Evidential Probabilities for Rough Set in a Case of Competitiveness

Probabilistic rough set based on statistics and equivalence relations can provide membership, boundary approximations, subsets dependency, criterion dependency, three-way decision, and so forth. However, the probability is non-determinant due to randomness and users choices which is subjective in most cases. This research aims to provide determinant probabilities through relevant evidences on three-way decision, called evidential probabilities for rough set (EPRS) to consider the subjective criteria. In this article a research position highlights the boundary regions in terms of subjective criteria showing how subjective criteria may provide a means to narrow the uncertainty by projecting the boundary regions through user preferences in providing better decision precisions. The idea is also projected on prospect theory by showing the adaptable tuning of reference point through decision based subjective preferences. A case study about nations competitiveness is estimated through EPRS and shows the evidential probability can be identified in reality.