

Author(s):

Bin Yang ◽

Ziqiong Lin ◽

William Zhu

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

Closure Operator ◽

Matroid Theory ◽

Upper Approximation ◽

Significant Generalization ◽

Eulerian Matroid ◽

Vital Structure

Rough set theory is an efficient and essential tool for dealing with vagueness and granularity in information systems. Covering-based rough set theory is proposed as a significant generalization of classical rough sets. Matroid theory is a vital structure with high applicability and borrows extensively from linear algebra and graph theory. In this paper, one type of covering-based approximations is studied from the viewpoint of Eulerian matroids. First, we explore the circuits of an Eulerian matroid from the perspective of coverings. Second, this type of covering-based approximations is represented by the circuits of Eulerian matroids. Moreover, the conditions under which the covering-based upper approximation operator is the closure operator of a matroid are presented. Finally, a matroidal structure of covering-based rough sets is constructed. These results show many potential connections between covering-based rough sets and matroids.

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Model of Covering Rough Sets in the Machine Intelligence

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.548.735 ◽

2012 ◽

Vol 548 ◽

pp. 735-739

Author(s):

Hong Mei Nie ◽

Jia Qing Zhou

Keyword(s):

Information Systems ◽

Set Theory ◽

Rough Set ◽

Equivalence Relation ◽

Rough Sets ◽

Rough Set Theory ◽

Machine Intelligence ◽

Upper Approximation ◽

Generalized Rough Sets

Rough set theory has been proposed by Pawlak as a useful tool for dealing with the vagueness and granularity in information systems. Classical rough set theory is based on equivalence relation. The covering rough sets are an improvement of Pawlak rough set to deal with complex practical problems which the latter one can not handle. This paper studies covering-based generalized rough sets. In this setting, we investigate common properties of classical lower and upper approximation operations hold for the covering-based lower and upper approximation operations and relationships among some type of covering rough sets.

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ON ATTRIBUTE REDUCTION WITH INTUITIONISTIC FUZZY ROUGH SETS

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488512500043 ◽

2012 ◽

Vol 20 (01) ◽

pp. 59-76 ◽

Cited By ~ 3

Author(s):

ZHIMING ZHANG ◽

JINGFENG TIAN

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

Theoretical Foundation ◽

Attribute Reduction ◽

Upper Approximation ◽

Intuitionistic Fuzzy ◽

Intuitionistic Fuzzy Rough Sets ◽

Axiomatic Approaches

Intuitionistic fuzzy (IF) rough sets are the generalization of traditional rough sets obtained by combining the IF set theory and the rough set theory. The existing research on IF rough sets mainly concentrates on the establishment of lower and upper approximation operators using constructive and axiomatic approaches. Less effort has been put on the attribute reduction of databases based on IF rough sets. This paper systematically studies attribute reduction based on IF rough sets. Firstly, attribute reduction with traditional rough sets and some concepts of IF rough sets are reviewed. Then, we introduce some concepts and theorems of attribute reduction with IF rough sets, and completely investigate the structure of attribute reduction. Employing the discernibility matrix approach, an algorithm to find all attribute reductions is also presented. Finally, an example is proposed to illustrate our idea and method. Altogether, these findings lay a solid theoretical foundation for attribute reduction based on IF rough sets.

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Topological properties of a pair of relation-based approximation operators

Filomat ◽

10.2298/fil1719175z ◽

2017 ◽

Vol 31 (19) ◽

pp. 6175-6183

Author(s):

Yan-Lan Zhang ◽

Chang-Qing Li

Keyword(s):

Data Mining ◽

Set Theory ◽

Rough Set ◽

Rough Set Theory ◽

Equivalence Relations ◽

Topological Properties ◽

Upper Approximation ◽

Approximation Operators ◽

Rough Approximation ◽

Basic Concepts

Rough set theory is an important tool for data mining. Lower and upper approximation operators are two important basic concepts in the rough set theory. The classical Pawlak rough approximation operators are based on equivalence relations and have been extended to relation-based generalized rough approximation operators. This paper presents topological properties of a pair of relation-based generalized rough approximation operators. A topology is induced by the pair of generalized rough approximation operators from an inverse serial relation. Then, connectedness, countability, separation property and Lindel?f property of the topological space are discussed. The results are not only beneficial to obtain more properties of the pair of approximation operators, but also have theoretical and actual significance to general topology.

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Application of Rough Set Theory in Stochastic Fatigue Analysis of Vehicle Frame

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.430-432.1814 ◽

2012 ◽

Vol 430-432 ◽

pp. 1814-1817

Author(s):

Li Hui Zhao ◽

Chang Hong Liu

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Set Theory ◽

Random Variable ◽

Fatigue Analysis ◽

Random Parameters ◽

Lower Approximation ◽

A Value ◽

Interval Operation ◽

Confidence Degree

Considering the up-down deflection of vehicle frame as a random variable when a car runs unsteadily, the alternating stress cased by deflection is random. The probability density function is determined by date of the alternating stress acting on the frame. Using the concepts of upper and lower approximation in the rough set theory and confidence degree, random parameters of vehicle frame can be transferred into certain interval values. When the confidence degree took a value from 0 to 1, a series of intervals between the upper and lower approximation are determined respectively. With the algorithm of the interval operation, a method of fatigue analysis is put forward.

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