Top down relations on Fuzzy Labeled Transitions system

The formal stepwise refinement method is a powerful manner to design complex systems. It postulates system engineering gradually by starting from initial abstract specification and follows a rigorous refinement process to establish final specification. Fuzzy Labeled Transition Refinement Tree (FLTRT) is introduced to fulfill such purpose. It supports abstraction and handling incomplete information and by the way reducing complexity of refinement process. It is based on Fuzzy Labeled Transition System (FLTS) which is a generalization of well-known Labeled Transition System, enhanced by fuzziness facility. The FLTRT structure serves as a tree of potential concurrent design trajectories of the system. In this paper, we study bisimulation relations on FLTSs which are classified into two categories: horizontal and top-down bisimulation relations. The first category intends to identify equivalent specifications of the same abstraction level. However, the second one relates specifications that belong conceptually to different abstraction levels. Top-down bisimulation relation intends to check correctness of a given implementation with respect to its initial specification. FLTRT structure preserves the top-down bisimulation relation.