Decision-Making Approach with Fuzzy Type-2 Soft Graphs
Molodtsov’s theory of soft sets is free from the parameterizations insufficiency of fuzzy set theory. Type-2 soft set as an extension of a soft set has an essential mathematical structure to deal with parametrizations and their primary relationship. Fuzzy type-2 soft models play a key role to study...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/8872446 |
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| author | Sundas Shahzadi Musavarah Sarwar Muhammad Akram |
| author_facet | Sundas Shahzadi Musavarah Sarwar Muhammad Akram |
| author_sort | Sundas Shahzadi |
| collection | DOAJ |
| description | Molodtsov’s theory of soft sets is free from the parameterizations insufficiency of fuzzy set theory. Type-2 soft set as an extension of a soft set has an essential mathematical structure to deal with parametrizations and their primary relationship. Fuzzy type-2 soft models play a key role to study the partial membership and uncertainty of objects along with underlying and primary set of parameters. In this research article, we introduce the concept of fuzzy type-2 soft set by integrating fuzzy set theory and type-2 soft set theory. We also introduce the notions of fuzzy type-2 soft graphs, regular fuzzy type-2 soft graphs, irregular fuzzy type-2 soft graphs, fuzzy type-2 soft trees, and fuzzy type-2 soft cycles. We construct some operations such as union, intersection, AND, and OR on fuzzy type-2 soft graphs and discuss these concepts with numerical examples. The fuzzy type-2 soft graph is an efficient model for dealing with uncertainty occurring in vertex-neighbors structure and is applicable in computational analysis, applied intelligence, and decision-making problems. We study the importance of fuzzy type-2 soft graphs in chemical digestion and national engineering services. |
| format | Article |
| id | doaj-art-d2d820796a204bb8bff8e4429db7d531 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-d2d820796a204bb8bff8e4429db7d5312025-02-03T05:52:30ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/88724468872446Decision-Making Approach with Fuzzy Type-2 Soft GraphsSundas Shahzadi0Musavarah Sarwar1Muhammad Akram2Division of Science and Technology, University of Education, Lahore 54000, PakistanDepartment of Mathematics, Government College Women University, Sialkot, PakistanDepartment of Mathematics, University of the Punjab, New Campus, Lahore, PakistanMolodtsov’s theory of soft sets is free from the parameterizations insufficiency of fuzzy set theory. Type-2 soft set as an extension of a soft set has an essential mathematical structure to deal with parametrizations and their primary relationship. Fuzzy type-2 soft models play a key role to study the partial membership and uncertainty of objects along with underlying and primary set of parameters. In this research article, we introduce the concept of fuzzy type-2 soft set by integrating fuzzy set theory and type-2 soft set theory. We also introduce the notions of fuzzy type-2 soft graphs, regular fuzzy type-2 soft graphs, irregular fuzzy type-2 soft graphs, fuzzy type-2 soft trees, and fuzzy type-2 soft cycles. We construct some operations such as union, intersection, AND, and OR on fuzzy type-2 soft graphs and discuss these concepts with numerical examples. The fuzzy type-2 soft graph is an efficient model for dealing with uncertainty occurring in vertex-neighbors structure and is applicable in computational analysis, applied intelligence, and decision-making problems. We study the importance of fuzzy type-2 soft graphs in chemical digestion and national engineering services.http://dx.doi.org/10.1155/2020/8872446 |
| spellingShingle | Sundas Shahzadi Musavarah Sarwar Muhammad Akram Decision-Making Approach with Fuzzy Type-2 Soft Graphs Journal of Mathematics |
| title | Decision-Making Approach with Fuzzy Type-2 Soft Graphs |
| title_full | Decision-Making Approach with Fuzzy Type-2 Soft Graphs |
| title_fullStr | Decision-Making Approach with Fuzzy Type-2 Soft Graphs |
| title_full_unstemmed | Decision-Making Approach with Fuzzy Type-2 Soft Graphs |
| title_short | Decision-Making Approach with Fuzzy Type-2 Soft Graphs |
| title_sort | decision making approach with fuzzy type 2 soft graphs |
| url | http://dx.doi.org/10.1155/2020/8872446 |
| work_keys_str_mv | AT sundasshahzadi decisionmakingapproachwithfuzzytype2softgraphs AT musavarahsarwar decisionmakingapproachwithfuzzytype2softgraphs AT muhammadakram decisionmakingapproachwithfuzzytype2softgraphs |