On Preservation of Residuated Lattice Properties for Partial Algebras

DOI

10.2991/asum.k.210827.054How to use a DOI?

Keywords

Residuated lattice structures, Properties, Partial fuzzy set theory, Partial fuzzy logic, Undefined values

Abstract

This paper concentrates on investigating the preservation of the axioms and essential properties of residuated lattices in partial fuzzy set theory. We consider seven most-known partial algebras dealing with undefined values such as the Bochvar, Bochvar external, Sobociński, McCarthy, Nelson, Kleene, Łukasiewicz, and additional, two recent ones, namely the Lower estimation algebra and the Dragonfly algebra. We provide the sketch of proofs in details for the preservation of considered axioms and properties in these algebras. The paper concludes with the tables summarizing the results, which visibly show how close is a partial algebra to a residuated lattice.

Copyright

© 2021, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Nhung Cao
AU  - Martin Štěpnička
PY  - 2021
DA  - 2021/08/30
TI  - On Preservation of Residuated Lattice Properties for Partial Algebras
BT  - Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
PB  - Atlantis Press
SP  - 405
EP  - 412
SN  - 2589-6644
UR  - https://doi.org/10.2991/asum.k.210827.054
DO  - 10.2991/asum.k.210827.054
ID  - Cao2021
ER  -