On Fuzzy G* Algebras

Abstract

A matrix with entries that may only have the values 0 or 1 is called a Boolean matrix. A matrix containing members that fall between [0, 1] is called a fuzzy matrix. This study proposes a novel approach to Fuzzy G* algebra (FG*A). A few novel models in the fascinating area of fuzzy algebra have been developed. Because it simply assigns weight to diagonals, other fuzzy algebras have the drawback of not considering the matrix and not being a function of the overall components. To address this lack of thought, this study presents a novel method, the G* algebra of a fuzzy matrix. The unique solution to a particular set of equations can be found using the generalization inverse of a non-singular matrix. Any (potentially rectangular) matrix with complex components has this generalized inverse. Also, this paper demonstrated that Fuzzy G* algebra is always fuzzy dot subalgebra and fuzzy G* Idle algebra.