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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4785 |