Extensions and intentions in the rough set theory

Abstract. Neighborhood based rough sets are important generalizations of the classical rough sets of Pawlak, as neighborhood operators generalize equivalence classes. In this article, we introduce nine neighborhood based operators and we study the partial order relations between twenty-two different neighborhood operators obtained from one covering. Seven neighborhood operators result in new rough set approximation operators. We study how these operators are related to the other fifteen neighborhood based approximation operators in terms of partial order relations, as well as to seven non-neighborhood-based rough set approximation operators.

show abstract

“…are called the minimal [1] and maximal [14] description of x. They can be seen as the two extreme neighborhoods of x.…”

Section: Preliminariesmentioning

confidence: 99%

New Neighborhood Based Rough Sets

D'eer

Cornelis

2015

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…In what follows, we consider covering rough set model [17], which is a generalization of Pawlak's rough set [18]. For…”

Section: Theorem 4 Let ( ) G M Imentioning

confidence: 99%

Uncertain Concepts in a Formal Context

Yang¹,

Qin²

2015

Advances in Intelligent Systems Research

View full text Add to dashboard Cite

Abstract-Formal concept analysis (FCA) provides a theoretical framework for learning hierarchies of knowledge clusters. This paper is devoted to the study of uncertainty in FCA. We introduce the notions of uncertain concept and its accuracy degree in FCA, and present approaches to characterizing accuracy degree of uncertain concepts from approximation operators and covering rough set points of views.

show abstract

“…By using the indiscernibility relation, a rough set is characterized by a pair of sets, called the lower and upper approximations. In recent years, classical rough sets have been extended to several general models, such as covering rough set model 7 , fuzzy rough set model 8 , variable precision rough set model 9 , generalized rough set model 10 , probabilistic rough set model 11 , etc.…”

Section: Introductionmentioning

confidence: 99%

Incremental update of rough set approximation under the grade indiscernibility relation

Luo¹,

Liu²,

Qin³

et al. 2017

IJCIS

View full text Add to dashboard Cite

The incremental updating of lower and upper approximations under the variation of information systems is an important issue in rough set theory. Many incremental updating approaches with respect to different kinds of indiscernibility relations have been proposed. The grade indiscernibility relation is a fuzzification of classical Pawlak's indiscernibility relation which can characterize the similarity between objects more precisely. Based on fuzzy rough set model, this paper discusses the approaches for dynamically acquiring of the upper and lower approximations with respect to the grade indiscernibility relation when adding and removing an attribute or an object, and changing the attribute value of the object, respectively. Since the approaches are used in succession, they make the approximations can be updated correctly and effectively when any kind of possible change in the information system. Finally, extensive experiments on data sets from University of California, Irvine (UCI) show that the incremental methods effectively reduce the computing time in comparison with the traditional non-incremental method.

show abstract

Extensions and intentions in the rough set theory

Cited by 539 publications

References 3 publications

New Neighborhood Based Rough Sets

New Neighborhood Based Rough Sets

Uncertain Concepts in a Formal Context

Incremental update of rough set approximation under the grade indiscernibility relation

Contact Info

Product

Resources

About