μ-Fuzzy Filters in Distributive Lattices
In this paper, we introduce the concept of μ-fuzzy filters in distributive lattices. We study the special class of fuzzy filters called μ-fuzzy filters, which is isomorphic to the set of all fuzzy ideals of the lattice of coannihilators. We observe that every μ-fuzzy filter is the intersection of al...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2020/8841670 |
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| Summary: | In this paper, we introduce the concept of μ-fuzzy filters in distributive lattices. We study the special class of fuzzy filters called μ-fuzzy filters, which is isomorphic to the set of all fuzzy ideals of the lattice of coannihilators. We observe that every μ-fuzzy filter is the intersection of all prime μ-fuzzy filters containing it. We also topologize the set of all prime μ-fuzzy filters of a distributive lattice. Properties of the space are also studied. We show that there is a one-to-one correspondence between the class of μ-fuzzy filters and the lattice of all open sets in Xμ. It is proved that the space Xμ is a T0 space. |
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| ISSN: | 1687-7101 1687-711X |