scholarly journals Topological Structures of Lower and Upper Rough Subsets in a Hyperring

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Nabilah Abughazalah ◽  
Naveed Yaqoob ◽  
Kiran Shahzadi
Keyword(s):  
Rough Sets ◽  
Topological Spaces ◽  
Topological Structures ◽  
Lower And Upper Approximations

In this paper, we study the connection between topological spaces, hyperrings (semi-hypergroups), and rough sets. We concentrate here on the topological parts of the lower and upper approximations of hyperideals in hyperrings and semi-hypergroups. We provide the conditions for the boundary of hyp-ideals of a hyp-ring to become the hyp-ideals of hyp-ring.

New Approaches of Rough Sets via Ideals

2016 ◽  
pp. 247-264 ◽  
Author(s):  
Ali Kandil ◽  
M. M. Yakout ◽  
A. Zakaria
Keyword(s):  
Rough Sets ◽  
Present Method ◽  
Boundary Region ◽  
Topological Spaces ◽  
Membership Functions ◽  
New Approaches ◽  
Approximation Operators ◽  
Definition Of ◽  
Lower And Upper Approximations

An ideal I on a nonempty set X is a subfamily of P(X) which is closed under finite unions and subsets. In this chapter, a new definition of approximation operators and rough membership functions via ideal has been introduced. The concepts of lower and upper approximations via ideals have been mentioned. These new definitions are comparing with Pawlak's, Yao's and Allam's definitions. It's therefore shown that the current definitions are more generally. Also, it's shown that the present method decreases the boundary region. In addition to these points, the topology generated via present method finer than Allam's one which is a generalization of that obtained by Yao's method. Finally, T1 topological spaces are obtained by relations and ideals which are not discrete.

Analysing diabetes using rough sets

2020 ◽  
pp. 533-538
Author(s):  
S. Arjun Raj ◽  
M. Vigneshwaran
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
International Diabetes Federation ◽  
Published Data ◽  
Lower And Upper Approximations

In this article we use the rough set theory to generate the set of decision concepts in order to solve a medical problem.Based on officially published data by International Diabetes Federation (IDF), rough sets have been used to diagnose Diabetes.The lower and upper approximations of decision concepts and their boundary regions have been formulated here.

Missing Data Estimation Using Rough Sets

2010 ◽  
pp. 94-116
Author(s):  
Tshilidzi Marwala
Keyword(s):  
Missing Data ◽  
Rough Set ◽  
Rough Sets ◽  
Real Data ◽  
Valuable Insight ◽  
Lower And Upper Approximations ◽  
Decision Tables ◽  
Missing Data Estimation ◽  
Data Estimation ◽  
Insight Into

A number of techniques for handling missing data have been presented and implemented. Most of these proposed techniques are unnecessarily complex and, therefore, difficult to use. This chapter investigates a hot-deck data imputation method, based on rough set computations. In this chapter, characteristic relations are introduced that describe incompletely specified decision tables and then these are used for missing data estimation. It has been shown that the basic rough set idea of lower and upper approximations for incompletely specified decision tables may be defined in a variety of different ways. Empirical results obtained using real data are given and they provide a valuable insight into the problem of missing data. Missing data are predicted with an accuracy of up to 99%.

A Matrix Method for Calculation of the Approximations under the Asymmetric Similarity Relation Based Rough Sets

2011 ◽  
Vol 187 ◽  
pp. 251-256
Author(s):  
Lei Wang ◽  
Tian Rui Li ◽  
Jun Ye
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Matrix Representation ◽  
Point Of View ◽  
Similarity Relation ◽  
The Matrix ◽  
Lower And Upper Approximations ◽  
Incomplete Information Systems ◽  
Asymmetric Similarity

The essence of the rough set theory (RST) is to deal with the inconsistent problems by two definable subsets which are called the lower and upper approximations respectively. Asymmetric Similarity relation based Rough Sets (ASRS) model is one kind of extensions of the classical rough set model in incomplete information systems. In this paper, we propose a new matrix view of ASRS model and give the matrix representation of the lower and upper approximations of a concept under ASRS model. According to this matrix view, a new method is obtained for calculation of the lower and upper approximations under ASRS model. An example is given to illustrate processes of calculating the approximations of a concept based on the matrix point of view.

On Fuzzy Rough Compactness

2017 ◽  
Vol 6 (1-2) ◽  
pp. 1 ◽  
Author(s):  
Solomon Anita Shanthi ◽  
Natesan Thillaigovindan ◽  
Rajamanickam Poovizhi
Keyword(s):  
Topological Space ◽  
Rough Sets ◽  
Topological Spaces ◽  
Fuzzy Rough Sets

The notion of rough topological space has been well defined and studied by a number of researchers. Connectedness and compactness of fuzzy soft topological spaces have also been studied by some authors. In this paper we introduce the notion of compactness in fuzzy rough sets and establish some interesting theorems.

Neutrosophic Nano Ideal Topological Structures

2018 ◽  
Author(s):  
Parimala Mani ◽  
Karthika M ◽  
jafari S ◽  
Smarandache F ◽  
Ramalingam Udhayakumar
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Topological Structures ◽  
Basic Properties ◽  
Closed Sets ◽  
Structural Space ◽  
New Type

Neutrosophic nano topology and Nano ideal topological spaces induced the authors to propose this new concept. The aim of this paper is to introduce a new type of structural space called neutrosophic nano ideal topological spaces and investigate the relation between neutrosophic nano topological space and neutrosophic nano ideal topological spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and characterizations related to these sets are given.

scholarly journals On Topological Structures of Fuzzy Parametrized Soft Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Serkan Atmaca ◽  
İdris Zorlutuna
Keyword(s):  
Topological Structure ◽  
Topological Spaces ◽  
Soft Sets ◽  
Topological Structures ◽  
Basic Properties

We introduce the topological structure of fuzzy parametrized soft sets and fuzzy parametrized soft mappings. We define the notion of quasi-coincidence for fuzzy parametrized soft sets and investigated its basic properties. We study the closure, interior, base, continuity, and compactness and properties of these concepts in fuzzy parametrized soft topological spaces.

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