Traces of Ternary Relations Based on Bandler–Kohout Compositions

Lemnaouar Zedam (), Hamza Boughambouz and Bernard De Baets
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Lemnaouar Zedam: KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure Links 653, B-9000 Gent, Belgium
Hamza Boughambouz: KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure Links 653, B-9000 Gent, Belgium
Bernard De Baets: KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure Links 653, B-9000 Gent, Belgium

Mathematics, 2024, vol. 12, issue 7, 1-17

Abstract: 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.

Keywords: ternary relation; Bandler–Kohout compositions; traces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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