Some neighborhood-related fuzzy covering-based rough set models and their applications for decision making

Gongao Qi, Bin Yang, Wei Li
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引用次数: 4

Abstract

Fuzzy rough set (FRS) has a great effect on data mining processes and the fuzzy logical operators play a key role in the development of FRS theory. In order to further generalize the FRS theory to more complicated data environments, we firstly propose four types of fuzzy neighborhood operators based on fuzzy covering by overlap functions and their implicators in this paper. Meanwhile, the derived fuzzy coverings from an original fuzzy covering are defined and the equalities among overlap function-based fuzzy neighborhood operators based on a finite fuzzy covering are also investigated. Secondly, we prove that new operators can be divided into seventeen groups according to equivalence relations, and the partial order relations among these seventeen classes of operators are discussed, as well. Go further, the comparisons with $ t$-norm-based fuzzy neighborhood operators given by D'eer et al. are also made and two types of neighborhood-related fuzzy covering-based rough set models, which are defined via different fuzzy neighborhood operators that are on the basis of diverse kinds of fuzzy logical operators proposed. Furthermore, the groupings and partially order relations are also discussed. Finally, a novel fuzzy TOPSIS methodology is put forward to solve a biosynthetic nanomaterials select issue, and the rationality and enforceability of our new approach is verified by comparing its results with nine different methods.
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基于邻域模糊覆盖的粗糙集模型及其决策应用
模糊粗糙集在数据挖掘过程中起着重要的作用,模糊逻辑算子在模糊粗糙集理论的发展中起着关键作用。为了将FRS理论进一步推广到更复杂的数据环境中,本文首先提出了四种基于重叠函数模糊覆盖的模糊邻域算子及其隐含子。同时,定义了由原始模糊覆盖导出的模糊覆盖,并研究了基于有限模糊覆盖的重叠函数模糊邻域算子之间的等式。其次,根据等价关系证明了新算子可分为17类,并讨论了这17类算子之间的偏序关系。进一步,与D'eer等人给出的基于$ t$范数的模糊邻域算子进行了比较,提出了两类基于邻域的模糊覆盖粗糙集模型,这两类模型是在不同种类的模糊逻辑算子的基础上,通过不同的模糊邻域算子定义的。在此基础上,讨论了群和部分序关系。最后,提出了一种新的模糊TOPSIS方法来解决生物合成纳米材料的选择问题,并通过与9种不同方法的结果比较,验证了该方法的合理性和可执行性。
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