Sensor, Filter, and Fusion Models with Rough Petri Nets

This paper considers models of sensors, filters, and sensor fusion with Petri nets defined in the context of rough sets. Sensors and filters are fundamental computational units in the design of systems. The intent of this work is to construct Petri nets to simulate conditional computation in approximate reasoning systems, which are dependent on filtered input from selected sensors considered relevant in problem solving. In this paper, coloured Petri nets provide a computational framework for the definition of a family of Petri nets based on rough set theory. Sensors are modeled with what are known as receptor processes in rough Petri nets. Filters are modeled as Lukasiewicz guards on some transitions in rough Petri nets. A Lukasiewicz guard is defined in the context of multivalued logic. Lukasiewicz guards are useful in culling from a collection of active sensors those sensors with the greatest relevance in a problem-solving effort such as classification of a "perceived" phenomenon in the environment of an agent. The relevance of a sensor is computed using a discrete rough integral. The form of sensor fusion considered in this paper consists in selecting only those sensors considered relevant in solving a problem. The contribution of this paper is the modeling of sensors, filters, and fusion in the context of receptor processes, Lukasiewicz guards, and rough integration, respectively.