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The paper studies how to evaluate arguments in graphs where both arguments and attacks are weighted. It proposes a broad family of gradual semantics that assign to each argument a numerical value representing its strength, i.e., how robust is the argument against attacks. It shows that five existing gradual semantics are instances of the family, and extends each of them in various ways for accounting for weights of attacks. The extended versions of each semantics differ in the way they deal with weights of attacks. Furthermore, they are all instances of the family. The paper shows also that the family captures additional semantics, like Euler-Max-based that is investigated in the paper. The new semantics are analyzed against properties from the literature and are compared with existing semantics that deal with weighted attacks.
Amgoud et al. (Wed,) studied this question.