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

2021 ◽  
Author(s):  
Shubham Tonde ◽  
Vanita Agarwal
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Upper Approximation

scholarly journals Covering-Based Rough Sets on Eulerian Matroids

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
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.

Model of Covering Rough Sets in the Machine Intelligence

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.

ON ATTRIBUTE REDUCTION WITH INTUITIONISTIC FUZZY ROUGH SETS

2012 ◽  
Vol 20 (01) ◽  
pp. 59-76 ◽  
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.

scholarly journals Topological properties of a pair of relation-based approximation operators

Filomat ◽  
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.

scholarly journals Rough Set Theory and its Applications: A recent Survey

2020 ◽  
pp. 548-552
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Intelligent Agents ◽  
Rough Set Theory ◽  
Boundary Region ◽  
Process Industry ◽  
Decision Making Process ◽  
Upper Approximation ◽  
Analysis Process ◽  
The Universe

Rough set theory is a mathematical method proposed by Pawlak . Rough set theory has been developed to manage uncertainties in information that presents missing and noises. Rough set theory is an expansion of the conventional set theory that supports approximations in decision making process. Fundamental of assumption of rough set theory is that with every object of the universe has some information associated it. Rough set theory is correlate two crisp sets, called lower and upper approximation. The lower approximation of a set consists of all elements that surely belong to the set, and the upper approximation of the set constitutes of all elements that possibly belong to the set. The boundary region of the set consists of all elements that cannot be classified uniquely as belonging to the set or as belonging to its complement, with respect to the available knowledge Rough sets are applied in several domains, such as, pattern recognition, medicine, finance, intelligent agents, telecommunication, control theory ,vibration analysis, conflict resolution, image analysis, process industry, marketing, banking risk assessment etc. This paper gives detail survey of rough set theory and its properties and various applications of rough set theory.

scholarly journals Idealization of j-approximation spaces

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 287-301
Author(s):  
Mona Hosny
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Current Work ◽  
Core Concept ◽  
Approximation Spaces ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Generalized Rough Set ◽  
The Ideal

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).

scholarly journals Multigranulations Rough Set Method of Attribute Reduction in Information Systems Based on Evidence Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Minlun Yan
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Attribute Reduction ◽  
Decision Rules ◽  
Evidence Theory ◽  
Point Of View ◽  
Upper Approximation

Attribute reduction is one of the most important problems in rough set theory. However, from the granular computing point of view, the classical rough set theory is based on a single granulation. It is necessary to study the issue of attribute reduction based on multigranulations rough set. To acquire brief decision rules from information systems, this paper firstly investigates attribute reductions by combining the multigranulations rough set together with evidence theory. Concepts of belief and plausibility consistent set are proposed, and some important properties are addressed by the view of the optimistic and pessimistic multigranulations rough set. What is more, the multigranulations method of the belief and plausibility reductions is constructed in the paper. It is proved that a set is an optimistic (pessimistic) belief reduction if and only if it is an optimistic (pessimistic) lower approximation reduction, and a set is an optimistic (pessimistic) plausibility reduction if and only if it is an optimistic (pessimistic) upper approximation reduction.

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

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.

Topological structures of a type of granule based covering rough sets

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3129-3141
Author(s):  
Yan-Lan Zhang ◽  
Chang-Qing Li
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Granular Computing ◽  
Rough Set Theory ◽  
Equivalence Relations ◽  
Topological Spaces ◽  
Topological Properties ◽  
Binary Relations ◽  
Upper Approximation ◽  
Approximation Operators

Rough set theory is one of important models of granular computing. Lower and upper approximation operators are two important basic concepts in rough set theory. The classical Pawlak approximation operators are based on partition and have been extended to covering approximation operators. Covering is one of the fundamental concepts in the topological theory, then topological methods are useful for studying the properties of covering approximation operators. This paper presents topological properties of a type of granular based covering approximation operators, which contains seven pairs of approximation operators. Then, topologies are induced naturally by the seven pairs of covering approximation operators, and the topologies are just the families of all definable subsets about the covering approximation operators. Binary relations are defined from the covering to present topological properties of the topological spaces, which are proved to be equivalence relations. Moreover, connectedness, countability, separation property and Lindel?f property of the topological spaces are discussed. The results are not only beneficial to obtain more properties of the pairs of covering approximation operators, but also have theoretical and actual significance to general topology.

scholarly journals δβ-I APPROXIMATION SPACES

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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