Accelerated development in the field of electronics and integrated circuit technology further pushed the need for better heat dissipating devices with reduced component dimensions. In the design optimization of microchannel heat transfer systems, multiple objectives must be satisfied but correlations limit the satisfaction levels. End users define their preferences associated with the desired quality/quantity of each parameter and specify the priorities among each preference. In this paper, an optimization strategy based on the prioritized performances is developed to find the optimal design variables for the preferences in three different aspects namely: minimized thermal resistances, minimized pressure drop, and maximized heat flux. The preferences are often fuzzy and correlated but can be modeled mathematically using Gaussian membership functions with respect to different levels of user preferences. The overall performances are maximized to find the most favorable solution on the Pareto frontier. Two different types of single-phase liquid cooling (straight and U-shaped microchannel heat sinks) have been utilized as heat exchangers of electronic chips and made as practical examples for the proposed optimization strategy. The optimal design points vary with respect to the priorities of the preferences. The proposed methodology finds the most favored solution on the Pareto frontiers. It is novel to reveal that the chosen significant factors were maximized with results yielding to lower thermal resistance, lower pressure drop, and higher heat flux in the microchannel heat sink based on the design preferences with different priorities.