Revolutionizing Fuzzy Modelling through Graded Mean Integration using Python

Abstract

The research introduces a novel approach to optimize the Economic Order Quantity (EOQ) models in fuzzy modelling systems by incorporating Graded Mean Integration (GMI). Traditional EOQ models are extended by considering fuzzy parameters, such as the ordering cost and holding cost, which are represented by triangular fuzzy numbers. The total inventory cost is formulated with fuzzy parameters and then integrated using the GMI approach to handle the uncertainty in the cost components. The resulting fuzzy modelling cost function is differentiated to obtain the optimal lot size under fuzzy conditions. The study presents the solution to the problem through partial derivatives, considering the defuzzification process using GMI. The optimization process is carried out by solving for the fuzzy optimal order quantity, and the results demonstrate the effectiveness of the GMI approach in determining the most cost-effective modelling policy under uncertain conditions. Python-based visualizations are utilized to illustrate the fuzzy modelling cost curve, the impact of fuzzy parameters on the optimal order quantity, and the defuzzification process, providing a clear understanding of the model's behavior. These visual tools enhance the decision-making process by offering graphical representations of the cost dynamics in fuzzy environments. This method provides a more realistic and flexible approach to inventory management, particularly when dealing with imprecise data in real-world scenarios.