Wyniki wyszukiwania - BazTech

1

Rough sets based on Galois connections

Madrid Nicolás, Medina Jesús, Ramírez-Poussa Eloísa

International Journal of Applied Mathematics and Computer Science

|

2020

|

Vol. 30, no. 2

299--313

EN

Rough set theory is an important tool to extract knowledge from relational databases. The original definitions of approximation operators are based on an indiscernibility relation, which is an equivalence one. Lately, different papers have motivated the possibility of considering arbitrary relations. Nevertheless, when those are taken into account, the original definitions given by Pawlak may lose fundamental properties. This paper proposes a possible solution to the arising problems by presenting an alternative definition of approximation operators based on the closure and interior operators obtained from an isotone Galois connection. We prove that the proposed definition satisfies interesting properties and that it also improves object classification tasks.

2

Precise Sets in Approximation Spaces and Textures

Dost Ş.

Fundamenta Informaticae

|

2018

|

Vol. 158, nr 4

353--368

EN

In this paper, we propose the notion of precise sets in texture spaces. Precise sets are defined by using textural sections and presections under a direlation. We obtain some properties of definability; it is proved that the family of precise sets under reflexive and transitive direlation is an Alexandroff ditopology. It is observed that sections and presections, which are approximation operators in the textural meaning, are Galois connections. Finally, effective results are given for definability by using textural precise sets.

3

Applications of Bipartite Graphs and their Adjacency Matrices to Covering-based Rough Sets

Wang J., Zhu W.

Fundamenta Informaticae

|

2017

|

Vol. 156, nr 2

237--254

EN

In this paper, bipartite graphs and their adjacency matrices are applied to equivalently represent covering-based rough sets through three sides, which are approximation operators, properties and reducible elements. Firstly, a bipartite graph is constructed through a covering. According to the constructed bipartite graph, two equivalent representations of a pair of covering upper and lower approximation operators are presented. And an algorithm is designed for computing the pair of covering approximation operators from the viewpoint of these equivalent representations. Some properties and reducible elements of covering-based rough sets are also investigated through the constructed bipartite graph. Finally, an adjacency matrix of the constructed bipartite graph is proposed, and reducible elements in the covering are obtained through the proposed adjacency matrix. Moreover, an equivalent representation of the covering upper approximation operator is presented through the proposed adjacency matrix. In a word, these results show two interesting views, which are graphs and matrices, to investigate covering-based rough sets.

4

Topological Structure of Relation-based Generalized Rough Sets

Zhang Y.-L., Li J., Li C.

Fundamenta Informaticae

|

2016

|

Vol. 147, nr 4

477--491

EN

Rough set theory is an important tool to deal with vagueness and granularity in information systems. Lower and upper approximation operators are two important basic concepts in the rough set theory. The classical Pawlak rough set approximations is based on equivalence relations and has been extended to relation-based generalized rough set approximations. In this paper, properties of relation-based generalized rough set approximations are examined, and topological properties of relation-based generalized rough set approximations presents. Necessary and sufficient conditions for the relation-based generalized upper (lower) approximation operators to be topological closure (interior) operators are proposed.