Most of the life cycle cost of a product can be pre-determined by the end of the conceptual design phase, which begins with the establishment of a function structure by decomposing an overall function into a set of sub-functions. However, today's products have become complex and accordingly entail intricate function structures that consist of a number of sub-functions; each of them is elaborated by its own design principles. Because of the existence of many choices for design principles of a sub-function, many combinations are possible to satisfy the requirements of the overall function. It is therefore necessary to narrow down the large set of combinations to a manageable size while minimizing the loss of compatible (feasible and preferable) combinations in order to prepare a set of design concept alternatives for the design concept selection phase. Furthermore, since the design concept elaboration process requires a large body of intensive and multidisciplinary knowledge, it is practically performed through the collaboration of different design teams having their own tastes, their own individuality and different design identities about a design; in other words, design teams design their subfunctions according to their own local criteria even though they take into account the overall functionality and global criteria. Another difficulty during the conceptual design stage is that information about the design problem is limited and imperfect due to incompleteness, vagueness and uncertainty while the impact of decisions is so crucial. Considering the above characteristics and complexities of collaborative conceptual design problems, this thesis first introduces three heuristics: (i) pair-wise comparison, (ii) unified domain approach and (iii) domain set ordering heuristic to extract the set of compatible combinations of design principles from all possible combinations considering global design constraints and each design team's local criteria. Subsequently this thesis presents a robust decision support method to select design concepts taking into account multiple participants and their global criteria in order to minimize the need for critical refinement and serious modifications of the design at the subsequent design phase. Finally, the functionality of a COllaborative COnceptual DEsign support system (CO2DE) based on the proposed methods is demonstrated with a case study of a robotic vacuum cleaner design. CO2DE can speed up the overall product design process by reducing design iterations and help the company gain competitive advantage in the long run.