相似度三支决策模糊粗糙集模型的决策代价研究

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Title:

Decision costs of the similarity three-way decision-theoretic fuzzy rough set model

作者:

曾婷^1,2, 唐孝^1,2, 谭阳^1,2, 丁本香^1,2

1. 四川师范大学 数学科学学院, 四川 成都 610066;
2. 四川师范大学 智能信息与量子信息研究所, 四川 成都 610066

Author(s):

ZENG Ting^1,2, TANG Xiao^1,2, TAN Yang^1,2, DING Benxiang^1,2

1. School of Mathematical Science, Sichuan Normal University, Chengdu 610066, China;
2. Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu 610066, China

关键词:

三支决策; 模糊粗糙集; 决策代价; 模糊数; 阈值对; 属性值; 区间值; 多重集

Keywords:

three-way decisions; fuzzy rough set; decision costs; fuzzy number; threshold pair; attribute value; interval value; multiset

分类号:

TP18;O23

DOI:

10.11992/tis.201909015

摘要:

在三支决策模糊粗糙集模型中，一些学者基于相似度三支决策模糊粗糙集模型建立了目标函数来得到最优阈值对 $\left( {\alpha ,\;\beta } \right)$ 的计算方法，但在该过程的研究中，学者并没有在相似度三支决策模糊粗糙集模型中讨论关于决策代价的描述问题。基于模糊信息系统用新的函数来描述决策代价成为计算阈值对 $\left( {\alpha ,\;\beta } \right)$ 的一种方法，首先，在模糊信息系统中，通过建立一个描述决策代价的函数，将模糊信息系统中的模糊数与三支决策的决策代价联系在一起；然后对隶属频率进行拟合，得到了三支决策中决策代价的数值描述；最后，通过两个实例说明了该方法的可行性和适用性。

Abstract:

In the three-way decision-theoretic fuzzy rough set model, several scholars established the objective function based on the similarity three-way decision-theoretic fuzzy rough set model to derive the method for calculating the optimal threshold pair (α, β). However, during this research, the authors did not discuss the description of the decision costs in the similarity three-way decision-theoretic fuzzy rough set model. The new function describing the decision costs is used in the method for calculating the threshold pair (α, β) based on the fuzzy information system. First, in the fuzzy information system, the fuzzy number is associated with the decision costs of three-way decisions by establishing a function describing the decision costs. Then, the numerical description of the decision costs of three-way decisions is obtained by fitting the membership frequency. Finally, two examples are given to illustrate the feasibility and applicability of the method.