In this paper, we propose a fuzzy Petri net model for a rule-based decision making system which contains uncertain conditions and vague rules. Using the transformation method introduced in the paper, one can obtain the fuzzy Petri net of the rule-based system. Since the fuzzy Petri net can be represented by some matrices, the algebraic form of a state equation of the fuzzy Petri net is systematically derived. Both forward and backward reasoning are performed by using the state equations. Since the proposed reasoning methods require only simple arithmetic operations under a parallel rule firing scheme, it is possible to perform real-time decision making with applications to control systems and diagnostic systems. The methodology presented is also applicable to classical (nonfuzzy) knowledge base systems if the nonfuzzy system is considered as a special case of a fuzzy system with truth values being equal to the extreme values only. Finally, an illustrative example of a rule-based decision making system is given for automobile engine diagnosis.