@article{Wu2025, 
author = {Jiachao Wu},
title = {Relative attack strength and its application in argumentation frameworks},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {7},
pages = {16355-16370},
keywords = {argumentation framework, weighted argumentation framework, weighted arguments, fuzzy semantics},
url = {https://www.sciopen.com/article/10.3934/math.2025731},
doi = {10.3934/math.2025731},
abstract = {Adjusting the values of arguments is a widely applied method to establish the semantics of argumentation frameworks (AFs). In this process, the influence of a single attacker's value is mentioned or implicitly used many times. However, this effect has not been studied specifically. As a result, its role in semantic exploration cannot be brought into full play. Thus, my objective was to study this effect, so as to provide a new tool for semantics research. In this paper, the strength of this influence was called the relative attack strength (RAS). It was formally defined and computed by a three-variable function    r  a  s. Then, nine basic properties of RAS were studied. As an application, I established a new semantics for fuzzy AFs based on RAS, which covered the Gödel semantics. The main contribution lies in the proposal of RAS and the discussion of its properties. This provides a new tool for the further study of argumentation semantics. The other contribution is the establishment of new semantics. On one hand, it fills a gap in theory. On the other hand, it shows the effectiveness of RAS in semantic research of AFs.}
}