This paper proposes a novel algorithm, named dual multiobjective quantum-inspired evolutionary (DMQEA) algorithm augmented fuzzy cognitive map (FCM). DMQEA was developed to help users select preferable solutions out of the non-dominated ones and has been proven to be an effective way compared to other multi-objective optimization methods, such as MQEA, MQEA-PS, etc. DMQEA, in this paper, has been coupled with decision supporting tool, fuzzy cognitive maps (FCMs) to support selecting best models which can reflect users' preferences. Even though the attempts with single optimization such as genetic algorithms (GAs) or particle swarm optimization (PSO) have been frequently carried out, there have been only few attempt to incorporate FCM with multicriteria decision making algorithm, especially to reflect user's preference. This study aims to integrate DMQEA with FCM to build models according to user's preference. In robotics field, the interaction with human operators is an important issue and DMQEA-FCM can aid robots in their decision making process in the context of the interaction.