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 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.

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.

Aximatics for Rough Set Model Based on Vague Relations

2011 ◽  
Vol 282-283 ◽  
pp. 283-286
Author(s):  
Hai Dong Zhang ◽  
Yan Ping He
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
General Framework ◽  
Axiomatic Approach ◽  
Constructive Approach ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Axiomatic Approaches ◽  
Set Approximation

This paper presents a general framework for the study of rough set approximation operators in vague environment in which both constructive and axiomatic approaches are used. In constructive approach, by means of a vague relation defined by us, a new pair of vague rough approximation operators is first defined. Also some properties about the approximation operators are then discussed. In axiomatic approach, an operator-oriented characterization of vague rough sets is proposed, that is, vague rough approximation operators are defined by axioms.

scholarly journals Topological properties of a pair of relation-based approximation operators

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6175-6183
Author(s):  
Yan-Lan Zhang ◽  
Chang-Qing Li
Keyword(s):  
Data Mining ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Equivalence Relations ◽  
Topological Properties ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Basic Concepts

Rough set theory is an important tool for data mining. Lower and upper approximation operators are two important basic concepts in the rough set theory. The classical Pawlak rough approximation operators are based on equivalence relations and have been extended to relation-based generalized rough approximation operators. This paper presents topological properties of a pair of relation-based generalized rough approximation operators. A topology is induced by the pair of generalized rough approximation operators from an inverse serial relation. Then, connectedness, countability, separation property and Lindel?f property of the topological space are discussed. The results are not only beneficial to obtain more properties of the pair of approximation operators, but also have theoretical and actual significance to general topology.

scholarly journals A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Tianyu Xue ◽  
Zhan’ao Xue ◽  
Huiru Cheng ◽  
Jie Liu ◽  
Tailong Zhu
Keyword(s):  
Rough Sets ◽  
Rough Set Theory ◽  
Binary Relations ◽  
Approximation Space ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Fuzzy Binary Relation ◽  
Novel Method ◽  
Interval Valued

Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators.

N-soft rough sets and its applications

2021 ◽  
Vol 40 (1) ◽  
pp. 565-573
Author(s):  
Di Zhang ◽  
Pi-Yu Li ◽  
Shuang An
Keyword(s):  
Decision Making ◽  
Hybrid Model ◽  
Rough Sets ◽  
Real Life ◽  
Decision Problems ◽  
Multi Criteria Decision Making ◽  
Approximation Space ◽  
Soft Sets ◽  
Approximation Operators ◽  
Rough Approximation

In this paper, we propose a new hybrid model called N-soft rough sets, which can be seen as a combination of rough sets and N-soft sets. Moreover, approximation operators and some useful properties with respect to N-soft rough approximation space are introduced. Furthermore, we propose decision making procedures for N-soft rough sets, the approximation sets are utilized to handle problems involving multi-criteria decision-making(MCDM), aiming at electing the optional objects and the possible optional objects based on their attribute set. The algorithm addresses some limitations of the extended rough sets models in dealing with inconsistent decision problems. Finally, an application of N-soft rough sets in multi-criteria decision making is illustrated with a real life example.

scholarly journals A Decision-Making Approach Based on a Multi Q-Hesitant Fuzzy Soft Multi-Granulation Rough Model

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 711 ◽  
Author(s):  
Kholood Alsager ◽  
Noura Alshehri ◽  
Muhammad Akram
Keyword(s):  
Decision Making ◽  
Fault Detection ◽  
Hybrid Model ◽  
Rough Set ◽  
Rough Sets ◽  
General Framework ◽  
Fuzzy Soft Set ◽  
Rough Model ◽  
Approximation Operators ◽  
Rough Approximation

In this paper, we propose a new hybrid model, multi Q-hesitant fuzzy soft multi-granulation rough set model, by combining a multi Q-hesitant fuzzy soft set and multi-granulation rough set. We demonstrate some useful properties of these multi Q-hesitant fuzzy soft multi-granulation rough sets. Furthermore, we define multi Q-hesitant fuzzy soft ( M k Q H F S ) rough approximation operators in terms of M k Q H F S relations and M k Q H F S multi-granulation rough approximation operators in terms of M k Q H F S relations. We study the main properties of lower and upper M k Q H F S rough approximation operators and lower and upper M k Q H F S multi-granulation rough approximation operators. Moreover, we develop a general framework for dealing with uncertainty in decision-making by using the multi Q-hesitant fuzzy soft multi-granulation rough sets. We analyze the photovoltaic systems fault detection to show the proposed decision methodology.

scholarly journals Further Study of MultigranulationT-Fuzzy Rough Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Wentao Li ◽  
Xiaoyan Zhang ◽  
Wenxin Sun
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Approximation Space ◽  
Fuzzy Rough Sets ◽  
Fuzzy Rough Set ◽  
Upper Approximation ◽  
Fuzzy Approximation ◽  
Approximation Operators ◽  
Special Instance

The optimistic multigranulationT-fuzzy rough set model was established based on multiple granulations underT-fuzzy approximation space by Xu et al., 2012. From the reference, a natural idea is to consider pessimistic multigranulation model inT-fuzzy approximation space. So, in this paper, the main objective is to make further studies according to Xu et al., 2012. The optimistic multigranulationT-fuzzy rough set model is improved deeply by investigating some further properties. And a complete multigranulationT-fuzzy rough set model is constituted by addressing the pessimistic multigranulationT-fuzzy rough set. The full important properties of multigranulationT-fuzzy lower and upper approximation operators are also presented. Moreover, relationships between multigranulation and classicalT-fuzzy rough sets have been studied carefully. From the relationships, we can find that theT-fuzzy rough set model is a special instance of the two new types of models. In order to interpret and illustrate optimistic and pessimistic multigranulationT-fuzzy rough set models, a case is considered, which is helpful for applying these theories to practical issues.

scholarly journals Comparative Studies of Covering Rough Set Models

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Zhaohao Wang
Keyword(s):  
Rough Set ◽  
Comparative Studies ◽  
Rough Sets ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Definition Of ◽  
Covering Rough Set

Many different proposals exist for the definition of lower and upper approximation operators in covering-based rough sets and so many different covering rough set models are built correspondingly. It is meaningful to explore the connection of these covering rough set models for their applications in practice. In this paper, we establish relationships between the most commonly used operators in covering rough set models. We investigate the conditions under which two types of upper approximation operations are identical.

scholarly journals Matroidal Structure of Generalized Rough Sets Based on Tolerance Relations

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Hui Li ◽  
Yanfang Liu ◽  
William Zhu
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Matroid Theory ◽  
Upper Approximation ◽  
Tolerance Relation ◽  
The Family ◽  
Generalized Rough Set ◽  
The Relationship ◽  
Generalized Rough Sets

Rough set theory provides an effective tool to deal with uncertain, granular, and incomplete knowledge in information systems. Matroid theory generalizes the linear independence in vector spaces and has many applications in diverse fields, such as combinatorial optimization and rough sets. In this paper, we construct a matroidal structure of the generalized rough set based on a tolerance relation. First, a family of sets are constructed through the lower approximation of a tolerance relation and they are proved to satisfy the circuit axioms of matroids. Thus we establish a matroid with the family of sets as its circuits. Second, we study the properties of the matroid including the base and the rank function. Moreover, we investigate the relationship between the upper approximation operator based on a tolerance relation and the closure operator of the matroid induced by the tolerance relation. Finally, from a tolerance relation, we can get a matroid of the generalized rough set based on the tolerance relation. The matroid can also induce a new relation. We investigate the connection between the original tolerance relation and the induced relation.

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