Given a location-based social network, how to find the communities that are highly relevant to query users and have top overall scores in multiple attributes according to user preferences? Typically, in the face of such a problem setting, we can model the network as a multi-attributed road-social network, in which each user is linked with location information and $d$ ($\geq\! 1$) numerical attributes. In practice, user preferences (i.e., weights) are usually inherently uncertain and can only be estimated with bounded accuracy, because a human user is not able to designate exact values with absolute precision. Inspired by this, we introduce a normative community model suitable for multi-criteria decision making, called multi-attributed community (MAC), based on the concepts of $k$-core and a novel dominance relationship specific to preferences. Given uncertain user preferences, namely, an approximate representation of weights, the MAC search reports the exact communities for each of the possible weight settings. We devise an elegant index structure to maintain the dominance relationships, based on which two algorithms are developed to efficiently compute the top-$j$ MACs. The efficiency and scalability of our algorithms and the effectiveness of MAC model are demonstrated by extensive experiments on both real-world and synthetic road-social networks.