Topologies of Approximation Spaces of Rough Set Theory

2008 ◽  
pp. 176-186 ◽  
Author(s):  
Milan Vlach
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Approximation Spaces

Similarity measure for multi-granularity rough approximations of vague sets

2021 ◽  
Vol 40 (1) ◽  
pp. 1609-1621
Author(s):  
Jie Yang ◽  
Wei Zhou ◽  
Shuai Li
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Target Concept ◽  
Uncertainty Measure ◽  
Approximation Spaces ◽  
Vague Sets ◽  
Rough Approximation ◽  
Vague Concept

Vague sets are a further extension of fuzzy sets. In rough set theory, target concept can be characterized by different rough approximation spaces when it is a vague concept. The uncertainty measure of vague sets in rough approximation spaces is an important issue. If the uncertainty measure is not accurate enough, different rough approximation spaces of a vague concept may possess the same result, which makes it impossible to distinguish these approximation spaces for charactering a vague concept strictly. In this paper, this problem will be solved from the perspective of similarity. Firstly, based on the similarity between vague information granules(VIGs), we proposed an uncertainty measure with strong distinguishing ability called rough vague similarity (RVS). Furthermore, by studying the multi-granularity rough approximations of a vague concept, we reveal the change rules of RVS with the changing granularities and conclude that the RVS between any two rough approximation spaces can degenerate to granularity measure and information measure. Finally, a case study and related experiments are listed to verify that RVS possesses a better performance for reflecting differences among rough approximation spaces for describing a vague concept.

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).

A comparison of two types of rough approximations based on Nj-neighborhoods

2021 ◽  
pp. 1-14
Author(s):  
Tareq M. Al-Shami ◽  
Ibtesam Alshammari ◽  
Mohammed E. El-Shafei
Keyword(s):  
Topological Space ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Mathematical Tool ◽  
Approximation Spaces ◽  
Uncertain Knowledge ◽  
Accuracy Measures

In 1982, Pawlak proposed the concept of rough sets as a novel mathematical tool to address the issues of vagueness and uncertain knowledge. Topological concepts and results are close to the concepts and results in rough set theory; therefore, some researchers have investigated topological aspects and their applications in rough set theory. In this discussion, we study further properties of Nj-neighborhoods; especially, those are related to a topological space. Then, we define new kinds of approximation spaces and establish main properties. Finally, we make some comparisons of the approximations and accuracy measures introduced herein and their counterparts induced from interior and closure topological operators and E-neighborhoods.

scholarly journals Multiset concepts in two-universe approximation spaces

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
O. A. Embaby ◽  
Nadya A. Toumi
Keyword(s):  
Decision Making ◽  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Approximation Space ◽  
Approximation Spaces ◽  
Lower And Upper Approximations ◽  
Two Universes ◽  
Basic Sets

Abstract Rough set theory over two universes is a generalization of rough set model to find accurate approximations for uncertain concepts in information systems in which uncertainty arises from existence of interrelations between the three basic sets: objects, attributes, and decisions. In this work, multisets are approximated in a crisp two-universe approximation space using binary ordinary relation and multi relation. The concept of two universe approximation is applied for defining lower and upper approximations of multisets. Properties of these approximations are investigated, and the deviations between them and corresponding notions are obtained; some counter examples are given. The suggested notions can help in the modification of the decision-making for events in which objects have repetitions such as patients visiting a doctor more than one time; an example for this case is given.

scholarly journals On Fuzzy Rough Sets and Their Topological Structures

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Weidong Tang ◽  
Jinzhao Wu ◽  
Dingwei Zheng
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Fuzzy Relations ◽  
Fuzzy Rough Sets ◽  
Approximation Spaces ◽  
Topological Structures ◽  
Fuzzy Approximation ◽  
Approximation Operators

The core concepts of rough set theory are information systems and approximation operators of approximation spaces. Approximation operators draw close links between rough set theory and topology. This paper is devoted to the discussion of fuzzy rough sets and their topological structures. Fuzzy rough approximations are further investigated. Fuzzy relations are researched by means of topology or lower and upper sets. Topological structures of fuzzy approximation spaces are given by means of pseudoconstant fuzzy relations. Fuzzy topology satisfying (CC) axiom is investigated. The fact that there exists a one-to-one correspondence between the set of all preorder fuzzy relations and the set of all fuzzy topologies satisfying (CC) axiom is proved, the concept of fuzzy approximating spaces is introduced, and decision conditions that a fuzzy topological space is a fuzzy approximating space are obtained, which illustrates that we can research fuzzy relations or fuzzy approximation spaces by means of topology and vice versa. Moreover, fuzzy pseudoclosure operators are examined.

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.

Foundations of Rough Sets from Vagueness Perspective

2011 ◽  
pp. 1-37 ◽  
Author(s):  
Piotr Wasilewski ◽  
Dominik Slezak
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Algebraic Structures ◽  
Approximation Spaces ◽  
Types Of Knowledge

We present three types of knowledge, which can be specified according to the Rough Set theory. Then, we present three corresponding types of algebraic structures appearing in the Rough Set theory. This leads to three following types of vagueness: crispness, classical vagueness, and a new concept of “intermediate” vagueness. We also propose two classifications of information systems and approximation spaces. Based on them, we differentiate between information and knowledge.

scholarly journals Reasoning on vague ontologies using rough set theory

2021 ◽  
Vol 7 (1) ◽  
pp. 0-0
Keyword(s):  
Incomplete Information ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Approximation Spaces ◽  
Automatic Reasoning ◽  
Fuzzy Concept ◽  
Open World ◽  
Tableau Algorithm ◽  
Open World Assumption

Web ontologies can contain vague concepts, which means the knowledge about them is imprecise and then query answering will not possible due to the open world assumption. A concept description can be very exact (crisp concept) or exact (fuzzy concept) if its knowledge is complete, otherwise it is inexact (vague concept) if its knowledge is incomplete. In this paper, we propose a method based on the rough set theory for reasoning on vague ontologies. With this method, the detection of vague concepts will insert into the original ontology new rough vague concepts where their description is defined on approximation spaces to be used by extended Tableau algorithm for automatic reasoning. The extended Tableau algorithm by this rough set-based vagueness is intended to answer queries even with the presence of incomplete information.

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