What is Hierarchical Decomposition

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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. Learn more in: Distributed Coordination Architecture for Cooperative Task Planning and Execution of Intelligent Multi-Robot Systems

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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: . Learn more in: Fuzzy Classification on Relational Databases