Weak QMV algebras and some ring-like structures

doi:10.1007/s00500-017-2577-8

CSpace > 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
	2017-05-01
发表期刊	SOFT COMPUTING
ISSN	1432-7643
卷号	21 期号:10 页码:2537-2547
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.
关键词	Quantum logic QMV algebras Weak QMV algebras Semirings Bimonoid
DOI	10.1007/s00500-017-2577-8
语种	英语
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
WOS类目	Computer Science, Artificial Intelligence ; Computer Science, Interdisciplinary Applications
WOS记录号	WOS:000400234600010
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26001
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.