A new class of group decision making model under fuzzy preferences and a fuzzy majority is proposed which combines the traditional, widely employed and successful decision (making) by consensus, and the new idea, based on recent results from decision and, cognitive sciences, management science, psychology, etc. suggesting that decision by consensus may often lead to noninnovative enough decisions, and a different approach based on individuals (agents) who are not consensory but express different, maybe dissensory opinions, with a higher innovation potential, may be better. Here, in the new model, after the first phase of traditional decision by consensus, we use the concepts of Kacprzyk and Zadrożny's [28] consensory and dissensory agents, and then use primarily testimonies of dissensory agents which can imply innovative options to be chosen by using Kacprzyk [17], [18], and Kacprzyk, Zadrożny, Fedrizzi and Nurmi [29] group decision solution concepts, notably various fuzzy cores (i.e. fuzzy sets of options preferred over most other options).