Representation and Analysis of Uncertainty Using Fuzzy Petri Nets

This article proposes a generalized definition of the fuzzy Petri net FPN and the reasoning structures of transitions in the FPN. Three types of fuzzy variables, local fuzzy variables, fuzzy marking variables, and global fuzzy variables, are used to model uncertainty based on different aspects of fuzzy information. A fuzzy Petri net is used to model the incomplete, uncertain, and approximate information associated with firing of transitions and changing of states in robotics and manufacturing systems. Using FPNs to model a system, a fuzzy reasoning strategy may be used to infer new fuzzy values in output places after the corresponding enabled transition is fired. A global fuzzy variable is used to sequence operations with key precedence relations for a manufacturing system. A local fuzzy variable is used to represent the uncertainty in local configuration variables of the system and may be used to control on-line reasoning about sensor-based execution. Several basic types of fuzzy Petri nets are analyzed, and the necessary and/or sufficient conditions of safeness, liveness, and reversibility are given. An example of modeling sensory transitions in a robotic system is discussed to illustrate reasoning about input local fuzzy variables to obtain mutually exclusive tokens in the output places.

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