Covering-Based Rough Fuzzy, Intuitionistic Fuzzy and Neutrosophic Nano Topology and Applications
In recent years, “mathematical orientations on real-life problems”, which continue to increase, began to make a significant impact. Information systems for many decision-making problems consist of uncertain, incomplete, indeterminate and indiscernible structures and components....
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2019-01-01
|
| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/8913431/ |
| _version_ | 1818427979848482816 |
|---|---|
| author | Mohammed A. Al Shumrani Selcuk Topal Florentin Smarandache Cenap Ozel |
| author_facet | Mohammed A. Al Shumrani Selcuk Topal Florentin Smarandache Cenap Ozel |
| author_sort | Mohammed A. Al Shumrani |
| collection | DOAJ |
| description | In recent years, “mathematical orientations on real-life problems”, which continue to increase, began to make a significant impact. Information systems for many decision-making problems consist of uncertain, incomplete, indeterminate and indiscernible structures and components. Classical set theory and interpretation methods fail to represent, express and solve the problems of these types or cause to make wrong decisions. For this reason, in this study, we provide definitions and methods to present information and problem representations in more detail and precision. This paper introduces three new topologies called covering-based rough fuzzy, covering-based rough intuitionistic fuzzy and covering-based rough neutrosophic nano topology. Some fundamental definitions such as open set, closed set, interior, closure and basis are given. Neutrosophic definitions and properties are mainly investigated. We give some real life applications of covering-based rough neutrosophic nano topology in the final part of the paper and an explanatory example of decision making application by defining core point. |
| first_indexed | 2024-12-14T14:54:20Z |
| format | Article |
| id | doaj.art-a749918047414831973cdafc20746559 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-14T14:54:20Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-a749918047414831973cdafc207465592022-12-21T22:57:02ZengIEEEIEEE Access2169-35362019-01-01717283917284610.1109/ACCESS.2019.29559238913431Covering-Based Rough Fuzzy, Intuitionistic Fuzzy and Neutrosophic Nano Topology and ApplicationsMohammed A. Al Shumrani0https://orcid.org/0000-0003-2760-8086Selcuk Topal1https://orcid.org/0000-0001-7074-2569Florentin Smarandache2https://orcid.org/0000-0002-5560-5926Cenap Ozel3https://orcid.org/0000-0001-8005-7039Department of Mathematics, King Abdulaziz University, Jeddah, Saudi ArabiaDepartment of Mathematics, Bitlis Eren University, Bitlis, TurkeyDepartment of Mathematics, The University of New Mexico, Albuquerque, NM, USADepartment of Mathematics, King Abdulaziz University, Jeddah, Saudi ArabiaIn recent years, “mathematical orientations on real-life problems”, which continue to increase, began to make a significant impact. Information systems for many decision-making problems consist of uncertain, incomplete, indeterminate and indiscernible structures and components. Classical set theory and interpretation methods fail to represent, express and solve the problems of these types or cause to make wrong decisions. For this reason, in this study, we provide definitions and methods to present information and problem representations in more detail and precision. This paper introduces three new topologies called covering-based rough fuzzy, covering-based rough intuitionistic fuzzy and covering-based rough neutrosophic nano topology. Some fundamental definitions such as open set, closed set, interior, closure and basis are given. Neutrosophic definitions and properties are mainly investigated. We give some real life applications of covering-based rough neutrosophic nano topology in the final part of the paper and an explanatory example of decision making application by defining core point.https://ieeexplore.ieee.org/document/8913431/Approximation spacecore pointcovering-based topologyfuzzy nano topologyfuzzy setsintuitionistic nano topology |
| spellingShingle | Mohammed A. Al Shumrani Selcuk Topal Florentin Smarandache Cenap Ozel Covering-Based Rough Fuzzy, Intuitionistic Fuzzy and Neutrosophic Nano Topology and Applications IEEE Access Approximation space core point covering-based topology fuzzy nano topology fuzzy sets intuitionistic nano topology |
| title | Covering-Based Rough Fuzzy, Intuitionistic Fuzzy and Neutrosophic Nano Topology and Applications |
| title_full | Covering-Based Rough Fuzzy, Intuitionistic Fuzzy and Neutrosophic Nano Topology and Applications |
| title_fullStr | Covering-Based Rough Fuzzy, Intuitionistic Fuzzy and Neutrosophic Nano Topology and Applications |
| title_full_unstemmed | Covering-Based Rough Fuzzy, Intuitionistic Fuzzy and Neutrosophic Nano Topology and Applications |
| title_short | Covering-Based Rough Fuzzy, Intuitionistic Fuzzy and Neutrosophic Nano Topology and Applications |
| title_sort | covering based rough fuzzy intuitionistic fuzzy and neutrosophic nano topology and applications |
| topic | Approximation space core point covering-based topology fuzzy nano topology fuzzy sets intuitionistic nano topology |
| url | https://ieeexplore.ieee.org/document/8913431/ |
| work_keys_str_mv | AT mohammedaalshumrani coveringbasedroughfuzzyintuitionisticfuzzyandneutrosophicnanotopologyandapplications AT selcuktopal coveringbasedroughfuzzyintuitionisticfuzzyandneutrosophicnanotopologyandapplications AT florentinsmarandache coveringbasedroughfuzzyintuitionisticfuzzyandneutrosophicnanotopologyandapplications AT cenapozel coveringbasedroughfuzzyintuitionisticfuzzyandneutrosophicnanotopologyandapplications |