A general model of decision-theoretic three-way approximations of fuzzy sets based on a heuristic algorithm
A general model of decision-theoretic three-way approximations of fuzzy sets based on a heuristic algorithm
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DOI：
10.1016/j.ins.2018.10.051
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Qinghua Zhang;Deyou Xia;Kaixuan Liu;Guoyin Wang
中科院分区：
文献类型：
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作者：
Qinghua Zhang;Deyou Xia;Kaixuan Liu;Guoyin Wang
邓建立了一个模糊集的决策理论三向近似模型，该模型可以通过将影子集与三向决策相结合来计算一对可解释阈值(α，β)。在该模型中，重要的贡献是用值0.5来代替阴影集中区间[0，1]的不确定区域，该值表示具有最高不确定性的隶属度。从决策成本最小的原则出发，虽然在基于值0.5的某些数据分布中可以精确地实现最低总成本，但在某些情况下，所获得的总成本与最小成本之间存在差异。因此，本文在邓的模型的基础上，提出了模糊集的广义三向逼近的概念，用一个变量值(0 <；c<； 1)代替了0.5。在此基础上，建立了由影集的升降运算构成的损失函数。此外，还讨论了不同重要性的所需阈值(α，β)与变量值的关系。为了优化损失函数，引入粒子群算法作为一种启发式算法，通过最小化总代价来搜索最优值。实验结果表明，该模型是邓的模型的扩展，可以为数据分析提供更丰富的洞察力。这些结论进一步丰富了影子集和三向决策，使复杂问题简化了几个隶属度。
A model of decision-theoretic three-way approximations of fuzzy sets that can calculate a pair of interpretable thresholds (α, β) by combining shadowed sets with three-way decisions was established by Deng. In that model, the significant contribution is that the value 0.5, which denotes a membership grade with the highest uncertainty, is used to replace the uncertain region with the interval [0,1] in shadowed sets. From the principle of the minimum decision cost, although the lowest overall cost can be achieved precisely in some data distributions based on the value 0.5, there is a difference between the obtained overall cost and the least cost in some cases. Therefore, in this paper, based on Deng’s model, the concept of a general three-way approximation of a fuzzy set is proposed to replace 0.5 with a variable valuec(0 <c< 1). Then, the loss function composed of the elevation and reduction operations in shadowed sets is established. In addition, the relationship between the required thresholds (α, β) with the different significance and variable valuecis discussed. To optimize the loss function, particle swarm optimization (PSO) as a heuristic algorithm is introduced to search for the optimal valuecby minimizing the total cost. Finally, the experimental results indicate that the proposed model, which is an extension of Deng’s model, can provide richer insight into data analysis. These conclusions further enrich shadowed sets and three-way decisions to simplify complex problems by a few membership grades.