基于区间二型模糊决策粗糙集的三支决策方法
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山东财经大学

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C934

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国家自然科学基金项目(71771140) ,国家自然科学基金项目(面上项目,重点项目,重大项目)


Three-way decisions based on decision-theoretic rough sets with interval type-2 fuzzy information
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Shandong University of Finance and Economics

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    摘要:

    考虑到区间二型模糊数在描述高度不确定性信息方面的优势,把区间二型模糊数拓展到决策粗糙集中,提出两种区间二型模糊三支决策方法。在没有类标签的区间二型模糊信息系统中,解释损失函数与确定条件概率是需要解决的两个关键问题。首先,根据区间二型模糊数的性质,把其引入决策粗糙集中,为损失函数提供了一种新的解释。其次,基于贝叶斯决策过程,构造了区间二型模糊决策粗糙集的基础模型。然后,选取区间二型模糊数的组合排序与可能度排序,设计两种策略来推导区间二型模糊决策粗糙集的决策规则。对于条件概率,利用灰色关联分析方法对其评估。在此基础上,给出两种在区间二型模糊信息系统下的基于区间二型模糊决策粗糙集的三支决策方法。这两种方法不仅考虑了决策风险,而且给出了方案的排序结果和客观分类结果,补充完善了灰色关联分析的决策结果。最后,将通过算例分析佐证所提方法的有效性。

    Abstract:

    Considering the advantage of interval type-2 fuzzy sets (IT2FSs) in describing highly uncertain information, this paper extends IT2FSs to decision-theoretic rough sets (DTRSs), and proposes two novel interval type-2 fuzzy (IT2F) decision-making approaches for deriving three-way decisions. In the IT2F information system without class labels, the interpretation of loss function and the determination of conditional probability are two fundamental issues to be addressed. Based on the properties of IT2FSs, IT2FSs are firstly introduced into DTRSs, which offers a novel illustration for the loss function. Then, in light of Bayesian decision procedure, an IT2F DTRS (IT2FDTRS) model is established. In addition, two methods are designed for deriving three-way decisions with the aid of two IT2F ranking techniques, namely, the combined ranking method and the possibility degree. Meanwhile, IT2F grey relational analysis is used to determine the conditional probability. Furthermore, two three-way decision methods are proposed based on the IT2FDTRS in the IT2F information system. The proposed approaches not only considers the decision risk, but also tells us the ranking results and objective classification results of alternatives, which can replenish the decision results of grey relational analysis. Finally, a practical example is provided to demonstrate the validity of the proposed three-way decision methods.

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  • 收稿日期:2020-11-07
  • 最后修改日期:2021-02-13
  • 录用日期:2021-03-03
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