A new score function for optimizing transportation problems in complex Pythagorean fuzzy environment

Transportation problems are a crucial area in logistics and operations research that focuses on effectively transporting products and resources from origin to destination. The complex nature of real-world situations requires the utilization of advanced mathematical models and optimization approaches to formulate effective solutions. Quantifying the accurate supply, demand, and transportation costs of transportation problems is highly challenging due to the market’s unpredictable economic and environmental conditions. Several methodologies have been proposed to address the issue of transportation problems with uncertain parameters, utilizing fuzzy theory and its derivatives. Complex Pythagorean fuzzy numbers (CPyFNs) are highly suitable and effective for representing uncertain and ambiguous information in real-world scenarios. This article introduces an innovative analysis of transportation problems in the complex Pythagorean fuzzy information framework. Initially,we establish an improved score function value to evaluate the ordering of CPyFNs more precisely and propose several ranking rules. The following section of the study presents mathematical formulations and optimization models for transportation problems, where the parameters are expressed as CPyFNs. The solution approach is formulated using Vogel’s approximation method (VAM) and modified distribution method (MODI) to solve transportation problems in a complex Pythagorean fuzzy setting. An illustrative numerical example is provided to showcase the practicality and effectiveness of the proposed method in real-life scenarios. The significance of the research and the extent of future investigation are also emphasized.