自然科学版
陕西师范大学学报(自然科学版)
三支决策专题
基于重叠函数的模糊粗糙集及其应用
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文小凤1,张小红1*,王敬前1,雷涛2
(1 陕西科技大学 数学与数据科学学院,陕西 西安 710021;2 陕西科技大学 电子信息与人工智能学院,陕西 西安 710021)
张小红,男,教授,博士生导师,研究方向为模糊逻辑、粗糙集和人工智能。E-mail:zhangxiaohong@sust.edu.cn
摘要:
重叠函数和连续三角模有着密切联系,广义重叠函数是对重叠函数的进一步拓广,(广义)重叠函数在图像处理、数据分类、不确定多属性决策等方面有着重要的应用。基于连续三角模的模糊粗糙集模型,利用(广义)重叠函数及其剩余蕴涵提出了一种新的模糊粗糙集模型,分析和研究了新的模糊上下近似算子的基本性质。同时,利用前述模糊上下近似算子提出一种不确定多属性决策新方法,并通过一个具体案例说明了新方法的可行性和有效性。
关键词:
重叠函数;广义重叠函数;连续三角模;模糊粗糙集;多属性决策
收稿日期:
2020-12-28
中图分类号:
O159
文献标识码:
A
文章编号:
1672-4291(2022)03-0024-09
基金项目:
国家自然科学基金(61976130)
Doi:
10.15983/j.cnki.jsnu.2022104
Fuzzy rough sets based on overlap functions and their application
WEN Xiaofeng1, ZHANG Xiaohong1*,WANG Jingqian1, LEI Tao2
(1 School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xian 710021, Shaanxi, China;2 School of Electronic Information and Artificial Intelligence,Shaanxi University of Science and Technology, Xian 710021, Shaanxi, China)
Abstract:
Overlap function is closely related to continuous triangular norm and general overlap function is a further extension of overlap function.There are several important applications of (general) overlap function, such as image processing, data classification, uncertain multi-attribute decision making and so on. In this paper, the fuzzy rough set model based on continuous triangular norm is extended, a new kind of fuzzy rough set model is proposed by using (general) overlap function and its residual implication, and the basic properties of the new fuzzy upper and lower approximation operators are analyzed and studied. At the same time, a new uncertainty multi-attribute decision making method is proposed by using the fuzzy upper and lower approximation operators, and the feasibility and effectiveness of the new method is illustrated by a specific case.
KeyWords:
overlap function; general overlap function; continuous triangular norm; fuzzy rough set; multi-attribute decision making