Similarity of L-fuzzy Relations Based on L-topologies Induced by L-fuzzy Rough Approximation Operators
This paper proposes similarity of L-fuzzy relations based on L-topologies induced by L-fuzzy rough approximation operators. First, the notion L-fuzzy rough set is generalized and the relationship between generalized L-fuzzy rough sets and L-topologies on an arbitrary universe is investigated. It sho...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Tsinghua University Press
2017-03-01
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| Series: | Fuzzy Information and Engineering |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1616865817300730 |
| _version_ | 1797707186588090368 |
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| author | Prasenjit Mandal A.S. Ranadive |
| author_facet | Prasenjit Mandal A.S. Ranadive |
| author_sort | Prasenjit Mandal |
| collection | DOAJ |
| description | This paper proposes similarity of L-fuzzy relations based on L-topologies induced by L-fuzzy rough approximation operators. First, the notion L-fuzzy rough set is generalized and the relationship between generalized L-fuzzy rough sets and L-topologies on an arbitrary universe is investigated. It shows that Alexandrov L-topologies can be induced by L-fuzzy relations without any preconditions. Second, the concept of similarity of L-fuzzy relations is introduced and variations of an L-fuzzy relation are investigated. Third, algebraic structures on similarity of L-fuzzy relations are obtained. Finally, we prove that the subset of the transitive L-fuzzy relations similar to a fixed L-fuzzy relation is a complete distributive lattice. |
| first_indexed | 2024-03-12T06:03:38Z |
| format | Article |
| id | doaj.art-4f34c0c474794f378b3a6f0decdabe7f |
| institution | Directory Open Access Journal |
| issn | 1616-8658 |
| language | English |
| last_indexed | 2024-03-12T06:03:38Z |
| publishDate | 2017-03-01 |
| publisher | Tsinghua University Press |
| record_format | Article |
| series | Fuzzy Information and Engineering |
| spelling | doaj.art-4f34c0c474794f378b3a6f0decdabe7f2023-09-03T03:53:05ZengTsinghua University PressFuzzy Information and Engineering1616-86582017-03-0191214410.1016/j.fiae.2017.03.002Similarity of L-fuzzy Relations Based on L-topologies Induced by L-fuzzy Rough Approximation OperatorsPrasenjit Mandal0A.S. Ranadive1Bhalukdungri Jr. High School, Raigara, Purulia, West Bengal, 723153, IndiaDepartment of Pure and Applied Mathematics, Guru Ghasidas University, Bilaspur, C.G., IndiaThis paper proposes similarity of L-fuzzy relations based on L-topologies induced by L-fuzzy rough approximation operators. First, the notion L-fuzzy rough set is generalized and the relationship between generalized L-fuzzy rough sets and L-topologies on an arbitrary universe is investigated. It shows that Alexandrov L-topologies can be induced by L-fuzzy relations without any preconditions. Second, the concept of similarity of L-fuzzy relations is introduced and variations of an L-fuzzy relation are investigated. Third, algebraic structures on similarity of L-fuzzy relations are obtained. Finally, we prove that the subset of the transitive L-fuzzy relations similar to a fixed L-fuzzy relation is a complete distributive lattice.http://www.sciencedirect.com/science/article/pii/S1616865817300730L-fuzzy relationSimilarityL-topologyGeneralized L-fuzzy rough setGeneralized residuated lattice |
| spellingShingle | Prasenjit Mandal A.S. Ranadive Similarity of L-fuzzy Relations Based on L-topologies Induced by L-fuzzy Rough Approximation Operators Fuzzy Information and Engineering L-fuzzy relation Similarity L-topology Generalized L-fuzzy rough set Generalized residuated lattice |
| title | Similarity of L-fuzzy Relations Based on L-topologies Induced by L-fuzzy Rough Approximation Operators |
| title_full | Similarity of L-fuzzy Relations Based on L-topologies Induced by L-fuzzy Rough Approximation Operators |
| title_fullStr | Similarity of L-fuzzy Relations Based on L-topologies Induced by L-fuzzy Rough Approximation Operators |
| title_full_unstemmed | Similarity of L-fuzzy Relations Based on L-topologies Induced by L-fuzzy Rough Approximation Operators |
| title_short | Similarity of L-fuzzy Relations Based on L-topologies Induced by L-fuzzy Rough Approximation Operators |
| title_sort | similarity of l fuzzy relations based on l topologies induced by l fuzzy rough approximation operators |
| topic | L-fuzzy relation Similarity L-topology Generalized L-fuzzy rough set Generalized residuated lattice |
| url | http://www.sciencedirect.com/science/article/pii/S1616865817300730 |
| work_keys_str_mv | AT prasenjitmandal similarityoflfuzzyrelationsbasedonltopologiesinducedbylfuzzyroughapproximationoperators AT asranadive similarityoflfuzzyrelationsbasedonltopologiesinducedbylfuzzyroughapproximationoperators |