A Generalized Definition of Fuzzy Subrings
In this study, under the condition that L is a completely distributive lattice, a generalized definition of fuzzy subrings is introduced. By means of four kinds of cut sets of fuzzy subset, the equivalent characterization of L-fuzzy subring measures are presented. The properties of L-fuzzy subring m...
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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/10.1155/2022/5341207 |
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| _version_ | 1832549019887337472 |
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| author | Ying-Ying An Fu-Gui Shi Lan Wang |
| author_facet | Ying-Ying An Fu-Gui Shi Lan Wang |
| author_sort | Ying-Ying An |
| collection | DOAJ |
| description | In this study, under the condition that L is a completely distributive lattice, a generalized definition of fuzzy subrings is introduced. By means of four kinds of cut sets of fuzzy subset, the equivalent characterization of L-fuzzy subring measures are presented. The properties of L-fuzzy subring measures under these two kinds of product operations are further studied. In addition, an L-fuzzy convexity is directly induced by L-fuzzy subring measure, and it is pointed out that ring homomorphism can be regarded as L-fuzzy convex preserving mapping and L-fuzzy convex-to-convex mapping. Next, we give the definition and related properties of the measure of L-fuzzy quotient ring and give a new characterization of L-fuzzy quotient ring when the measure of L-fuzzy quotient ring is 1. |
| format | Article |
| id | doaj-art-3b4cd75c2e2445ab875390ad79214ef2 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-3b4cd75c2e2445ab875390ad79214ef22025-02-03T06:12:26ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/5341207A Generalized Definition of Fuzzy SubringsYing-Ying An0Fu-Gui Shi1Lan Wang2School of Mathematical ScienceSchool of Mathematical ScienceSchool of Mathematical ScienceIn this study, under the condition that L is a completely distributive lattice, a generalized definition of fuzzy subrings is introduced. By means of four kinds of cut sets of fuzzy subset, the equivalent characterization of L-fuzzy subring measures are presented. The properties of L-fuzzy subring measures under these two kinds of product operations are further studied. In addition, an L-fuzzy convexity is directly induced by L-fuzzy subring measure, and it is pointed out that ring homomorphism can be regarded as L-fuzzy convex preserving mapping and L-fuzzy convex-to-convex mapping. Next, we give the definition and related properties of the measure of L-fuzzy quotient ring and give a new characterization of L-fuzzy quotient ring when the measure of L-fuzzy quotient ring is 1.http://dx.doi.org/10.1155/2022/5341207 |
| spellingShingle | Ying-Ying An Fu-Gui Shi Lan Wang A Generalized Definition of Fuzzy Subrings Journal of Mathematics |
| title | A Generalized Definition of Fuzzy Subrings |
| title_full | A Generalized Definition of Fuzzy Subrings |
| title_fullStr | A Generalized Definition of Fuzzy Subrings |
| title_full_unstemmed | A Generalized Definition of Fuzzy Subrings |
| title_short | A Generalized Definition of Fuzzy Subrings |
| title_sort | generalized definition of fuzzy subrings |
| url | http://dx.doi.org/10.1155/2022/5341207 |
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