基于软粗糙集的犹豫模糊三支决策方法  

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

作　　者：冯锋 万喆 徐泽水 柳晓燕 FENG Feng;WAN Zhe;XU Ze-shui;LIU Xiao-yan(School of Science,Xi’an University of Posts and Telecommunications,Xi’an 710121,China;Business School,Sichuan University,Chengdu 610064,China)

机构地区：[1]西安邮电大学理学院,西安710121 [2]四川大学商学院,成都610064

出　　处：《控制与决策》2023年第3期834-842,共9页Control and Decision

基　　金：国家自然科学基金项目(71771155);陕西省自然科学基础研究计划项目(2018JM1054)。

摘　　要：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.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.

关 键 词：犹豫模糊集 三支决策 软集 粗糙集 典范软集 

分 类 号：C934[经济管理—管理学]