Quaternion Fuzzy Numbers
This paper explores the extension of fuzzy real numbers to fuzzy quaternion numbers, aiming to enhance our understanding of their properties and establish results similar to those in Mathematical Analysis. The concept of quaternions, introduced by William Rowan Hamilton in 1837, provided a powerful algebraic framework for managing vectors in two-dimensional space. Hamilton’s non-commutative algebra of quaternions made significant contributions to physics, mathematics, computer graphics, engineering, and theoretical physics. The study of fuzzy complex numbers, initiated by Buckley in 1989 and further developed by Zhang in 1992, demonstrated closure under arithmetic operations and similarities with Mathematical Analysis. Building on these advancements, Tamir proposed an axiomatic approach to fuzzy complex numbers in 2011, paving the way for the extension of these concepts to fuzzy quaternion numbers. In 2013, Moura et al. [3] developed the concept of fuzzy quaternion numbers as a natural extension of fuzzy real numbers and discuss some important concepts such as their arithmetic properties, distance, supremum, infimum and limit of sequences. Fuzzy number, it was shown that these numbers have important metrical properties, on quaternion and aggregation operator. This article is an extension of the work carried out by [3] on the construction of fuzzy quaternion numbers. In this continuation, we explore new arithmetic and algebraic properties of fuzzy quaternions. We present new metric, supremum, and infimum properties, and further investigate sequences of fuzzy quaternion numbers in more detail.
Index Terms– quaternions fuzzy numbers, fuzzy, analysis fuzzy
