In the context of abstract fuzzy algebra, the study of algebraic structures is undertaken through the employment of fuzzy set theory as a substitute for classical set theory. In this regard, Lie algebra structures are no exception. The present work is thus dedicated to fuzzy Lie algebra structures, which are fundamentally fuzzy vector spaces. The work, comprises a concise collection of results concerning fuzzy bases of a fuzzy Lie algebra, providing necessary and sufficient conditions, and offering illustrative examples to demonstrate the practical application of these results.
Filippone, G., Galici, M., La Rosa, G., Piazza, F., Tabacchi, M.E. (2025). A new definition of fuzzy nilpotent Lie algebras. In 2025 IEEE International Conference on Fuzzy Systems (FUZZ) (pp. 1-5) [10.1109/fuzz62266.2025.11152208].
A new definition of fuzzy nilpotent Lie algebras
Filippone, Giuseppe;Galici, Mario;La Rosa, Gianmarco;Piazza, Federica;Tabacchi, Marco Elio
2025-01-01
Abstract
In the context of abstract fuzzy algebra, the study of algebraic structures is undertaken through the employment of fuzzy set theory as a substitute for classical set theory. In this regard, Lie algebra structures are no exception. The present work is thus dedicated to fuzzy Lie algebra structures, which are fundamentally fuzzy vector spaces. The work, comprises a concise collection of results concerning fuzzy bases of a fuzzy Lie algebra, providing necessary and sufficient conditions, and offering illustrative examples to demonstrate the practical application of these results.
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