In multi-objective optimization, the utility function plays a critical role in aligning solutions with the priorities and satisfaction of decision-makers (DMs). Traditional approaches often assume a single utility function for each objective function. However, in practical decision-making environments, each objective may have multiple utility functions due to varying priorities, constraints, and uncertainties. This chapter presents a Bayesian-based model for multi-objective optimization, where each objective function is associated with multiple utility functions. By inducing the probability of utilities and handling uncertainty, the model enhances decision-making in complex and practical environments. Illustrative examples demonstrate its effectiveness in both dependent and independent variable scenarios.