A Hybrid IVPNS–TOPSIS Framework for Optimizing Gig Economy Logistics: A Sensitivity and Comparative Study

This paper proposes a novel hybrid decision-support system for the selection of delivery agents in gig economy (GE) logistics under uncertainty. The proposed method combines interval-valued Pythagorean neutrosophic sets (IVPNS) and an improved Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to simultaneously represent the truth, uncertainty, and falsehood of linguistic assessments. Compared to existing neutrosophic multi-criteria decision-making (MCDM) methods, the proposed approach encompasses a robust aggregation method and a stability-based ranking procedure to efficiently handle ambiguous and inconsistent data. The relevance of the model is illustrated through a case study based on real-world scenarios where several delivery agents are evaluated using key performance indicators such as delivery speed, customer satisfaction, professionalism, availability, and delivery costs. The results indicate that the comparative evaluation among classical TOPSIS, fuzzy TOPSIS, intuitionistic fuzzy TOPSIS, and VIKOR shows strong agreement, confirmed by a high Spearman rank correlation coefficient. The proposed IVPN-TOPSIS framework provides a reliable, flexible, and computationally efficient decision-support mechanism, significantly enhancing decision accuracy and consistency in highly unpredictable GE logistics settings. The framework is well-suited to a wide range of complex real-world decision-making problems characterized by uncertainty and lack of information.