Using Nash Equilibrium to Reduce Number of Attacks Between the Arguments in Dung’s Argumentation Framework

Abstract

For intelligent systems, argumentation is a very important factor to point out in Artificial Intelligence (AI) as it represents an essential component. It is one of the critical approaches to making a decision, whereas Dung introduces a mathematical model that classifies attacks among arguments based on ordered pairs. Furthermore, weights’ addition to the arguments is one of the most important developments. It is done by several methods of weight calculation; hence, the Fuzzy weights method is a suitable method when working with game theory (GT). To this end, this paper introduced the GT in a Nash equilibrium method to redraw the acceptable arguments. It depends on the fuzzy weight for reducing the acceptable arguments and acceptable attacks between those arguments. This paper provides an automatic model for reducing the number of arguments and attacks between them called the shorthand model based on the gaming argumentation framework SGAF by extending the gaming argumentation framework GAF. This work uses the Cash on Delivery (COD) Payment Model as a case study.