Multi-objective linear optimization using fuzzy logic-based arithmetic and visual representations with forward and backward tracking

This paper presents a new formulation of multi-objective linear optimization using the fuzzy logic-based arithmetic (or visual) representations developed originally by Gabr and Dorrah. A modified dual simplex algorithm is proposed as part of the formulation implementation procedure operating in a fully fuzzy environment. Moreover, forward and backward tracking mechanisms are incorporated with the above formulation for fuzzy level management and control. Cognitive mapping is used to describe the interaction between various parameters of the optimization formulation. Applications of the proposed approach to the multi-objective linear optimization of three stand alone electric pump stations of different sizes (Small, Medium and Large) are provided. The implementation is carried out using spread-sheet representation with the suggested optimization algorithms programmed in Visual Basic Applications (VBA). The results demonstrate the high efficacy and applicability of the fuzzy logic-based arithmetic and visual representations for real life problems operating in a fully fuzzy environment.