Fuzziness and Lie Algebras

Abstract

In this paper a very concise history of the relationship between fuzzy theory is given, from its origins to the fuzzification of algebraic structures, and Lie algebras, with special attention on exploring the use of fuzzy theory to generalise definitions and results of abstract algebra, and a focus on the fuzzification of Lie algebras. In order to reinforce the idea that strong links exist between the two disciplines, focus has been also put on the more recent and intriguing link between the two, namely the transfer principle, with suggestions on how this can be implemented in further research. The paper is meant as a starting point for renewing the discussion and fuelling further research on the topic.