An Uncertainty Measure Based on Lower and Upper Approximations for Generalized Rough set Models

AbstractThe initiation and majority on rough sets for algebraic hyperstructures such as hypermodules over a hyperring have been concentrated on a congruence relation. The congruence relation, however, seems to restrict the application of the generalized rough set model for algebraic sets. In this paper, in order to solve this problem, we consider the concept of set-valued homomorphism for hypermodules and we give some examples of set-valued homomorphism. In this respect, we show that every homomorphism of the hypermodules is a set-valued homomorphism. The notions of generalized lower and upper approximation operators, constructed by means of a set-valued mapping, which is a generalization of the notion of lower and upper approximations of a hypermodule, are provided. We also propose the notion of generalized lower and upper approximations with respect to a subhypermodule of a hypermodule discuss some significant properties of them.

Download Full-text

Analysing diabetes using rough sets

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.2.1 ◽

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.

Download Full-text

Uncertainty Measure of Covering Generated Rough Set

2006 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology Workshops ◽

10.1109/wi-iatw.2006.139 ◽

2006 ◽

Cited By ~ 9

Author(s):

Jun Hu ◽

Guoyin Wang ◽

Qinghua Zhang

Keyword(s):

Rough Set ◽

Uncertainty Measure

Download Full-text

Variable Precision Rough Set Model Based on Covering Relation and Uncertainty Measure

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.694-697.2856 ◽

2013 ◽

Vol 694-697 ◽

pp. 2856-2859

Author(s):

Mei Yun Wang ◽

Chao Wang ◽

Da Zeng Tian

Keyword(s):

Rough Set ◽

Uncertainty Measure ◽

Probabilistic Measure ◽

Covering Relation ◽

Practical Applications ◽

Variable Precision ◽

Model Based ◽

Equivalent Relation ◽

Proposed Model ◽

Variable Precision Rough Set

The variable precision probabilistic rough set model is based on equivalent relation and probabilistic measure. However, the requirements of equivalent relation and probabilistic measure are too strict to satisfy in some practical applications. In order to solve the above problem, a variable precision rough set model based on covering relation and uncertainty measure is proposed. Moreover, the upper and lower approximation operators of the proposed model are given, while the properties of the operators are discussed.

Download Full-text

Missing Data Estimation Using Rough Sets

Computational Intelligence for Missing Data Imputation, Estimation, and Management ◽

10.4018/978-1-60566-336-4.ch005 ◽

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%.

Download Full-text

A survey on granular computing and its uncertainty measure from the perspective of rough set theory

Granular Computing ◽

10.1007/s41066-019-00204-3 ◽

2019 ◽

Vol 6 (1) ◽

pp. 3-17 ◽

Cited By ~ 1

Author(s):

Yunlong Cheng ◽

Fan Zhao ◽

Qinghua Zhang ◽

Guoyin Wang

Keyword(s):

Set Theory ◽

Rough Set ◽

Granular Computing ◽

Rough Set Theory ◽

Uncertainty Measure

Download Full-text

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.187.251 ◽

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.

Download Full-text