Decision-making under uncertainty remains a key issue in Machine Learning (ML), particularly in the deployment of safety-critical systems, where reliable quantification of system behavior is essential for evaluating behavioral impacts and strengthening confidence in ML models. This contribution, influenced by fuzzy set theory and grounded in Bayesian statistics, addresses challenges related to data precision and the performance-accuracy trade-off in Bayesian inference (BI). To this end, we introduce a possibility-based contrastive grade of prediction as an alternative quantification method to existing latent posterior-based approaches for parameter estimation (approximation) and model selection. Unlike conventional Bayesian inference, which represents uncertainty within the probabilistic framework, the proposed model adopts a possibility-based representation that allows uncertain and potentially conflicting information to be characterized more flexibly. Rather than focusing on isolated aspects of a problem, the resulting mathematical framework provides a systematic approach to data mining while mitigating overly confident, yet implausible predictions generated by highly specialized deep learning architectures.