模糊论辩框架的数学表示

THE MATHEMATICAL REPRESENTATION OF FUZZY ARGUMENTATION FRAMEWORKS

随着形式论辩理论的快速发展,论辩框架已经逐渐成为人工智能领域的一个重要分支.近年来,为了刻画自然语言中的不确定性,不确定性理论开始广泛应用于论辩框架,进而产生了各种不确定性论辩框架.模糊论辩框架便是其中的一个重要分支.本文通过梳理相关的研究,基于模糊集理论提出了模糊论辩框架的两种数学表示形式;对具有有限个论证的模糊论辩框架,提出了模糊有向图和矩阵的数学表示方法.这些工作为模糊论辩框架的深入研究奠定了一定的数学基础.

With the rapid development of formal argumentation,the argumentation framework theory has gradually become an important branch of artificial intelligence.In recent years,to describe the uncertain information in natural language argumentation situations,the uncertainty theory has been widely applied in AFs.Various uncertainty AFs have been proposed and fuzzy AF is one of the important branches.Based on fuzzy set theory,this paper proposes two mathematical definitions of fuzzy AFs.In addition,the fuzzy AFs with finite arguments are represented by fuzzy directed graphs and matrices.These work lays a certain mathematical foundation for the further study of fuzzy AFs.