Traces of Ternary Relations Based on Bandler–Kohout Compositions
Recently, we have introduced and studied all possible four-point compositions (one degree of freedom) and five-point compositions (two degrees of freedom) of ternary relations in analogy with the usual composition of binary relations. In this paper, we introduce and study new types of compositions o...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/7/952 |
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| author | Lemnaouar Zedam Hamza Boughambouz Bernard De Baets |
| author_facet | Lemnaouar Zedam Hamza Boughambouz Bernard De Baets |
| author_sort | Lemnaouar Zedam |
| collection | DOAJ |
| description | Recently, we have introduced and studied all possible four-point compositions (one degree of freedom) and five-point compositions (two degrees of freedom) of ternary relations in analogy with the usual composition of binary relations. In this paper, we introduce and study new types of compositions of ternary relations inspired by the compositions of binary relations introduced by Bandler and Kohout (BK-compositions, for short). Moreover, we pay particular attention to the link between BK-compositions and the traces of binary relations and use it as source of inspiration to introduce traces of ternary relations. Moreover, we show that these new notions of BK-compositions and traces are useful tools to solve some relational equations in an unknown ternary relation. |
| first_indexed | 2024-04-24T10:40:09Z |
| format | Article |
| id | doaj.art-6a64b1396a2d4365b9f54a5cd0194382 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-24T10:40:09Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6a64b1396a2d4365b9f54a5cd01943822024-04-12T13:22:28ZengMDPI AGMathematics2227-73902024-03-0112795210.3390/math12070952Traces of Ternary Relations Based on Bandler–Kohout CompositionsLemnaouar Zedam0Hamza Boughambouz1Bernard De Baets2KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure Links 653, B-9000 Gent, BelgiumKERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure Links 653, B-9000 Gent, BelgiumKERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure Links 653, B-9000 Gent, BelgiumRecently, we have introduced and studied all possible four-point compositions (one degree of freedom) and five-point compositions (two degrees of freedom) of ternary relations in analogy with the usual composition of binary relations. In this paper, we introduce and study new types of compositions of ternary relations inspired by the compositions of binary relations introduced by Bandler and Kohout (BK-compositions, for short). Moreover, we pay particular attention to the link between BK-compositions and the traces of binary relations and use it as source of inspiration to introduce traces of ternary relations. Moreover, we show that these new notions of BK-compositions and traces are useful tools to solve some relational equations in an unknown ternary relation.https://www.mdpi.com/2227-7390/12/7/952ternary relationBandler–Kohout compositionstraces |
| spellingShingle | Lemnaouar Zedam Hamza Boughambouz Bernard De Baets Traces of Ternary Relations Based on Bandler–Kohout Compositions Mathematics ternary relation Bandler–Kohout compositions traces |
| title | Traces of Ternary Relations Based on Bandler–Kohout Compositions |
| title_full | Traces of Ternary Relations Based on Bandler–Kohout Compositions |
| title_fullStr | Traces of Ternary Relations Based on Bandler–Kohout Compositions |
| title_full_unstemmed | Traces of Ternary Relations Based on Bandler–Kohout Compositions |
| title_short | Traces of Ternary Relations Based on Bandler–Kohout Compositions |
| title_sort | traces of ternary relations based on bandler kohout compositions |
| topic | ternary relation Bandler–Kohout compositions traces |
| url | https://www.mdpi.com/2227-7390/12/7/952 |
| work_keys_str_mv | AT lemnaouarzedam tracesofternaryrelationsbasedonbandlerkohoutcompositions AT hamzaboughambouz tracesofternaryrelationsbasedonbandlerkohoutcompositions AT bernarddebaets tracesofternaryrelationsbasedonbandlerkohoutcompositions |