Non-linear interval-valued intuitionistic fuzzy number (IVIFN) approach for an EPQ model with optimal investment in defective items considering learning effects

Abstract

In recent years, research has primarily focused on addressing imprecision in linear forms; however, uncertainty often occurs in non-linear forms as well. This study extends the concept of Linear Interval-Valued Intuitionistic Fuzzy Numbers (LIVIFN) to Non-Linear Interval-Valued Intuitionistic Fuzzy Numbers (NLIVIFN), establishing their formulation and parametric structure along with their logical significance. Different geometric representations of NLIVIFN are analysed and classified. Furthermore, an intuitification technique is developed, which holds significant value for improving crispification skills. A realistic example is presented to demonstrate the impact of NLIVIFN on an Economic Production Quantity (EPQ) model, focusing on an imperfect product with learning and reworking of defective items. A procedure is introduced to determine the optimal shipment size and defective percentage by minimizing the average expected total cost. Results indicate that investment in learning leads to a 98% recovery rate of defective items, providing economic benefits to manufacturers. Additionally, a 50% increase in demand stimulates learning, increasing production by 36% and reducing defective item production by 51%. Finally, a comparative analysis underscores the value of this novel work, showcasing its effectiveness in addressing non-linear uncertainties and enhancing production processes, cost efficiency, and decision-making in supply chain management.