覆盖多粒度梯形模糊数决策理论粗糙集模型

Covering multigranulation trapezoidal fuzzy decision-theoretic rough set model

作为经典Pawlak粗糙集模型的推广,基于论域上的等价关系,针对风险决策分类问题,多粒度粗糙集已有研究。其特点是在力争决策的期望损失(亦称决策的条件风险)最小的条件下,比较客观地确定对象分类区域的概率描述临界值,进而进行对象的最佳分类决策。然而,在实际应用中论域上的等价关系很难把握,况且特征状态的风险损失往往带有某种不确定性。凡此,无疑在一定程度上限制了多粒度决策理论粗糙集的应用。对此进行了研究:提出了覆盖多粒度梯形模糊数决策理论粗糙集模型,分别就平均、乐观和悲观的情形进行了讨论和刻划;得到了覆盖多粒度梯形模糊数决策理论粗糙集与已有相关模型之间的关系;结果和算例表明了模型的广泛性。

As an extension of the classical Pawlak rough set theory based on the equivalence relation on the universe, in view of the risk decision classification problem, multigranulation decision-theoretic rough sets have been researched by scholars. The main idea aims to select a series of actions, determine probability value of the thresholds of the object classi-fication area, obtain the best decisions of which the overall expected loss function（also called decision-making risk）is as small as possible. However, taking account to the difficulty of getting the equivalence relation in an incomplete infor-mation system, the uncertainty of the risk or cost of actions in different states, and the lacking of multigranulation decision-theoretic rough sets, covering multigranulation trapezoidal fuzzy decision-theoretic rough set models are proposed in this paper. In addition, the average, optimistic and pessimistic covering multigranulation trapezoidal fuzzy decision-theoretic rough set models are investigated respectively. Finally, the relationships between covering multigranulation trapezoidal fuzzy decision-theoretic rough sets and the existing models are discussed. The results obtained and examples illustrate the generality of the models.