Fuzzy Octonion Numbers: Some Analytical Properties

Abstract

An algebric result states that the sets of real, complex, quaternion and octonion numbers are the only normed division algebras. The mathematical analysis results concerning fuzzy and interval real, complex and quaternion numbers have been extensively studied in the literature. Thereby, it is natural to explore and study the fuzzy and interval extension for the last normed division algebra: The octonions. In this manuscript we show and discuss some important concepts and properties of mathematical analysis with respect to fuzzy and interval octonion numbers, namely, the existence of partial orders, metrics, supremum and infimun and limit of sequences of fuzzy octonion numbers. This work complete the picture of the study of the fuzzy mathematical analysis related to the normed division algebras since the sedenions are not an integral domain.