| Weak QMV algebras and some ring-like structures | |
Lu, Xian1; Shang, Yun2,3 ; Lu, Ru-qian2,3; Zhang, Jian1,4; Ma, Feifei1,4
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| 2017-05-01 | |
| Source Publication | SOFT COMPUTING
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| ISSN | 1432-7643 |
| Volume | 21Issue:10Pages:2537-2547 |
| Abstract | 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. |
| Keyword | Quantum logic QMV algebras Weak QMV algebras Semirings Bimonoid |
| DOI | 10.1007/s00500-017-2577-8 |
| Language | 英语 |
| Funding Project | 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 Research Area | Computer Science |
| WOS Subject | Computer Science, Artificial Intelligence ; Computer Science, Interdisciplinary Applications |
| WOS ID | WOS:000400234600010 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/26001 |
| Collection | 数学所 |
| Corresponding Author | Shang, Yun |
| Affiliation | 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 |
| Recommended Citation 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. |
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