Volume 14, Issue 1, 2021, Pages 1784 - 1795
Transitive Closures of Ternary Fuzzy Relations
Authors
Lemnaouar Zedam1, 2, *, Bernard De Baets2
1Laboratory of Pure and Applied Mathematics, Department of Mathematics, University of M'sila, P.O. Box 166 Ichbilia, 28000, M'sila, Algeria
2KERMIT, Department of Data Analysis and Mathematical Modelling, Ghent University, Coupure Links 653, B-9000, Gent, Belgium
*Corresponding author. Email: lemnaouar.zedam@univ-msila.dz
Corresponding Author
Lemnaouar Zedam
Received 2 June 2020, Accepted 31 May 2021, Available Online 12 June 2021.
- DOI
- 10.2991/ijcis.d.210607.001How to use a DOI?
- Keywords
- Ternary fuzzy relation; relational composition; transitivity; transitive closure
- Abstract
Recently, we have introduced six types of composition of ternary fuzzy relations. These compositions are close in spirit to the composition of binary fuzzy relations. Based on these types of composition, we have introduced several types of transitivity of a ternary fuzzy relation and investigated their basic properties. In this paper, we prove additional properties and characterizations of these types of transitivity of a ternary fuzzy relation. Also, we provide a representation theorem for ternary fuzzy relations satisfying these types of transitivity. Finally, we focus on the problem of closing a ternary fuzzy relation with respect to the proposed types of transitivity.
- Copyright
- © 2021 The Authors. Published by Atlantis Press B.V.
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
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TY - JOUR AU - Lemnaouar Zedam AU - Bernard De Baets PY - 2021 DA - 2021/06/12 TI - Transitive Closures of Ternary Fuzzy Relations JO - International Journal of Computational Intelligence Systems SP - 1784 EP - 1795 VL - 14 IS - 1 SN - 1875-6883 UR - https://doi.org/10.2991/ijcis.d.210607.001 DO - 10.2991/ijcis.d.210607.001 ID - Zedam2021 ER -