基于软粗糙集的犹豫模糊三支决策方法

三支决策理论采取“三分而治”的处理思路,为复杂问题求解提供了一种简洁高效的解决方案.对此,借助软集理论研究犹豫模糊集和三支决策方法,通过定义犹豫模糊集的值空间和值陪集,引入犹豫模糊集的典范软集、单位区间参数化软集和导出犹豫模糊集等概念,解决犹豫模糊集和软集的相互表示问题.此外,利用软粗糙集理论建立一种基于犹豫模糊集的广义粗糙模型,借助给定的预决策集,计算软上近似集并确定评价函数,进而提出一种基于软粗糙集的犹豫模糊三支决策方法.最后,通过两个数值实例和相关对比分析,验证所提出三支决策方法的合理性和有效性.

Hesitant fuzzy three-way decision method based on soft rough sets

Three-way decision is a philosophy of thinking in three. It provides a simple and efficient solution for addressing complicated problems. In this paper, hesitant fuzzy sets and three-way decision methods are investigated by virtue of soft set theory. Value spaces and value cosets of hesitant fuzzy sets are defined. The notions of canonical soft sets, unit interval parameterized soft sets and derived hesitant fuzzy sets are presented to solve the mutual representation problems regarding hesitant fuzzy sets and soft sets. In addition, a generalized rough model based on hesitant fuzzy sets is established with the help of soft rough sets. Based on the given pre-decision set, soft upper approximations are calculated to determine the evaluation function. A novel hesitant fuzzy three-way decision method based on soft rough sets is proposed. Finally, two numerical examples with related comparative analysis are given to verify the effectiveness and cogency of the proposed method.