(untitled) (Contemporary Mathematics, 2025)
An effective transportation system is fundamental for socioeconomic development, public safety, and environmental sustainability. A critical component of such a system is the Vehicle Selection Problem (VSP), which is inherently a Complex Decision-Making (CDM) problem due to conflicting and uncertain criteria such as fuel efficiency, purchase cost, maintenance cost, and warranty. To address this complexity, this study develops two novel logarithmic-based distance measures within the q-Rung Orthopair Fuzzy (q-ROF) framework. The proposed distance metrics incorporate membership, non-membership, and hesitation degrees, along with the cardinality of the universe of discuss, ensuring a more comprehensive representation of uncertainty. Their metric properties are rigorously proven, and they are integrated with the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to solve a VSP. The case study involving seven vehicle brands and seven evaluation criteria, assessed by domain experts, demonstrates the effectiveness of the proposed approach. Comparative analysis with existing logarithmic-based distance measures shows that the new methods provide superior accuracy, stability, and discrimination ability in ranking alternatives. The findings highlight the practical significance of the proposed q-ROF distance measures, offering a robust decision-support tool for vehicle selection and other CDM scenarios under uncertainty.