Based on the electric vehicle (EV) arrival times and the duration of EV connection to the charging station, we identify charging patterns and derive groups of charging stations with similar charging patterns applying two approaches. The ruled based approach derives the charging patterns by specifying a set of time intervals and a threshold value. In the second approach, we combine the modified l-p norm (as a matrix dissimilarity measure) with hierarchical clustering and apply them to automatically identify charging patterns and groups of charging stations associated with such patterns. A dataset collected in a large network of public charging stations is used to test both approaches. Using both methods, we derived charging patterns. The first, rule-based approach, performed well at deriving predefined patterns and the latter, hierarchical clustering, showed the capability of delivering unexpected charging patterns.

The assignment of weights to attacks in a classical Argumentation Framework allows to compute semantics by taking into account the different importance of each argument. We represent a Weighted Argumentation Framework by a non-binary matrix, and we characterize the basic extensions (such as w-admissible, w-stable, w-complete) by analysing sub-blocks of this matrix. Also, we show how to reduce the matrix into another one of smaller size, that is equivalent to the original one for the determination of extensions. Furthermore, we provide two algorithms that allow to build incrementally w-grounded and w-preferred extensions starting from a w-admissible extension.

The matrices and their sub-blocks are introduced into the study of determining various extensions in the sense of Dung's theory of argumentation frameworks. It is showed that each argumentation framework has its matrix representations, and the core semantics defined by Dung can be characterized by specific sub-blocks of the matrix. Furthermore, the elementary permutations of a matrix are employed by which an efficient matrix approach for finding out all extensions under a given semantics is obtained. Different from several established approaches, such as the graph labelling algorithm, Constraint Satisfaction Problem algorithm, the matrix approach not only put the mathematic idea into the investigation for finding out various extensions, but also completely achieve the goal to compute all the extensions needed.