Adaptive fuzzy petri nets for dynamic knowledge representation and inference X. Li, F. Lara-Rosano * Centre for Instrumentation Research, National University of Mexico (UNAM), Apartado Postal 70-418, Mexico City, D.F. 04510, Mexico Abstract Knowledge in some fields like Medicine, Science and Engineering is very dynamic because of the continuous contributions of research and development. Therefore, it would be very useful to design knowledge-based systems capable to be adjusted like human cognition and thinking, according to knowledge dynamics. Aiming at this objective, a more generalized fuzzy Petri net model for expert systems is proposed, which is called AFPN (Adaptive Fuzzy Petri Nets). This model has both the features of a fuzzy Petri net and the learning ability of a neural network. Being trained, an AFPN model can be used for dynamic knowledge representation and inference. After the introduction of the AFPN model, the reasoning algorithm and the weight learning algorithm are developed. An example is included as an illustration.  2000 Published by Elsevier Science Ltd. Keywords: Petri nets; Knowledge-based systems; Fuzzy reasoning; Knowledge representation; Adaptive expert systems; Neural learning 1. Introduction Petri Nets (PN) models and net theory have become an important computational paradigm to represent and analyze a broad class of systems. As a computational paradigm for intelligent systems, net theory provides a graphical language to visualize, communicate and interpret engineering problems, as well as a specification and engineering language which can be used as a development, simulation and implementation tool (Pedrycz & Gomide, 1994). PN have the ability to represent and analyze in an easy way concurrently and synchronization phenomena, like concur- rent evolutions, where various processes that evolve simul- taneously are partially independent. Furthermore, PN approach can be easily combined with other techniques and theories such as object-oriented programming, fuzzy sets, neural networks, etc. These combined PN are widely used in computer systems, manufacturing systems, robotic systems, knowledge-based systems, process control, as well as other kinds of engineering applications. Because normal PN cannot deal with vague or fuzzy information such as “very high” and “good”, several Fuzzy Petri Nets (FPN) have been introduced. As a model of knowledge-based systems, FPN are used for fuzzy knowledge representation and reasoning. In fact, by imple- menting the FPN model, major features offered by the PN model, such as correctness, circular rules, consistency, and completeness checking, can also be applied. PN have an inherent quality in representing logic in an intuitive and visual way and also can be implemented to simulate systems in operation. Therefore, a complex fuzzy expert system reasoning path can be reduced to a simple sprouting tree when applying a FPN-based reasoning algorithm as an inference engine. Besides these applications, FPN theory also provides means to manipulate imprecise and vague information. So, many FPN models are proposed to support fuzzy reasoning and decision making (Bugarn & Barro, 1994; Cao & Sanderson, 1995; Chen, Ke & Chang, 1990; Looney, 1994; Scarpelli & Gomide, 1993; Scarpelli, Gomide & Yager, 1996; Yeung & Tsang, 1994, 1998). There are some other applications of FPN in knowledge- based systems, such as inconsistency checking (Scarpelli & Gomide, 1994), uncertainty management (Konar & Mandal, 1996), and knowledge learning (Looney, 1994). For more details, a brief summary and discussion of FPN and its application are given in Section 2. In this paper, we pay attention to knowledge representa- tion (by weighted fuzzy production rules) and inference with FPN. The proposed model is called Adaptive Fuzzy Petri Nets (AFPN). This model can not only be implemented to do knowledge inference, but also has a learning ability like a neural network, implying that the system knowledge can be learned. Expert Systems with Applications 19 (2000) 235–241 PERGAMON Expert Systems with Applications 0957-4174/00/$ - see front matter  2000 Published by Elsevier Science Ltd. PII: S0957-4174(00)00036-1 www.elsevier.com/locate/eswa * Corresponding author. Tel.: +52-5622-8601; fax: +52-5622-8620. E-mail address: lararf@servidor.unam.mx (F. Lara-Rosano).