基于重叠函数的模糊粗糙集及其应用

文小凤; 张小红; 王敬前; 雷涛

doi:10.15983/j.cnki.jsnu.2022104

陕西师范大学学报(自然科学版) >

2022 , Vol. 50 >Issue 3: 24 - 32

DOI: https://doi.org/10.15983/j.cnki.jsnu.2022104

三支决策专题

基于重叠函数的模糊粗糙集及其应用

文小凤 ,
张小红 ,
王敬前 ,
雷涛

展开

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

收稿日期: 2020-12-28

网络出版日期: 2022-05-10

基金资助

国家自然科学基金(61976130)

收起

Fuzzy rough sets based on overlap functions and their application

WEN Xiaofeng ,
ZHANG Xiaohong ,
WANG Jingqian ,
LEI Tao

Expand

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

Received date: 2020-12-28

Online published: 2022-05-10

Fold

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

本文引用格式

文小凤 , 张小红 , 王敬前 , 雷涛 . 基于重叠函数的模糊粗糙集及其应用[J]. 陕西师范大学学报(自然科学版), 2022 , 50(3) : 24 -32 . DOI: 10.15983/j.cnki.jsnu.2022104

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.

Key words： overlap function; general overlap function; continuous triangular norm; fuzzy rough set; multi-attribute decision making

参考文献

[1] ZADEH L A.Fuzzy sets[J].Information and Control, 1965, 8: 338-353.
[2] PAWLAK Z.Rough sets[J].International Journal of Computer and Information Science, 1982, 11: 341-356.
[3] DUBOIS D, PRADE H.Rough fuzzy sets and fuzzy rough sets[J].International Journal of General Systems, 1990,17:191-209.
[4] 顾秀梅, 秦克云, 张家锋.基于三角模的模糊粗糙集与模糊关系之间的联系[J].海南师范学院学报(自然科学版), 2006,19(4): 301-304.
GU X M,QIN K Y,ZHANG J F.Connections between fuzzy rough sets based on triangular norm and the fuzzy relation[J].Journal of Hainan Normal University (Natural Science),2006,19(4):301-304.
[5] MORSI N N, YAKOUT M M.Axiomatics for fuzzy rough sets[J].Fuzzy Sets and Systems, 1998, 100(1/2/3): 327-342.
[6] WANG C Y, HU B Q.Fuzzy rough sets based on generalized residuated lattices[J].Information Sciences, 2013, 248: 31-49.
[7] WANG C Y.A comparative study of variable precision fuzzy rough sets based on residuated lattices[J].Fuzzy Sets and Systems, 2019, 373: 94-115.
[8] ANNA M R, ETIENCE E K.A comparative study of fuzzy rough sets[J].Fuzzy Sets and Systems, 2002, 126(2): 137-155.
[9] WU W Z , YEE L, MI J S.On characterizations of (I,T)-fuzzy rough approximation operators[J].Fuzzy Sets and Systems, 2005, 154(1): 76-102.
[10] SUN B Z, GONG Z T, CHEN D G.Fuzzy rough set theory for the interval-valued fuzzy information systems[J].Information Sciences, 2008, 178(13): 2794-2815.
[11] 徐小来, 雷英杰, 谭巧英.基于直觉模糊三角模的直觉模糊粗糙集[J].控制与决策, 2008,23(8): 900-904.
XU X L,LEI Y J,TAN Q Y.Intuitionistic fuzzy rough sets based on intuitionistic fuzzy triangle norm[J].Control and Decision,2008,23(8):900-904.
[12] ZHANG K, ZHAN J M, WU W Z.Novel fuzzy rough set models and corresponding applications to multi-criteria decision-making[J].Fuzzy Sets and Systems, 2020, 383: 92-126.
[13] DUBOIS D, PRADE H.Putting rough sets and fuzzy sets together[M]//Intelligent Decision Support.Dordrecht,Netherlands:Springer, 1992: 203-232.
[14] 苗夺谦,胡声丹.基于粒计算的不确定性分析[J].西北大学学报(自然科学版),2019,49(4):487-495.
MIAO D Q,HU S D.Uncertainty analysis based on granular computing[J].Journal of Northwest University (Natural Science Edition),2019,49(4):487-495.
[15] 李兵洋, 肖健梅, 王锡淮.基于多目标领域差分进化和模糊粗糙集的属性约简算法[J].控制与决策,2019, 34(5): 947-955.
LI B Y,XIAO J M,WANG X H.Attribute reduction with fuzzy rough set based on multiobjective neighborhood difference algorithm[J].Control and Decision,2019,34(5):947-955.
[16] LIN Y J, LI Y W,WANG C X, et al.Attribute reduction for multi-label learning with fuzzy rough set[J].Knowledge-Based Systems, 2018, 152(15): 51-61.
[17] ZHAN J M, SUN B Z, CARLOS J, et al.Covering based multigranulation (I,T)-fuzzy rough set models and applications in multi-attribute group decision-making[J].Information Sciences, 2019, 476: 290-318.
[18] 张小红, 裴道武, 代建华.模糊数学与Rough集理论[M].北京: 清华大学出版社, 2013: 222-226.
ZHANG X H,PEI D W,DAI J H.Fuzzy mathematics and Rough set theory [M].Beijing:Tsinghua University Press,2013:222-226.
[19] LYNN D, NELE V, CHRIS C, et al.Implicator-conjunctor based models of fuzzy rough sets: definitions and properties[J].Lecture Notes in Computer Science, 2013, 8170(1): 169-179.
[20] BUSTINCE H, FERNANDEZ J, MESIAR R, et al.Overlap index, overlap functions and migrativity[C]//Joint 2009 International Fuzzy Systems Association Word Congress and 2009 European Society of Fuzzy Logic and Technology Conference.Lisbon, Portugal:DBLP, 2009, 65: 300-305.
[21] BUSTINCE H, BARRENECHA E, PAGOLA M.Image thresholding using restrited equivalent functions and maximizing the measures of similarity[J].Fuzzy Sets and Systems, 2007, 158(5): 496-516.
[22] AMO A, MONTERO J, BIGING G, et al.Fuzzy classification systems[J].European Journal of Operational Research, 2004, 156(2): 495-507.
[23] BEDREGAL B, DIMURO G P, BUSTINCE H, et al.New results on overlap and grouping functions[J].Information Sciences, 2013, 249: 148-170.
[24] DIMURO G P, BEDREGAL B.On residual implications derived from overlap functions[J].Information Science,2015, 312: 78-88.
[25] BUSTINCE H, FERNANDEZ J, MESIAR R, et al.Overlap functions[J].Nonlinear Analysis, 2010, 72(3): 1488-1499.
[26] ELKANO M, GALAR M, SANZ J, et al.Enhancing multiclass classification in FARC-HD fuzzy classifier: on the synergy between n-dimensional overlap functions and decomposition strategies[J].IEEE Transactions on Fuzzy Systems, 2015, 23(5): 1562-1580.
[27] 乔军胜.重叠函数与分组函数的相关问题研究[D].武汉:武汉大学,2018.
QIAO J S.Some new results on overlap and grouping functions[D].Wuhan:Wuhan University,2018.
[28] MIGUEL L D, GÓMEZ D, TINGUARO R J, et al.General overlap functions[J].Fuzzy Sets and Systems, 2019, 372: 81-96.
[29] YAO Y Y.Tri-level thinking: models of three-way decision[J].International Journal of Machine Learning and Cybernetics, 2020,11(5): 947-959.
[30] YAO Y Y.Set-theoretic models of three-way decision[J].Granular Computing, 2021,6(1):133-148.

Options

文章导航

模态框（Modal）标题

摘要

本文引用格式

Abstract

参考文献