Fundamenta Informaticae - Volume 47, issue 3-4

Authors: Peters, James F. | Ramanna, S. | Borkowski, M. | Skowron, Andrzej | Suraj, Zbigniew

Article Type: Research Article

Abstract: 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 Łukasiewicz guards on some transitions in rough Petri nets. A Łukasiewicz guard is defined in the context of multivalued logic. Łukasiewicz 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, Łukasiewicz guards, and rough integration, respectively. Show more

Keywords: approximation, enabling, filter, fusion, guard, multivalued logic, Petri net, rough measure, rough integral, rough sets, sensor

Citation: Fundamenta Informaticae, vol. 47, no. 3-4, pp. 307-323, 2001

Authors: Schmidt, Karsten

Article Type: Research Article

Abstract: Given a (possibly partially defined) state, all count vectors of transition sequences reaching that state are solutions to a corresponding Petri net state equation. We propose a search strategy where sequences corresponding to a minimal solution of the state equation are explored first. Then step by step the search space is relaxed to arbitrary count vectors. This heuristics relies on the observation that in many (though provably not in all) cases, minimal solutions of the state …equation can be realized as a firing sequence. If no target state is reachable, either the state equation does not have solutions, or our search method would yield the full state space. We study the impact of the state equation on reachability, present an algorithm that exploits information from the state equation and discuss its application in stateless search as well as its combination with stubborn set reduction. Show more

Keywords: computer aided verification, Petri nets, reachability analysis, state equation

Citation: Fundamenta Informaticae, vol. 47, no. 3-4, pp. 325-335, 2001

Authors: Skowron, Andrzej | Stepaniuk, Jaroslaw

Article Type: Research Article

Abstract: Information sources provide us with granules of information that must be transformed, analyzed and built into structures that support problem solving. One of the main goals of information granule calculi is to develop algorithmic methods for construction of complex information granules from elementary ones by means of available operations and inclusion (closeness) measures. These constructed complex granules represent a form of information fusion. Such granules should satisfy some constraints like quality criteria …or/and degrees of granule inclusion in (closeness to) a given information granule. Information granule decomposition methods are important components of those methods. We discuss some information granule decomposition methods. Show more

Keywords: rough set theory, information granulation, granular computing, information fusion, decomposition, pattern, schemes of approximate reasoning

Citation: Fundamenta Informaticae, vol. 47, no. 3-4, pp. 337-350, 2001

Authors: Wróblewski, Jakub

Article Type: Research Article

Abstract: The problem of improving rough set based expert systems by modifying a notion of reduct is discussed. The notion of approximate reduct is introduced, as well as some proposals of quality measure for such a reduct. The complete classifying system based on approximate reducts is presented and discussed. It is proved that the problem of finding optimal set of classifying agents based on approximate reducts is NP-hard; the genetic algorithm is applied to find the suboptimal …set. Experimental results show that the classifying system is effective and relatively fast. Show more

Keywords: Rough sets, approximate reduct, voting

Citation: Fundamenta Informaticae, vol. 47, no. 3-4, pp. 351-360, 2001