Constructing shadowed sets and three-way approximations of fuzzy sets
Constructing shadowed sets and three-way approximations of fuzzy sets
复制标题
DOI：
10.1016/j.ins.2017.05.036
复制
发表时间：
2017-10
期刊：
影响因子：
--
通讯作者：
Yiyu Yao;Shu Wang;Xiaofei Deng
中科院分区：
文献类型：
--
作者：
Yiyu Yao;Shu Wang;Xiaofei Deng
Pedrycz提出的阴影集是模糊集的三向近似的一个例子。一个模糊集的近似方法是将一个阈值或以上的隶属度提升到1，将另一个阈值或以下的隶属度降低到0，并将两个阈值之间的隶属度映射到单位区间[0，1]。在这种三向近似的构造过程中的一个基本问题是单位区间[0，1]上的一对阈值的解释和确定。本文采用了三值集的一种广义定义，即用三值集{n，m，p}代替{0，[0，1]，1}。我们引入了一个基于优化的框架，用于构建三向近似。在这个框架内，我们严格审查现有的研究和结果，并根据三个原则提出新的配方，即，不确定性不变性原理、最小距离原理和最小成本原理。最后，我们提出了一个最小成本模型的基础上的语义距离函数之间的隶属度等级在[0，1]和值在{n，m，p}。
Shadowed sets, proposed by Pedrycz, are an example of three-way approximations of fuzzy sets. A fuzzy set is approximated by elevating membership grades at or above one threshold to 1, reducing membership grades at or below another threshold to 0, and mapping membership grades between the two thresholds to the unit interval [0, 1]. A fundamental issue in such a construction process of three-way approximations is the interpretation and determination of a pair of thresholds on the unit interval [0, 1]. In this paper, we adopt a generalized definition of three-valued sets by using a set of three values {n, m, p} to replace {0, [0, 1], 1}. We introduce an optimization-based framework for constructing three-way approximations. Within the framework, we critically review existing studies and results and present new formulations according to three principles, i.e., a principle of uncertainty invariance, a principle of minimum distance, and a principle of least cost. Finally, we propose a least-cost model based on a semantic distance function between membership grades in [0, 1] and values in {n, m, p}.