Generalized rough set models determined by multiple neighborhoods generated from a similarity relation

2017 ◽  
Vol 22 (7) ◽  
pp. 2081-2094 ◽  
Author(s):  
Jianhua Dai ◽  
Shuaichao Gao ◽  
Guojie Zheng
Keyword(s):  
Rough Set ◽  
Similarity Relation ◽  
Generalized Rough Set ◽  
Multiple Neighborhoods

GENERALIZED FUZZY ROUGH SETS BY CONDITIONAL PROBABILITY RELATIONS

2002 ◽  
Vol 16 (07) ◽  
pp. 865-881 ◽  
Author(s):  
ROLLY INTAN ◽  
MASAO MUKAIDONO
Keyword(s):  
Conditional Probability ◽  
Rough Set ◽  
Real World ◽  
Rough Sets ◽  
Similarity Relation ◽  
Fuzzy Rough Set ◽  
Fuzzy Similarity ◽  
Fuzzy Similarity Relation ◽  
Real World Applications ◽  
The Universe

In 1982, Pawlak proposed the concept of rough sets with a practical purpose of representing indiscernibility of elements or objects in the presence of information systems. Even if it is easy to analyze, the rough set theory built on a partition induced by equivalence relation may not provide a realistic view of relationships between elements in real-world applications. Here, coverings of, or nonequivalence relations on, the universe can be considered to represent a more realistic model instead of a partition in which a generalized model of rough sets was proposed. In this paper, first a weak fuzzy similarity relation is introduced as a more realistic relation in representing the relationship between two elements of data in real-world applications. Fuzzy conditional probability relation is considered as a concrete example of the weak fuzzy similarity relation. Coverings of the universe is provided by fuzzy conditional probability relations. Generalized concepts of rough approximations and rough membership functions are proposed and defined based on coverings of the universe. Such generalization is considered as a kind of fuzzy rough set. A more generalized fuzzy rough set approximation of a given fuzzy set is proposed and discussed as an alternative to provide interval-value fuzzy sets. Their properties are examined.

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.

scholarly journals Soft Covering Based Rough Sets and Their Application

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Şaziye Yüksel ◽  
Zehra Güzel Ergül ◽  
Naime Tozlu
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Prostate Cancer Risk ◽  
Approximation Operator ◽  
Soft Sets ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Model Combining ◽  
Rough Approximation ◽  
Generalized Rough Set

Soft rough sets which are a hybrid model combining rough sets with soft sets are defined by using soft rough approximation operators. Soft rough sets can be seen as a generalized rough set model based on soft sets. The present paper aims to combine the covering soft set with rough set, which gives rise to the new kind of soft rough sets. Based on the covering soft sets, we establish soft covering approximation space and soft covering rough approximation operators and present their basic properties. We show that a new type of the soft covering upper approximation operator is smaller than soft upper approximation operator. Also we present an example in medicine which aims to find the patients with high prostate cancer risk. Our data are 78 patients from Selçuk University Meram Medicine Faculty.

scholarly journals Generalization of Pawlak’s Approximations in Hypermodules by Set-Valued Homomorphisms

2017 ◽  
Vol 42 (1) ◽  
pp. 59-81 ◽  
Author(s):  
Saeed Mirvakili ◽  
Seid Mohammad Anvariyeh ◽  
Bijan Davvaz
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Congruence Relation ◽  
Upper Approximation ◽  
Algebraic Sets ◽  
Set Valued Mapping ◽  
Approximation Operators ◽  
Lower And Upper Approximations ◽  
Generalized Rough Set

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.

scholarly journals Soft Rough Approximation Operators and Related Results

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Zhaowen Li ◽  
Bin Qin ◽  
Zhangyong Cai
Keyword(s):  
Topological Space ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Soft Set ◽  
Soft Sets ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Generalized Rough Set ◽  
Special Case

Soft set theory is a newly emerging tool to deal with uncertain problems. Based on soft sets, soft rough approximation operators are introduced, and soft rough sets are defined by using soft rough approximation operators. Soft rough sets, which could provide a better approximation than rough sets do, can be seen as a generalized rough set model. This paper is devoted to investigating soft rough approximation operations and relationships among soft sets, soft rough sets, and topologies. We consider four pairs of soft rough approximation operators and give their properties. Four sorts of soft rough sets are investigated, and their related properties are given. We show that Pawlak's rough set model can be viewed as a special case of soft rough sets, obtain the structure of soft rough sets, give the structure of topologies induced by a soft set, and reveal that every topological space on the initial universe is a soft approximating space.

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