Maximal Ideal and Prime Ideal in an L-lattice
In this paper, the notions of an L-sublattice, L-ideal, and L-dual ideal of an L-lattice are introduced. The concepts of an L-maximal ideal and an L-prime ideal in an L-lattice are also defined. The present paper also gives the precise structures of an L-sublattice, L-ideal (dual ideal) generated by...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Tsinghua University Press
2024-09-01
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| Series: | Fuzzy Information and Engineering |
| Subjects: | |
| Online Access: | https://www.sciopen.com/article/10.26599/FIE.2024.9270044 |
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| Summary: | In this paper, the notions of an L-sublattice, L-ideal, and L-dual ideal of an L-lattice are introduced. The concepts of an L-maximal ideal and an L-prime ideal in an L-lattice are also defined. The present paper also gives the precise structures of an L-sublattice, L-ideal (dual ideal) generated by an L-subset of an L-lattice. Finally, it is proved that under certain conditions, an L-maximal ideal in an L-lattice is L-prime. It is important to note that, in our studies, the evaluation lattice changes from [0,1] to a lattice L and the parent structure shifts from an ordinary lattice to an L-lattice. |
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| ISSN: | 1616-8658 1616-8666 |