Designing mechatronic systems is known to be a very complex and tedious process due to the high number of system components, their multi-physical aspects, the couplings between the different domains involved in the product, and the interacting design objectives. This inherent complexity calls for the crucial need of a systematic and multi-objective design thinking methodology to replace the often-used sequential design approach that tends to deal with the different domains and their corresponding design objectives separately leading to functional but not necessarily optimal designs. Thus, a new approach based on a multi-criteria profile for mechatronic systems is presented in this paper for the conceptual design stage. Additionally, to facilitate fitting the intuitive requirements for decision-making in the presence of interacting criteria, three different methods are proposed and compared using a case study of designing a vision-guided quadrotor drone system. These methods benefit from three different aggregation techniques such as Choquet integral, Sugeno integral and fuzzy-based neural network. To validate the decision yielded by the results of global concept score for each aggregation methods, a computer simulation of a visual servoing system on all design alternatives for quadrotor drone has been performed. It is shown that although the Sugeno fuzzy can be a useful aggregation function for decisions under uncertainty, but the approaches using Choquet fuzzy and fuzzy integral-based neural network seem to be more precise and reliable in a multi-criteria design problem where interaction between the objectives cannot be overlooked.