Arithmetic Fuzzy Logic-based Representation approach versus Conventional Fuzzy Theory for modeling and analysis in fully fuzzy environment

The paper presents further development of the Arithmetic Fuzzy Logic-based Representation using the notion of 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 between the proposed Arithmetic Fuzzy Logic-based Representation technique and 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 multiplication and division operations after ignoring the second order relative variations terms. However, the suggested approach offers additional advantages of linearity, reversibility, simplicity, and applicability. Application of the proposed Arithmetic Fuzzy Logic-based Representation to a Case Study of a fuzzy PERT problem is presented to demonstrate the efficacy of the proposed technique. Finally, it is pointed out that, for similar situations, the solution of the Conventional Fuzzy Theory is very cumbersome and is completely impractical for high dimensional systems.