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 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 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 Soft Classes and Soft Rough Classes with Applications in Decision Making

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Faruk Karaaslan
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Rough Sets ◽  
Soft Set ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Novel Method ◽  
Lower And Upper Approximations

Rough set was defined by Pawlak in 1982. Concept of soft set was proposed as a mathematical tool to cope with uncertainty and vagueness by Molodtsov in 1999. Soft sets were combined with rough sets by Feng et al. in 2011. Feng et al. investigated relationships between a subset of initial universe of soft set and a soft set. Feng et al. defined the upper and lower approximations of a subset of initial universe over a soft set. In this study, we firstly define concept of soft class and soft class operations such as union, intersection, and complement. Then we give some properties of soft class operations. Based on definition and operations of soft classes, we define lower and upper approximations of a soft set. Subsequently, we introduce concept of soft rough class and investigate some properties of soft rough classes. Moreover, we give a novel decision making method based on soft class and present an example related to novel method.

scholarly journals Multiset concepts in two-universe approximation spaces

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
O. A. Embaby ◽  
Nadya A. Toumi
Keyword(s):  
Decision Making ◽  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Approximation Space ◽  
Approximation Spaces ◽  
Lower And Upper Approximations ◽  
Two Universes ◽  
Basic Sets

Abstract Rough set theory over two universes is a generalization of rough set model to find accurate approximations for uncertain concepts in information systems in which uncertainty arises from existence of interrelations between the three basic sets: objects, attributes, and decisions. In this work, multisets are approximated in a crisp two-universe approximation space using binary ordinary relation and multi relation. The concept of two universe approximation is applied for defining lower and upper approximations of multisets. Properties of these approximations are investigated, and the deviations between them and corresponding notions are obtained; some counter examples are given. The suggested notions can help in the modification of the decision-making for events in which objects have repetitions such as patients visiting a doctor more than one time; an example for this case is given.

scholarly journals Hashing Based Answer Selection

2020 ◽  
Vol 34 (05) ◽  
pp. 9330-9337
Author(s):  
Dong Xu ◽  
Wu-Jun Li
Keyword(s):  
Question Answering ◽  
Matrix Representation ◽  
Matrix Representations ◽  
Binary Matrix ◽  
Large Memory ◽  
The Matrix ◽  
Novel Method ◽  
Online Prediction ◽  
Memory Cost ◽  
Vector Representations

Answer selection is an important subtask of question answering (QA), in which deep models usually achieve better performance than non-deep models. Most deep models adopt question-answer interaction mechanisms, such as attention, to get vector representations for answers. When these interaction based deep models are deployed for online prediction, the representations of all answers need to be recalculated for each question. This procedure is time-consuming for deep models with complex encoders like BERT which usually have better accuracy than simple encoders. One possible solution is to store the matrix representation (encoder output) of each answer in memory to avoid recalculation. But this will bring large memory cost. In this paper, we propose a novel method, called hashing based answer selection (HAS), to tackle this problem. HAS adopts a hashing strategy to learn a binary matrix representation for each answer, which can dramatically reduce the memory cost for storing the matrix representations of answers. Hence, HAS can adopt complex encoders like BERT in the model, but the online prediction of HAS is still fast with a low memory cost. Experimental results on three popular answer selection datasets show that HAS can outperform existing models to achieve state-of-the-art performance.

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 Intuitionistic Fuzzy Soft Rough Set and Its Application in Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Haidong Zhang ◽  
Lan Shu ◽  
Shilong Liao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Mathematical Tool ◽  
Intuitionistic Fuzzy ◽  
Rough Approximation ◽  
Soft Rough Set

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. In this paper, we present concepts of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets, and investigate some properties of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets in detail. Furthermore, classical representations of intuitionistic fuzzy soft rough approximation operators are presented. Finally, we develop an approach to intuitionistic fuzzy soft rough sets based on decision making and a numerical example is provided to illustrate the developed approach.

scholarly journals Two Different Views for Generalized Rough Sets with Applications

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2275
Author(s):  
Radwan Abu-Gdairi ◽  
Mostafa A. El-Gayar ◽  
Mostafa K. El-Bably ◽  
Kamel K. Fleifel
Keyword(s):  
Decision Making ◽  
Information System ◽  
Rough Set ◽  
Rough Sets ◽  
Real Life ◽  
Binary Relations ◽  
Medical Field ◽  
Good Decision ◽  
Heart Attacks ◽  
Generalized Rough Sets

Rough set philosophy is a significant methodology in the knowledge discovery of databases. In the present paper, we suggest new sorts of rough set approximations using a multi-knowledge base; that is, a family of the finite number of general binary relations via different methods. The proposed methods depend basically on a new neighborhood (called basic-neighborhood). Generalized rough approximations (so-called, basic-approximations) represent a generalization to Pawlak’s rough sets and some of their extensions as confirming in the present paper. We prove that the accuracy of the suggested approximations is the best. Many comparisons between these approaches and the previous methods are introduced. The main goal of the suggested techniques was to study the multi-information systems in order to extend the application field of rough set models. Thus, two important real-life applications are discussed to illustrate the importance of these methods. We applied the introduced approximations in a set-valued ordered information system in order to be accurate tools for decision-making. To illustrate our methods, we applied them to find the key foods that are healthy in nutrition modeling, as well as in the medical field to make a good decision regarding the heart attacks problem.

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