This paper identi4es a generic axiom framework for prioritised fuzzy constraint satisfaction problems (PFCSPs), and proposes methods to instantiate it (i.e., to construct speci4c schemes which obey the generic axiom framework). In particular, we give 4ve methods to construct the priority operators that are used for calculating the local satisfaction degree of a prioritised fuzzy constraint, and identify priority T-norm operators that can be used for calculating the global satisfaction degree of a prioritised fuzzy constraint problem. Moreover, a number ofnumerical examples and real examples are used to validate our system, and thus we further obtain some insights into our system. In addition, we explore the relationship between weight schemes and prioritised FCSP schemes, and reveal that the weighted FCSP schemes are the dual ofprioritised FCSP schemes, which can, correspondingly, be called posterioritised FCSP schemes.