Transitive closures of ternary fuzzy relations
- Author
- Lemnaouar Zedam and Bernard De Baets (UGent)
- Organization
- 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.
- Keywords
- General Computer Science, Computational Mathematics, Ternary fuzzy relation, relational composition, transitivity, transitive closure, REPRESENTATION
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8715191
- MLA
- Zedam, Lemnaouar, and Bernard De Baets. “Transitive Closures of Ternary Fuzzy Relations.” INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS, vol. 14, no. 1, 2021, pp. 1784–95, doi:10.2991/ijcis.d.210607.001.
- APA
- Zedam, L., & De Baets, B. (2021). Transitive closures of ternary fuzzy relations. INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS, 14(1), 1784–1795. https://doi.org/10.2991/ijcis.d.210607.001
- Chicago author-date
- Zedam, Lemnaouar, and Bernard De Baets. 2021. “Transitive Closures of Ternary Fuzzy Relations.” INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 14 (1): 1784–95. https://doi.org/10.2991/ijcis.d.210607.001.
- Chicago author-date (all authors)
- Zedam, Lemnaouar, and Bernard De Baets. 2021. “Transitive Closures of Ternary Fuzzy Relations.” INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 14 (1): 1784–1795. doi:10.2991/ijcis.d.210607.001.
- Vancouver
- 1.Zedam L, De Baets B. Transitive closures of ternary fuzzy relations. INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS. 2021;14(1):1784–95.
- IEEE
- [1]L. Zedam and B. De Baets, “Transitive closures of ternary fuzzy relations,” INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS, vol. 14, no. 1, pp. 1784–1795, 2021.
@article{8715191,
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.}},
author = {{Zedam, Lemnaouar and De Baets, Bernard}},
issn = {{1875-6891}},
journal = {{INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS}},
keywords = {{General Computer Science,Computational Mathematics,Ternary fuzzy relation,relational composition,transitivity,transitive closure,REPRESENTATION}},
language = {{eng}},
number = {{1}},
pages = {{1784--1795}},
title = {{Transitive closures of ternary fuzzy relations}},
url = {{http://doi.org/10.2991/ijcis.d.210607.001}},
volume = {{14}},
year = {{2021}},
}
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