多粒度粗糙集模型的一致模语义分析

南京大学学报(自然科学版) ›› 2017, Vol. 53 ›› Issue (5): 954–.

多粒度粗糙集模型的一致模语义分析

贺晓丽1，2，魏　玲1*，折延宏2

出版日期:2017-09-25 发布日期:2017-09-25
作者简介: 1.西北大学数学学院，西安，710127；2.西安石油大学理学院，西安，710065
基金资助:
基金项目：国家自然科学基金(61772021，11371014，61472471)，陕西省创新人才推进计划－青年科技新星项目(2017KJXX－60)
收稿日期：2017－07－23
*通讯联系人，E－mail：wl@nwu.edu.cn

An uninorm based semantic analysis of multigranulation rough set models

He Xiaoli1，2，Wei Lin1*，She Yanhong2

Online:2017-09-25 Published:2017-09-25
About author: 1.School of Mathematics，Northwest University，Xi’an，710127，China；
2．College of Science，Xi’an Shiyou University，Xi’an，710065，China

摘要/Abstract

摘要： 一致模是单位元取自[0，1]中任意数值的新型聚合算子，是常见三角模与三角余模的自然推广．从一致模的角度出发对已有的多粒度粗糙集模型进行了细致分析，进一步，通过将边界域中对象的粗糙隶属度进一步细化，将对象在每个Pawlak空间中的粗糙隶属度进行聚合，给出了对象在多粒度空间中粗糙隶属度的全新定义，并对其语义表示特点进行了分析．

Abstract: An uninorm is a new type of aggregation operator whose identity element lies anywhere in[0，1]．It is the natural generalization of both t－norms and t－conorms.This paper seeks to investigate the existing multigranulation rough set models from the viewpoint of uninorms.Precisely，we prpose a new type of approach to information fusion in multigranulation space.To this end，we firstly review some basic notions about uninorms and rough set models in multigranulation spaces.Then we give a new definition of rough membership degree in multigranulation space with two equivalence relations imposed upon the universe.Based on the membership degree，we also classify the universe into three disjoint regions according to the essential idea of three－way decision.We also examine the properties of rough membership degree in detail.The obtained results show that if the rough membership degree in each Pawlak space is larger than or equal to the identity element of the concerted uninorm，then its rough membership degree in multigranulation space is larger than or equal to those in each Pawlak space，this is a type of optimistic information fusion.Contrarily，if the rough membership degree in each Pawlak space is less than or equal to the identity element of a uninorm，then the combined rough membership degree in multigranulation space is less than or equal to those in each Pawlak space，this is a type of pessimistic information fusion.Since both t－norms and t－conorms are treated as special cases of uninorms，we analyze the feature of information fusion by using these two types of uninorms.We also give the representation of the existing multigranulation rough set models by using uninorms.The obtained results show that the optimistic multigranulation rough set model can be expressed in terms of uninorms，on the contrast，the pessmistic multigranulation rough set model cannot be expressed by using uninorms.Noting that in the expression of optimistic multigranulation rough set models，the elements of boundary region are treated equally，concretely，the membership degreees of elements in boundary regions are 1,2，we further extend this result by considering the rough membership degegree proposed by Pawlak.Moreover，by using a more general notion of compromise operators，we give the new definition of rough membership degree in multigranulation space and presents its semantic feature.

贺晓丽1，2，魏　玲1*，折延宏2. 多粒度粗糙集模型的一致模语义分析[J]. 南京大学学报(自然科学版), 2017, 53(5): 954–.

He Xiaoli1，2，Wei Lin1*，She Yanhong2. An uninorm based semantic analysis of multigranulation rough set models[J]. Journal of Nanjing University(Natural Sciences), 2017, 53(5): 954–.

参考文献

[1]　Lin T Y，Yao Y Y，Zadeh L A．Data mining，rough sets and granular computing.Springer Berlin Heidelberg，2002，536.
[2] Yao Y Y．Perspectives of granular computing.In：2005 IEEE International Conference on Granular Computing.Beijing，China：IEEE Press，2005，1：85－90.
[3] Yao Y Y．The art of granular computing.In：Kryszkiewicz M，Peters J F，Rybinski H，et al.Rough sets and intelligent systems paradigms.Springer Berlin Heidelberg，2007：101－112.
[4] Pawlak Z．Rough sets.International Journal of Computer & Information Sciences，1982，11(5)：341－356.
[5] Pawlak Z．Rough sets：Theoretical aspects of reasoning about data.Springer Netherlands，1991，231.
[6] Qian Y H，Liang J Y，Yao Y Y，et al.MGRS：A multi－granulation rough set.Information Sciences，2010，180(6)：949－970.
[7] Qian Y H，Liang J Y，Dang C Y．Incomplete multigranulation rough set.IEEE Transactions on Systems，Man，and Cybernetics － Part A：Systems and Humans，2010，40(2)：420－431.
[8] Yager R R，Rybalov A．Uninorm aggregation operators.Fuzzy Sets and Systems，1996，80(1)：111－120.
[9] Yao Y Y，She Y H．Rough set models in multigranulation spaces.Information Sciences，2016，327：40－56.
[10] She Y H，He X L．On the structure of the multigranulation rough set model.Knowledge－Based Systems，2012，36：81－92.
[11] She Y H，He X L，Shi H X，et al.A multiple－valued logic approach for multigranulation rough set model.International Journal of Approximate Reasoning，2017，82：270－284.
[12] Zhang X H，Miao D Q，Liu C H，et al.Constructive methods of rough approximation operators and multigranulation rough sets.Knowledge－Based Systems，2016，91：114－125.
[13] Li Y M，Shi Z K．Remarks on uninorm aggregation operators.Fuzzy Sets and Systems，2000，114(3)：377－380.
[14] Luo X D，Jennings N R．A spectrum of compromise aggregation operators for multi－attribute decision making.Artificial Intelligence，2007，171(2－3)：161－184.
[15] Huang B，Guo C X，Zhuang Y L，et al.Intuitionistic fuzzy multigranulation rough sets.Information Sciences，2014，277：299－320.
[16] Xu W H，Wang Q R，Zhang X T．Multi－granulation fuzzy rough sets in a fuzzy tolerance approximation space.International Journal of Fuzzy Systems，2011，13(4)：246－259.
[17] Yang X B，Song X N，Dou H L，et al.Multi－granulation rough set：From crisp to fuzzy case.Annals of Fuzzy Mathematics and Informatics，2011，1(1)：55－70.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed