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Weak QMV algebras and some ring-like structures

文献类型：期刊论文

作者Lu, Xian1; Shang, Yun2,3; Lu, Ru-qian2,3; Zhang, Jian1,4; Ma, Feifei1,4
刊名SOFT COMPUTING
出版日期2017-05-01
卷号21期号:10页码:2537-2547
关键词Quantum logic QMV algebras Weak QMV algebras Semirings Bimonoid
ISSN号1432-7643
DOI10.1007/s00500-017-2577-8
英文摘要In this work, we propose a new quantum structure-weak quantum MV algebras (wQMV algebras)-and define coupled bimonoids and strong coupled bimonoids. We find that the coupled bimonoids and strong coupled bimonoids are ring-like structures corresponding to lattice-ordered wQMV algebras and lattice-ordered QMV algebras, respectively. Using an automated reasoning tool, we give the smallest 4-element wQMV algebra but not a QMV algebra. We also show that lattice-ordered wQMV algebras are the real nondistributive generalization of MV algebras. Certainly, most important properties of quantum MV algebras (QMV algebras) are preserved by wQMV algebras. Furthermore, we can conclude that lattice-ordered wQMV algebras are the simplest unsharp quantum logical structures by far, based on which computation theory could be set up.
资助项目National Research Foundation of China[61472412] ; National Research Foundation of China[61621003] ; National Key Research and Development Program of China[2016YFB1000902] ; CAS/SAFEA International Partnership Program for Creative Research Teams
WOS研究方向Computer Science
语种英语
WOS记录号WOS:000400234600010
出版者SPRINGER
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/26000]  
专题数学所
通讯作者Shang, Yun
作者单位1.Chinese Acad Sci, Inst Software, Beijing, Peoples R China
2.Chinese Acad Sci, AMSS, Inst Math, Beijing, Peoples R China
3.Chinese Acad Sci, AMSS, NCMIS, Beijing, Peoples R China
4.Chinese Acad Sci, Univ CAS, Beijing, Peoples R China
推荐引用方式
GB/T 7714		 Lu, Xian,Shang, Yun,Lu, Ru-qian,et al. Weak QMV algebras and some ring-like structures[J]. SOFT COMPUTING,2017,21(10):2537-2547.
APA Lu, Xian,Shang, Yun,Lu, Ru-qian,Zhang, Jian,&Ma, Feifei.(2017).Weak QMV algebras and some ring-like structures.SOFT COMPUTING,21(10),2537-2547.
MLA Lu, Xian,et al."Weak QMV algebras and some ring-like structures".SOFT COMPUTING 21.10(2017):2537-2547.

入库方式： OAI收割

来源：数学与系统科学研究院

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