On Three Types of Soft Rough Covering-Based Fuzzy Sets
Recently, the concept of a soft rough fuzzy covering (briefly, SRFC) by means of soft neighborhoods was defined and their properties were studied by Zhan’s model. As a generalization of Zhan’s method and in order to increase the lower approximation and decrease the upper approximation, the present w...
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doaj-18a7206a39e54ce1a0b2b6f557fc3b812021-02-15T12:53:05ZengHindawi LimitedJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66772986677298On Three Types of Soft Rough Covering-Based Fuzzy SetsMohammed Atef0Shokry Nada1Abdu Gumaei2Ashraf S. Nawar3Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Menoufia, EgyptDepartment of Mathematics and Computer Science, Faculty of Science, Menoufia University, Menoufia, EgyptResearch Chair of Pervasive and Mobile Computing, Department of Information Systems, College of Computer and Information Sciences, King Saud University, Riyadh 11543, Saudi ArabiaDepartment of Mathematics and Computer Science, Faculty of Science, Menoufia University, Menoufia, EgyptRecently, the concept of a soft rough fuzzy covering (briefly, SRFC) by means of soft neighborhoods was defined and their properties were studied by Zhan’s model. As a generalization of Zhan’s method and in order to increase the lower approximation and decrease the upper approximation, the present work aims to define the complementary soft neighborhood and hence three types of soft rough fuzzy covering models (briefly, 1-SRFC, 2-SRFC, and 3-SRFC) are proposed. We discuss their axiomatic properties. According to these results, we investigate three types of fuzzy soft measure degrees (briefly, 1-SMD, 2-SMD, and 3-SMD). Also, three kinds of ψ-soft rough fuzzy coverings (briefly, 1-ψ-SRFC, 2-ψ-SRFC, and 3-ψ-SRFC) and three kinds of D-soft rough fuzzy coverings (briefly, 1-D-SRFC, 2-D-SRFC, and 3-D-SRFC) are discussed and some of their properties are studied. Finally, the relationships among these three models and Zhan’s model are presented.http://dx.doi.org/10.1155/2021/6677298 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Mohammed Atef Shokry Nada Abdu Gumaei Ashraf S. Nawar |
spellingShingle |
Mohammed Atef Shokry Nada Abdu Gumaei Ashraf S. Nawar On Three Types of Soft Rough Covering-Based Fuzzy Sets Journal of Mathematics |
author_facet |
Mohammed Atef Shokry Nada Abdu Gumaei Ashraf S. Nawar |
author_sort |
Mohammed Atef |
title |
On Three Types of Soft Rough Covering-Based Fuzzy Sets |
title_short |
On Three Types of Soft Rough Covering-Based Fuzzy Sets |
title_full |
On Three Types of Soft Rough Covering-Based Fuzzy Sets |
title_fullStr |
On Three Types of Soft Rough Covering-Based Fuzzy Sets |
title_full_unstemmed |
On Three Types of Soft Rough Covering-Based Fuzzy Sets |
title_sort |
on three types of soft rough covering-based fuzzy sets |
publisher |
Hindawi Limited |
series |
Journal of Mathematics |
issn |
2314-4629 2314-4785 |
publishDate |
2021-01-01 |
description |
Recently, the concept of a soft rough fuzzy covering (briefly, SRFC) by means of soft neighborhoods was defined and their properties were studied by Zhan’s model. As a generalization of Zhan’s method and in order to increase the lower approximation and decrease the upper approximation, the present work aims to define the complementary soft neighborhood and hence three types of soft rough fuzzy covering models (briefly, 1-SRFC, 2-SRFC, and 3-SRFC) are proposed. We discuss their axiomatic properties. According to these results, we investigate three types of fuzzy soft measure degrees (briefly, 1-SMD, 2-SMD, and 3-SMD). Also, three kinds of ψ-soft rough fuzzy coverings (briefly, 1-ψ-SRFC, 2-ψ-SRFC, and 3-ψ-SRFC) and three kinds of D-soft rough fuzzy coverings (briefly, 1-D-SRFC, 2-D-SRFC, and 3-D-SRFC) are discussed and some of their properties are studied. Finally, the relationships among these three models and Zhan’s model are presented. |
url |
http://dx.doi.org/10.1155/2021/6677298 |
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