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Analysis of Approximate Petri Nets by Means of Occurrence Graphs

Suraj Z., Fryc B.

Fundamenta Informaticae

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2007

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Vol. 79, nr 3-4

541-551

EN

Approximate Petri nets (AP-nets) can be used for the knowledge representation and approximate reasoning. The AP-net model is defined on the basis of the rough set approach, fuzzy Petri nets and coloured Petri nets. One of the main advantages of AP-net model is a possibility to present the reachability set of a given AP-net by means of an occurrence graph. Such graphs can serve, among others, for analyzing and evaluating an approximate reasoning realized by using AP-net model. The main contribution of the paper is to present the algorithms for construction and analysis of occurrence graphs for the AP-nets, especially in the context of searching for the best decision and finding the shortest distance in order to compute such decision. This approach can be applied to the design and analysis of the formal models for expert systems, control systems, communication systems, etc.

2

Timed Approximate Petri Nets

Suraj Z., Fryc B.

Fundamenta Informaticae

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2006

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Vol. 71, nr 1

83-99

EN

Time is one of the most important considerations in designing practical systems. The notion of time plays a vital role in performance evaluation of real-time systems. A new class of timed approximate Petri nets (TAP-nets) is proposed in the paper. This net model combines high-level Petri nets with time and uncertain information. The approach presented in the paper for modelling of uncertainty, imprecision and vagueness is based on rough set theory and fuzzy Petri nets. The TAP-nets can be used for modelling and evaluating of approximate reasoning used to build expert systems, control systems, communication systems, etc. The main advantage of modelling practical systems using the TAP-nets is that the resulting models are simple, intuitive and allow the system analyst to evaluate the performance of such system models.

3

A Petri Net System - an Overview

Suraj Z., Fryc B., Matusiewicz Z., Pancerz K.

Fundamenta Informaticae

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2006

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Vol. 71, nr 1

101-120

EN

Petri nets are one of well established tools in both theoretical analysis and practical modelling of concurrent systems as well as approximate reasoning. However, practical usage of Petri nets is limited by the lack of computer tools which would allow to handle large and complex nets in a comfortable way. Three things are essential for modelling and analyzing by means of Petri nets - good editor, simulator and powerful analysis engine. Moreover, a program should have a graphical user interface providing an opportunity to work directly with the graphical representations of Petri nets and should be able to read and write data in formats of other popular simulators of Petri Nets. This paper presents a set of integrated graphical Petri net tools called Petri Net system (PN-system, in short). PN-system is a following version of PN-tools. This system can be used for constructing, editing and analyzing of different classes of Petri nets. PN-system is enhanced on fuzzy and adaptive fuzzy Petri nets' modules which allow to perform fuzzy reasoning automatically. It has got a graphical user interface. Moreover, PN-system can cooperate with the ROSECON system which is an original software tool for discovering concurrent models from data tables. PN-system is run on IBM PC platform under MS Windows operating system.

4

On Fuzzy Reasoning Using Matrix Representation of Extended Fuzzy Petri Nets

Fryc B., Pancerz K., Peters J.F., Suraj Z.

Fundamenta Informaticae

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2004

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Vol. 60, nr 1-4

143--157

EN

In 1990 Shyi-Ming Chen et al. presented a new approach to knowledge representation using fuzzy Petri nets (FPN). A fuzzy Petri net model allows a structural representation of knowledge and has a systematic procedure for supporting fuzzy reasoning. In this paper we propose an algebraic (matrix) representation of FPNs. We use this representation in a fuzzy reasoning algorithm which is simple to implement in modern programming languages such as C++, C# or Java. Furthermore, there exists MATLAB - a computer system which makes it possible to solve many computing problems, especially those with matrix and vector formulations. We present also an approach enabling us to carry out a fuzzy reasoning process using the MATLAB environment.