Set-theoretic models of three-way decision
Set-theoretic models of three-way decision
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DOI：
10.1007/s41066-020-00211-9
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发表时间：
2020-02
影响因子：
5.5
通讯作者：
Yiyu Yao
中科院分区：
文献类型：
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作者：
Yiyu Yao
三向决策理论是关于三人思维哲学、三人工作方法论和三人处理机制。我们通过三个部分、三个单元或三个角度来接近一个整体。三向决策的三分-作用-结果（TAO）模型涉及将整体三分为三部分并对这三个部分采取行动，以产生最佳结果。在本文中，我们在集合论背景下进一步探索了 TAO 模型，并做出了三项新贡献。第一个贡献是检查在两种客观/本体和主观/认知不确定性下用非标准集表示概念的三向决策。第二个贡献是引入了基于评估的三向决策框架。我们提出了三等分的分类并研究了评估空间的概念。第三个贡献是，在所提出的框架内，系统地研究了粗糙集、区间集、模糊集、阴影集、粗糙模糊集、区间模糊集（或等效地，模糊集、区间值模糊集、直觉模糊集）和软集的三向决策。
The theory of three-way decision is about a philosophy of thinking in threes, a methodology of working with threes, and a mechanism of processing in threes. We approach a whole through three parts, in terms of three units, or from three perspectives. A trisecting–acting–outcome (TAO) model of three-way decision involves trisecting a whole into three parts and acting on the three parts, in order to produce an optimal outcome. In this paper, we further explore the TAO model in a set-theoretic setting and make three new contributions. The first contribution is an examination of three-way decision with nonstandard sets for representing concepts under the two kinds of objective/ontic and subjective/epistemic uncertainty. The second contribution is an introduction of an evaluation-based framework of three-way decision. We present a classification of trisections and investigate the notion of an evaluation space. The third contribution is, within the proposed framework, a systematical study of three-way decision with rough sets, interval sets, fuzzy sets, shadowed sets, rough fuzzy sets, interval fuzzy sets (or equivalently, vague sets, interval-valued fuzzy sets, intuitionistic fuzzy sets), and soft sets.