IMTL-代数的零化算子和⊕理想及其相互关系
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摘要
主要对IMTL-代数中的零化算子和⊕理想的性质及其相互关系进行了研究。首先,将零化算子的概念引入到IMTL-代数中,在IMTL-代数中分别讨论了单点零化算子,多点零化算子的性质;其次,将⊕理想的概念引入IMTL-代数中,并对⊕理想的基本性质进行了讨论;最后,给出了IMTL-代数上零化子和⊕理想之间的相互依赖的关系和相互决定的方法。
The main purpose is to study the properties of annihilator operator and ⊕ ideal with relationships among them.Firstly, the concept of annihilator operator is introduced into IMTL-algebras. The properties of single-point annihilator operator and multiple-point annihilator operator have been investigated respectively. Secondly, ⊕ ideal is introduced to IMTL-algebras and its some basic properties are discussed. Finally, the dependent relationship and decision relationship between annihilators and ⊕ ideals are explored.
The main purpose is to study the properties of annihilator operator and ⊕ ideal with relationships among them.Firstly, the concept of annihilator operator is introduced into IMTL-algebras. The properties of single-point annihilator operator and multiple-point annihilator operator have been investigated respectively. Secondly, ⊕ ideal is introduced to IMTL-algebras and its some basic properties are discussed. Finally, the dependent relationship and decision relationship between annihilators and ⊕ ideals are explored.
引文
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[14]王霞霞,吴洪博.BL-代数的余零化子及其BL-同态像[J].吉林大学学报:理学版,2014,52(6):1112-1118.
[15]吴洪博,王娜.BR0-代数中MT理想的扩展及素MT理想的存在性[J].电子学报,2015,43(6):1137-1143.
[16]吴洪博,汪宁.基于正则FI代数的MT理想及其应用[J].电子学报,2013,41(7):60-63.
[17]程国胜.R0-代数中滤子与理想[J].模糊系统与数学,2001,15(1):58-61.
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[19]文贤红,吴洪博.MV-代数中的⊕理想与同余关系及其相关性质[J].计算机工程与应用,2015,51(2):60-63.
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[3]徐杨.格蕴涵代数[J].西南交通大学学报,1993,28(1):20-27.
[4]王国俊.非经典数理逻辑与近似推理[M].2版.北京:科学出版社,2006.
[5]Hajek P.Metamathematics of fuzzy logic[M].Dordredt:Kluwer Academic Publishers,1998.
[6]Esteva F,Godo L.Monoidal t-norm based logic:towards a logic for left-continuous t-norms[J].Fuzzy Sets and Systems,2001,124(3):271-288.
[7]吴洪博.基础R0-代数与基础L*系统[J].数学进展,2003,32(5):565-576.
[8]Turunen E.Mathematics behind fuzzy logic[M].Heidelberg:Physica-Verlag,1999.
[9]刘军,徐扬.格蕴涵代数的滤子与结构[J].科学通报,1997,42(10):1049-1052.
[10]龙希庆,徐扬.有限格蕴涵代数的零化子[J].模糊系统与数学,2011,25(3):9-12.
[11]赵建彬,朱华,陈树伟.格蕴涵代数中的零化子[J].郑州大学学报:理学版,2012,44(2):35-38.
[12]Zhang Xiaohong.On filters in MTL-algebras brief report[J].Advances in Systems Science Applications,2007,7(1):32-38.
[13]王娜,吴洪博.MTL-代数的演绎系统和余零化子及其相互关系[J].模糊系统与数学,2014,28(1):9-14.
[14]王霞霞,吴洪博.BL-代数的余零化子及其BL-同态像[J].吉林大学学报:理学版,2014,52(6):1112-1118.
[15]吴洪博,王娜.BR0-代数中MT理想的扩展及素MT理想的存在性[J].电子学报,2015,43(6):1137-1143.
[16]吴洪博,汪宁.基于正则FI代数的MT理想及其应用[J].电子学报,2013,41(7):60-63.
[17]程国胜.R0-代数中滤子与理想[J].模糊系统与数学,2001,15(1):58-61.
[18]覃锋.R0-代数的理想及其定义的简化[J].陕西师范大学学报,2004,32(3):18-21.
[19]文贤红,吴洪博.MV-代数中的⊕理想与同余关系及其相关性质[J].计算机工程与应用,2015,51(2):60-63.