A Novel Neutrosophic Distributional Competitiveness Index (NDCI) for Evaluating Time-Honored Brands under Digital Transformation: A Case Study of Anhui, China

In the era of rapid digital transformation, traditional brand ecosystems face growing uncertainty in competitiveness evaluation, especially in historically rich regions such as Anhui, China. This paper introduces a novel Neutrosophic Distributional Competitiveness Index (NDCI) based entirely on neutrosophic set theory, proposing a fully original mathematical framework for handling truth, indeterminacy, and falsity in multi-dimensional competitiveness factors. The NDCI leverages Neutrosophic Joint and Marginal Distributions to model complex interrelations among digital competitiveness criteria such as innovation adaptability, market perception, online influence, and heritage reputation under indeterminate environments. Furthermore, we incorporate complex-valued neutrosophic variables to handle periodic fluctuations and asymmetric digital transitions often observed in legacy brand behaviors. The proposed model is applied as a detailed case study on time-honored brands in Anhui province, where we quantify and visualize the neutrosophic truth (T), indeterminacy (I), and falsity (F) levels associated with each competitiveness component. Analytical equations are fully derived, and the modeling process is supported by a rigorous numerical example, tabulated datasets, and verification procedures. This paper contributes a unique perspective by creating a mathematically sound, logically complete, and contextually relevant methodology rooted entirely in neutrosophic theory unexplored previously in this specific application. The proposed index has implications for strategic brand resilience planning and digital transformation benchmarking under uncertainty.