New Algebraic Alternative for Hexagonal Fuzzy Numbers and Its Application in Determine M-P-Inverse Dian Ayu Puspita, Mashadi, Sri Gemawati
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Riau University, Pekanbaru, 28293, Indonesia
Abstract
Various authors have provided multiple alternatives for the algebra of hexagonal fuzzy numbers. One of the fundamental issues with the various algebraic alternatives presented by different authors is the absence of a inverse such that a x a inverse is identity. As a result, many applications of hexagonal fuzzy numbers have consistently yielded incompatible solutions. In this paper, the author constructs a new algebra by using two midpoints for the algebra of multiplication, division, and inversion of arbitrary hexagonal fuzzy numbers. The newly constructed algebra is then developed to determine the M-P-Inverse for any mx n hexagonal fuzzy matrix. Consequently, all applications of hexagonal fuzzy numbers using inverses and M-P-Inverses will yield compatible solutions.
Keywords: Fuzzy number arithmetic, Hexagonal fuzzy numbers, M-P-Inverse
