On the algebra of possibly paraconsistent sets
In this paper we define the notion of possibly paraconsistent sets. We introduce algebraic operations on them and we analyze their properties. Moreover, it is shown that our class can be considered as isomorphic to the classes of intuitionistic and weak rough sets (with the assumption that intersect...
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| Language: | English |
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University of New Mexico
2024-11-01
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| Series: | Neutrosophic Sets and Systems |
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| Online Access: | https://fs.unm.edu/NSS/51Witczak_Tomasz_PossiblyParaconsistentSets.pdf |
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| author | Tomasz Witczak |
| author_facet | Tomasz Witczak |
| author_sort | Tomasz Witczak |
| collection | DOAJ |
| description | In this paper we define the notion of possibly paraconsistent sets. We introduce algebraic operations on them and we analyze their properties. Moreover, it is shown that our class can be considered as isomorphic to the classes of intuitionistic and weak rough sets (with the assumption that intersection, union and complement are understood in an appropriate manner). Hence, the framework of paraconsistent sets can be treated as a new semantics for three-valued logic. Two less typical operations on possibly paraconsistent sets are studied too. They do not give us de Morgan algebra but rather a bisemilattice with only one absorption law. Finally, we pay attention to the fact that possibly paraconsistent sets can be treated as neutrosophic crisp sets of type 2. As for the exact isomorphism, it should be a matter of further research. |
| format | Article |
| id | doaj-art-8ec6b4d70bf345ce881b6fdf3730c79a |
| institution | Kabale University |
| issn | 2331-6055 2331-608X |
| language | English |
| publishDate | 2024-11-01 |
| publisher | University of New Mexico |
| record_format | Article |
| series | Neutrosophic Sets and Systems |
| spelling | doaj-art-8ec6b4d70bf345ce881b6fdf3730c79a2025-08-24T16:14:34ZengUniversity of New MexicoNeutrosophic Sets and Systems2331-60552331-608X2024-11-017363364810.5281/zenodo.13989349On the algebra of possibly paraconsistent setsTomasz WitczakIn this paper we define the notion of possibly paraconsistent sets. We introduce algebraic operations on them and we analyze their properties. Moreover, it is shown that our class can be considered as isomorphic to the classes of intuitionistic and weak rough sets (with the assumption that intersection, union and complement are understood in an appropriate manner). Hence, the framework of paraconsistent sets can be treated as a new semantics for three-valued logic. Two less typical operations on possibly paraconsistent sets are studied too. They do not give us de Morgan algebra but rather a bisemilattice with only one absorption law. Finally, we pay attention to the fact that possibly paraconsistent sets can be treated as neutrosophic crisp sets of type 2. As for the exact isomorphism, it should be a matter of further research.https://fs.unm.edu/NSS/51Witczak_Tomasz_PossiblyParaconsistentSets.pdfpossibly paraconsistent setsneutrosophic setsintuitionistic setsweak rough sets |
| spellingShingle | Tomasz Witczak On the algebra of possibly paraconsistent sets Neutrosophic Sets and Systems possibly paraconsistent sets neutrosophic sets intuitionistic sets weak rough sets |
| title | On the algebra of possibly paraconsistent sets |
| title_full | On the algebra of possibly paraconsistent sets |
| title_fullStr | On the algebra of possibly paraconsistent sets |
| title_full_unstemmed | On the algebra of possibly paraconsistent sets |
| title_short | On the algebra of possibly paraconsistent sets |
| title_sort | on the algebra of possibly paraconsistent sets |
| topic | possibly paraconsistent sets neutrosophic sets intuitionistic sets weak rough sets |
| url | https://fs.unm.edu/NSS/51Witczak_Tomasz_PossiblyParaconsistentSets.pdf |
| work_keys_str_mv | AT tomaszwitczak onthealgebraofpossiblyparaconsistentsets |