The categorical approach is proposed to the formalization of fuzzy graph grammars obtained as a result of generalization of sequential graph grammars. This approach takes into consideration the basic types of fuzziness that arise in constructing categories of fuzzy objects and describing transformations of fuzzy graphs generated by fuzzy sets. All the problems of undecidability that are well known for Chomsky grammars are proved to hold true for fuzzy graph grammars.

Managing a large data network, such as a national WAN, is a complex and cumbersome task. Existing network management software cannot meet the requirements of the increasing size and complexity of today's TCP/IP-based networks, because, in most cases, it provides only simple monitoring tools. We can't fully exploit a WAN without user-friendly, intelligent, network management software enhanced with diagnostic and decision support services.Expert systems provide a feasible and elegant solution in this direction. Currently, the development of expert systems for WAN management is only at the research and experimental stages. Formalizing such a task is difficult because network state information is usually inadequate and incomplete, the scale of behavior characteristics is large, and the network environment continually evolves. Moreover, an efficient network-monitoring schema must exist. 1 The implementation of such functionality must be in accordance with existing network monitoring technology-namely, the Management Information Base (MIB) and the Simple Network Management Protocol (SNMP)-to control existing real-world network devices.Network management also requires coordination among operators of autonomous network nodes. To closely resemble network management's distributed nature, multiagent problem-solving techniques can help model the functionality of individual agents as well as the interactions taking place between them. 2 Multiagent technology is preferable to other distributed problem-solving techniques because it offers enhanced modularity, reactions to environmental changes, and reusability. This article presents the architecture, implementation, operation, and evaluation of the ExperNet system, a multiagent expert system that we developed for Ukraine's national TCP/IP WAN under the framework of a joint EUfunded project. ExperNet helps network operators manage a WAN with its• monitoring tools for capturing network state; • platform for logic-based applications; • efficient and extensible expert system shell; • fast heuristic detection, diagnosis, and repair of network failures; • cooperative problem-solving strategies; and • user-friendly Web-based interface.The system architecture ExperNet consists of a hierarchically structured architecture, with each level consisting of one or more management nodes (see Figure 1). Each node encapsulates one or more lower-level management subnodes and manages a network area, assisted by a