This paper presents further development of the arithmetic fuzzy logic-based representation. The concept was originally proposed by Gabr and Dorrah for linear and nonlinear system using the notion of the normalized fuzzy matrices. The investigation is based on the dual cell representation, expressed by replacing each parameter with a pair of parentheses, the first is the actual value and the second is corresponding fuzzy level. The analogy of the proposed Arithmetic Fuzzy Logic-based Representation technique with the Conventional Fuzzy Theory are derived for various cases of operations of
addition, subtraction, multiplication and division. It is shown that the suggested approach is identical to that of the conventional fuzzy theory for addition operations and gives average weighted fuzziness interval results of the subtraction operations. Moreover, it yields similar results of multiplications and divisions operations after ignoring the second order relative variations terms. Finally, the suggested approach is demonstrated to offer additional advantages of linearity, reversibility, simplicity, and applicability.