Rough <i>q</i>-Rung Orthopair Fuzzy Sets and Their Applications in Decision-Making
Yager recently introduced the <i>q</i>-rung orthopair fuzzy set to accommodate uncertainty in decision-making problems. A binary relation over dual universes has a vital role in mathematics and information sciences. During this work, we defined upper approximations and lower approximatio...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/11/2010 |
| _version_ | 1797508368734093312 |
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| author | Muhammad Asim Bilal Muhammad Shabir Ahmad N. Al-Kenani |
| author_facet | Muhammad Asim Bilal Muhammad Shabir Ahmad N. Al-Kenani |
| author_sort | Muhammad Asim Bilal |
| collection | DOAJ |
| description | Yager recently introduced the <i>q</i>-rung orthopair fuzzy set to accommodate uncertainty in decision-making problems. A binary relation over dual universes has a vital role in mathematics and information sciences. During this work, we defined upper approximations and lower approximations of <i>q</i>-rung orthopair fuzzy sets using crisp binary relations with regard to the aftersets and foresets. We used an accuracy measure of a <i>q</i>-rung orthopair fuzzy set to search out the accuracy of a <i>q</i>-rung orthopair fuzzy set, and we defined two types of <i>q</i>-rung orthopair fuzzy topologies induced by reflexive relations. The novel concept of a rough <i>q</i>-rung orthopair fuzzy set over dual universes is more flexible when debating the symmetry between two or more objects that are better than the prevailing notion of a rough Pythagorean fuzzy set, as well as rough intuitionistic fuzzy sets. Furthermore, using the score function of <i>q</i>-rung orthopair fuzzy sets, a practical approach was introduced to research the symmetry of the optimal decision and, therefore, the ranking of feasible alternatives. Multiple criteria decision making (MCDM) methods for <i>q</i>-rung orthopair fuzzy sets cannot solve problems when an individual is faced with the symmetry of a two-sided matching MCDM problem. This new approach solves the matter more accurately. The devised approach is new within the literature. In this method, the main focus is on ranking and selecting the alternative from a collection of feasible alternatives, reckoning for the symmetry of the two-sided matching of alternatives, and providing a solution based on the ranking of alternatives for an issue containing conflicting criteria, to assist the decision-maker in a final decision. |
| first_indexed | 2024-03-10T05:02:06Z |
| format | Article |
| id | doaj.art-6528eb990860432fbcb788e7486d0174 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T05:02:06Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-6528eb990860432fbcb788e7486d01742023-11-23T01:43:20ZengMDPI AGSymmetry2073-89942021-10-011311201010.3390/sym13112010Rough <i>q</i>-Rung Orthopair Fuzzy Sets and Their Applications in Decision-MakingMuhammad Asim Bilal0Muhammad Shabir1Ahmad N. Al-Kenani2Department of Mathematics, Quaid-I-Azam University, Islamabad 45320, PakistanDepartment of Mathematics, Quaid-I-Azam University, Islamabad 45320, PakistanDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi ArabiaYager recently introduced the <i>q</i>-rung orthopair fuzzy set to accommodate uncertainty in decision-making problems. A binary relation over dual universes has a vital role in mathematics and information sciences. During this work, we defined upper approximations and lower approximations of <i>q</i>-rung orthopair fuzzy sets using crisp binary relations with regard to the aftersets and foresets. We used an accuracy measure of a <i>q</i>-rung orthopair fuzzy set to search out the accuracy of a <i>q</i>-rung orthopair fuzzy set, and we defined two types of <i>q</i>-rung orthopair fuzzy topologies induced by reflexive relations. The novel concept of a rough <i>q</i>-rung orthopair fuzzy set over dual universes is more flexible when debating the symmetry between two or more objects that are better than the prevailing notion of a rough Pythagorean fuzzy set, as well as rough intuitionistic fuzzy sets. Furthermore, using the score function of <i>q</i>-rung orthopair fuzzy sets, a practical approach was introduced to research the symmetry of the optimal decision and, therefore, the ranking of feasible alternatives. Multiple criteria decision making (MCDM) methods for <i>q</i>-rung orthopair fuzzy sets cannot solve problems when an individual is faced with the symmetry of a two-sided matching MCDM problem. This new approach solves the matter more accurately. The devised approach is new within the literature. In this method, the main focus is on ranking and selecting the alternative from a collection of feasible alternatives, reckoning for the symmetry of the two-sided matching of alternatives, and providing a solution based on the ranking of alternatives for an issue containing conflicting criteria, to assist the decision-maker in a final decision.https://www.mdpi.com/2073-8994/13/11/2010<i>q</i>-rung orthopair fuzzy set<i>q</i>-rung orthopair fuzzy topologiesaccuracy measuresimilarity relationsdecision-makingemergency preparedness |
| spellingShingle | Muhammad Asim Bilal Muhammad Shabir Ahmad N. Al-Kenani Rough <i>q</i>-Rung Orthopair Fuzzy Sets and Their Applications in Decision-Making Symmetry <i>q</i>-rung orthopair fuzzy set <i>q</i>-rung orthopair fuzzy topologies accuracy measure similarity relations decision-making emergency preparedness |
| title | Rough <i>q</i>-Rung Orthopair Fuzzy Sets and Their Applications in Decision-Making |
| title_full | Rough <i>q</i>-Rung Orthopair Fuzzy Sets and Their Applications in Decision-Making |
| title_fullStr | Rough <i>q</i>-Rung Orthopair Fuzzy Sets and Their Applications in Decision-Making |
| title_full_unstemmed | Rough <i>q</i>-Rung Orthopair Fuzzy Sets and Their Applications in Decision-Making |
| title_short | Rough <i>q</i>-Rung Orthopair Fuzzy Sets and Their Applications in Decision-Making |
| title_sort | rough i q i rung orthopair fuzzy sets and their applications in decision making |
| topic | <i>q</i>-rung orthopair fuzzy set <i>q</i>-rung orthopair fuzzy topologies accuracy measure similarity relations decision-making emergency preparedness |
| url | https://www.mdpi.com/2073-8994/13/11/2010 |
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