A Numerical Approach For The Algebra of Two-Fold 2×2 Fuzzy Real Matrices and Anti Fuzzy Matrices

This paper is dedicated to study for the first time the concept of square 2 × 2 fuzzy and anti-fuzzy two-fold matrix with real entries, where we present the two-fold algebraic operations between the these matrices and obtain their special properties such as associativity, commutative properties, and the existing of additive of multiplicative inverses. Also, we provide many examples to explain the two-fold algebraic properties and the two-fold algebraic structure.