In Taiwan, the most advantageous tender in governmental procurement is the selection of a general contractor based on a score or ranking evaluated by a committee. Due to personal, subjective preferences, the contractor selection of committee members may be different, causing cognitive difference between the results of the members’ selection and the preliminary opinions provided by the working group. Integrated, multi-criteria decision making techniques, combined with preference relation, Bayesian, fuzzy utility, and prospect theories are used to assess factors weighing up the duration/cost/quality, probability of external information, and utility function system. The paper proposes a Bayesian fuzzy prospect model for group decision making, based on probability and utility multiplied relation, and taking the sustainable development factors into consideration. This study aims to provide committees with an objective model to select the best contractor for public construction projects. The results of this study can avoid the lowest bidder being selected; besides, the score gap of contractor selection can be increased, and the difference between the top three contractors’ scores can be decreased as well. In addition to proposing an innovative decision-making system of contractor selection and an index weight-assessing system for sustainable development, this model will be widely applied and sustainably updated for other cases.