模糊论辩框架哥德尔语义的数值特征

doi:10.6040/j.issn.1671-9352.0.2021.803

摘要/Abstract

摘要： 模糊论辩框架的哥德尔语义体系涵盖几种基本的外延语义,却未对各外延语义的性质展开进一步研究。这为该语义系统的计算和快速识别带来一定的困难。文章通过对各外延语义的数值特征的深入研究,为上述问题提供一定的解决方案。借助于哥德尔三角模的基本性质,逐一推导哥德尔语义体系中无冲突集、可容许外延、完全外延、优选外延(稳定外延)和基外延的数值特征,并在无圈、奇数圈和偶数圈的模糊辩论框架中分别给出基外延的算法。这些结论是对该语义体系的理论推广;同时,绕过定义直接依据数值判定外延语义的方法,以及从空集计算基外延的算法,是对该语义体系在算法和快速识别方面的发展。

关键词: 论辩框架, 模糊集, 模糊论辩框架, 哥德尔语义, 哥德尔三角模

Abstract: The Gödel semantics in fuzzy argumentation frameworks covers several basic extension semantics, but does not further study the properties of each extension semantics. This brings some difficulties to the calculation and quick recognition of the semantic system. Through the in-depth study of the numerical properties of each extension semantics, this paper provides some solutions to the above problems. With the help of the basic properties of the Gödel t-norm, the numerical properties of the conflict-free set, the admissible extension, the complete extension, the preferred extension(the stable extension), and the grounded extension in the Gödel semantics are deduced one by one, and the algorithms of the grounded extension are given in fuzzy AFs without cycles and fuzzy AFs consisting of odd cycles or even cycles. These conclusions are the theoretical generalization of the semantic system. At the same time, the method of bypassing the definition and directly judging the extension semantics based on numerical values, as well as the algorithm of calculating the grounded extension from empty sets, are the development of the semantics in terms of algorithm and quick identification.

Key words: argumentation framework, fuzzy set, fuzzy argumentation framework, Gö, del semantics, Gö, del t-norm

中图分类号:

TP18

赵双燕,吴家超. 模糊论辩框架哥德尔语义的数值特征[J]. 《山东大学学报(理学版)》, 2022, 57(8): 53-59.

ZHAO Shuang-yan, WU Jia-chao. Numerical properties of Gödel semantics in fuzzy argumentation frameworks[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(8): 53-59.

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