Three-Dimensional Expansion and Graphical Concept of Generalized Triangular Fuzzy Set
We have studied the extended algebraic operations between two fuzzy numbers and calculated Zadeh’s max-min composition operator for two generalized triangular fuzzy sets in ℝ2. And we generalized the triangular fuzzy numbers from ℝ2 to ℝ3. We prove that the result of the three-dimensional case is an...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/3248127 |
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| _version_ | 1832562325767323648 |
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| author | Yong Sik Yun |
| author_facet | Yong Sik Yun |
| author_sort | Yong Sik Yun |
| collection | DOAJ |
| description | We have studied the extended algebraic operations between two fuzzy numbers and calculated Zadeh’s max-min composition operator for two generalized triangular fuzzy sets in ℝ2. And we generalized the triangular fuzzy numbers from ℝ2 to ℝ3. We prove that the result of the three-dimensional case is an extension of two-dimensional case and presented it in a graph. The extension is proved by showing that the result obtained by restricting the three-dimensional result to two-dimensional result is consistent with the existing two-dimensional result. |
| format | Article |
| id | doaj-art-82c4161a31964c02b5c35cc87aaa256f |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-82c4161a31964c02b5c35cc87aaa256f2025-02-03T01:22:56ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/3248127Three-Dimensional Expansion and Graphical Concept of Generalized Triangular Fuzzy SetYong Sik Yun0Department of MathematicsWe have studied the extended algebraic operations between two fuzzy numbers and calculated Zadeh’s max-min composition operator for two generalized triangular fuzzy sets in ℝ2. And we generalized the triangular fuzzy numbers from ℝ2 to ℝ3. We prove that the result of the three-dimensional case is an extension of two-dimensional case and presented it in a graph. The extension is proved by showing that the result obtained by restricting the three-dimensional result to two-dimensional result is consistent with the existing two-dimensional result.http://dx.doi.org/10.1155/2022/3248127 |
| spellingShingle | Yong Sik Yun Three-Dimensional Expansion and Graphical Concept of Generalized Triangular Fuzzy Set Journal of Mathematics |
| title | Three-Dimensional Expansion and Graphical Concept of Generalized Triangular Fuzzy Set |
| title_full | Three-Dimensional Expansion and Graphical Concept of Generalized Triangular Fuzzy Set |
| title_fullStr | Three-Dimensional Expansion and Graphical Concept of Generalized Triangular Fuzzy Set |
| title_full_unstemmed | Three-Dimensional Expansion and Graphical Concept of Generalized Triangular Fuzzy Set |
| title_short | Three-Dimensional Expansion and Graphical Concept of Generalized Triangular Fuzzy Set |
| title_sort | three dimensional expansion and graphical concept of generalized triangular fuzzy set |
| url | http://dx.doi.org/10.1155/2022/3248127 |
| work_keys_str_mv | AT yongsikyun threedimensionalexpansionandgraphicalconceptofgeneralizedtriangularfuzzyset |