scholarly journals A New Type of Single Valued Neutrosophic Covering Rough Set Model

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1074
Author(s):  
Jingqian Wang ◽  
Xiaohong Zhang
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Inclusion Relation ◽  
Approximation Space ◽  
Matrix Representations ◽  
Model Based ◽  
Approximation Operators ◽  
New Type ◽  
Novel Method ◽  
Covering Rough Set

Recently, various types of single valued neutrosophic (SVN) rough set models were presented based on the same inclusion relation. However, there is another SVN inclusion relation in SVN sets. In this paper, we propose a new type of SVN covering rough set model based on the new inclusion relation. Furthermore, the graph and matrix representations of the new SVN covering approximation operators are presented. Firstly, the notion of SVN β 2 -covering approximation space is proposed, which is decided by the new inclusion relation. Then, a type of SVN covering rough set model under the SVN β 2 -covering approximation space is presented. Moreover, there is a corresponding SVN relation rough set model based on a SVN relation induced by the SVN β 2 -covering, and two conditions under which the SVN β 2 -covering can induce a symmetric SVN relation are presented. Thirdly, the graph and matrix representations of the new SVN covering rough set model are investigated. Finally, we propose a novel method for decision making (DM) problems in paper defect diagnosis under the new SVN covering rough set model.

scholarly journals Two Types of Single Valued Neutrosophic Covering Rough Sets and an Application to Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 710 ◽  
Author(s):  
Jingqian Wang ◽  
Xiaohong Zhang
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Rough Sets ◽  
Approximation Space ◽  
Matrix Representations ◽  
Neutrosophic Sets ◽  
Approximation Spaces ◽  
The Matrix ◽  
Novel Method ◽  
Covering Rough Set

In this paper, to combine single valued neutrosophic sets (SVNSs) with covering-based rough sets, we propose two types of single valued neutrosophic (SVN) covering rough set models. Furthermore, a corresponding application to the problem of decision making is presented. Firstly, the notion of SVN β -covering approximation space is proposed, and some concepts and properties in it are investigated. Secondly, based on SVN β -covering approximation spaces, two types of SVN covering rough set models are proposed. Then, some properties and the matrix representations of the newly defined SVN covering approximation operators are investigated. Finally, we propose a novel method to decision making (DM) problems based on one of the SVN covering rough set models. Moreover, the proposed DM method is compared with other methods in an example.

scholarly journals Fuzzy covering-based rough set on two different universes and its application

2021 ◽  
Author(s):  
Bin Yang
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Multiple Criteria Decision Making ◽  
Multiple Criteria ◽  
Extension Principle ◽  
Upper Approximation ◽  
New Type ◽  
New Perspective ◽  
Definition Of ◽  
Two Universes

Abstract In this paper, we propose a new type of fuzzy covering-based rough set model over two different universes by using Zadeh’s extension principle. We mainly address the following issues in this paper. First, we present the definition of fuzzy β-neighborhood, which can be seen as a fuzzy mapping from a universe to the set of fuzzy sets on another universe and study its properties. Then we define a new type of fuzzy covering-based rough set model on two different universes and investigate the properties of this model. Meanwhile, we give a necessary and sufficient condition under which two fuzzy β-coverings to generate the same fuzzy covering lower approximation or the same fuzzy covering upper approximation. Moreover, matrix representations of thefuzzy covering lower and fuzzy covering upper approximation operators are investigated. Finally, we propose a new approach to a kind of multiple criteria decision making problem based on fuzzy covering-based rough set model over two universes. The proposed models not onlyenrich the theory of fuzzy covering-based rough set but also provide a new perspective for multiple criteria decision making with uncertainty.

scholarly journals Two Types of Intuitionistic Fuzzy Covering Rough Sets and an Application to Multiple Criteria Group Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 462 ◽  
Author(s):  
Jingqian Wang ◽  
Xiaohong Zhang
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Group Decision Making ◽  
Rough Sets ◽  
Group Decision ◽  
Multiple Criteria ◽  
Approximation Spaces ◽  
Intuitionistic Fuzzy ◽  
Definition Of ◽  
Covering Rough Set

Intuitionistic fuzzy rough sets are constructed by combining intuitionistic fuzzy sets with rough sets. Recently, Huang et al. proposed the definition of an intuitionistic fuzzy (IF) β -covering and an IF covering rough set model. In this paper, some properties of IF β -covering approximation spaces and the IF covering rough set model are investigated further. Moreover, we present a novel methodology to the problem of multiple criteria group decision making. Firstly, some new notions and properties of IF β -covering approximation spaces are proposed. Secondly, we study the characterizations of Huang et al.’s IF covering rough set model and present a new IF covering rough set model for crisp sets in an IF environment. The relationships between these two IF covering rough set models and some other rough set models are investigated. Finally, based on the IF covering rough set model, Huang et al. also defined an optimistic multi-granulation IF rough set model. We present a novel method to multiple criteria group decision making problems under the optimistic multi-granulation IF rough set model.

scholarly journals Some More Results on IF Soft Rough Approximation Space

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Sharmistha Bhattacharya (Halder) ◽  
Bijan Davvaz
Keyword(s):  
Data Mining ◽  
Decision Making ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Soft Set ◽  
Approximation Space ◽  
Rough Approximation ◽  
Frame Work ◽  
Set Approximation

Fuzzy sets, rough sets, and later on IF sets became useful mathematical tools for solving various decision making problems and data mining problems. Molodtsov introduced another concept soft set theory as a general frame work for reasoning about vague concepts. Since most of the data collected are either linguistic variable or consist of vague concepts so IF set and soft set help a lot in data mining problem. The aim of this paper is to introduce the concept of IF soft lower rough approximation and IF upper rough set approximation. Also, some properties of this set are studied, and also some problems of decision making are cited where this concept may help. Further research will be needed to apply this concept fully in the decision making and data mining problems.

scholarly journals Some New Covering-Based Multigranulation Fuzzy Rough Sets and Corresponding Application in Multicriteria Decision Making

2021 ◽  
Vol 2021 ◽  
pp. 1-25
Author(s):  
Zaibin Chang ◽  
Lingling Mao
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Rough Sets ◽  
Large Scale ◽  
Rough Set Theory ◽  
Multicriteria Decision Making ◽  
Matrix Representations ◽  
Fuzzy Rough Set ◽  
Multicriteria Decision ◽  
Multigranulation Rough Set

Multigranulation rough set theory is an important tool to deal with the problem of multicriteria information system. The notion of fuzzy β -neighborhood has been used to construct some covering-based multigranulation fuzzy rough set (CMFRS) models through multigranulation fuzzy measure. But the β -neighborhood has not been used in these models, which can be seen as the bridge of fuzzy covering-based rough sets and covering-based rough sets. In this paper, the new concept of multigranulation fuzzy neighborhood measure and some types of covering-based multigranulation fuzzy rough set (CMFRS) models based on it are proposed. They can be seen as the further combination of fuzzy sets: covering-based rough sets and multigranulation rough sets. Moreover, they are used to solve the problem of multicriteria decision making. Firstly, the definition of multigranulation fuzzy neighborhood measure is given based on the concept of β -neighborhood. Moreover, four types of CMFRS models are constructed, as well as their characteristics and relationships. Then, novel matrix representations of them are investigated, which can satisfy the need of knowledge discovery from large-scale covering information systems. The matrix representations can be more easily implemented than set representations by computers. Finally, we apply them to manage the problem of multicriteria group decision making (MCGDM) and compare them with other methods.

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.

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