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What is Hierarchical Decomposition

Handbook of Research on Advanced Intelligent Control Engineering and Automation
Analysis of complex systems by replacing some parts of a model with simple components such that substitution nodes with their surrounding arcs are behaviorally equivalent to the related sub-models. In a discrete event net, either a place or a transition can be a substitution node by associating a sub-model to it.
Published in Chapter:
Distributed Coordination Architecture for Cooperative Task Planning and Execution of Intelligent Multi-Robot Systems
Gen'ichi Yasuda (Nagasaki Institute of Applied Science, Japan)
DOI: 10.4018/978-1-4666-7248-2.ch015
Abstract
This chapter provides a practical and intuitive way of cooperative task planning and execution for complex robotic systems using multiple robots in automated manufacturing applications. In large-scale complex robotic systems, because individual robots can autonomously execute their tasks, robotic activities are viewed as discrete event-driven asynchronous, concurrent processes. Further, since robotic activities are hierarchically defined, place/transition Petri nets can be properly used as specification tools on different levels of control abstraction. Net models representing inter-robot cooperation with synchronized interaction are presented to achieve distributed autonomous coordinated activities. An implementation of control software on hierarchical and distributed architecture is presented in an example multi-robot cell, where the higher level controller executes an activity-based global net model of task plan representing cooperative behaviors performed by the robots, and the parallel activities of the associated robots are synchronized without the coordinator through the transmission of requests and the reception of status.
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Fuzzy Classification on Relational Databases
Having a multidimensional fuzzy classification, that is, the classification space has more than two dimensions, leads to a large number of classes whose semantics cannot be derived properly. In order to maintain classes with a meaningful definition, a multidimensional fuzzy classification can be decomposed into a hierarchy of fuzzy classifications. The hierarchical decomposition merges subsets of qualifying attributes to fuzzy subclassifications (composed attributes). The composed attributes are integrated as linguistic variables in classes of higher levels leading to a hierarchy of fuzzy classification. The value v(e) of an element e of a composed attribute can be derived by assigning to each fuzzy class Ck a grade gr(Ck) expressing the meaning of the composed attribute. By aggregating these grades multiplied with the membership degrees of the classified elements, the formula looks like this: .
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