Weak QMV algebras and some ring-like structures

doi:10.1007/s00500-017-2577-8

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 数学所

	Weak QMV algebras and some ring-like structures
	Lu, Xian 1; Shang, Yun2,3 ; Lu, Ru-qian2,3 ; Zhang, Jian 1,4; Ma, Feifei 1,4
刊名	SOFT COMPUTING
	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
DOI	10.1007/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
出版者	SPRINGER
WOS记录号	WOS:000400234600010
内容类型	期刊论文
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.