Rough Approximation Operators on a Complete Orthomodular Lattice
This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the distributive law. Furthermore, we study the r...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/3/164 |
| _version_ | 1797520252742926336 |
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| author | Songsong Dai |
| author_facet | Songsong Dai |
| author_sort | Songsong Dai |
| collection | DOAJ |
| description | This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the distributive law. Furthermore, we study the relationship among the distributive law, rough approximation and orthomodular lattice-valued relation. |
| first_indexed | 2024-03-10T07:54:09Z |
| format | Article |
| id | doaj.art-63863507c8e44d76823672f29295b1e6 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T07:54:09Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-63863507c8e44d76823672f29295b1e62023-11-22T12:02:19ZengMDPI AGAxioms2075-16802021-07-0110316410.3390/axioms10030164Rough Approximation Operators on a Complete Orthomodular LatticeSongsong Dai0School of Electronics and Information Engineering, Taizhou University, Taizhou 318000, ChinaThis paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the distributive law. Furthermore, we study the relationship among the distributive law, rough approximation and orthomodular lattice-valued relation.https://www.mdpi.com/2075-1680/10/3/164rough setcomplete orthomodular latticequantum logicdistributive law |
| spellingShingle | Songsong Dai Rough Approximation Operators on a Complete Orthomodular Lattice Axioms rough set complete orthomodular lattice quantum logic distributive law |
| title | Rough Approximation Operators on a Complete Orthomodular Lattice |
| title_full | Rough Approximation Operators on a Complete Orthomodular Lattice |
| title_fullStr | Rough Approximation Operators on a Complete Orthomodular Lattice |
| title_full_unstemmed | Rough Approximation Operators on a Complete Orthomodular Lattice |
| title_short | Rough Approximation Operators on a Complete Orthomodular Lattice |
| title_sort | rough approximation operators on a complete orthomodular lattice |
| topic | rough set complete orthomodular lattice quantum logic distributive law |
| url | https://www.mdpi.com/2075-1680/10/3/164 |
| work_keys_str_mv | AT songsongdai roughapproximationoperatorsonacompleteorthomodularlattice |