模糊一致连续集及其应用
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摘要
文章将偏序集上的一致集模糊化,引入模糊一致集的概念,研究其在完备情况下的若干性质.在模糊一致完备的情况下定义新的模糊way-below关系,给出模糊一致连续集的概念,探究一致连续集的相关性质.根据一致极小集的定义方式,给出模糊一致极小集的定义,探讨模糊一致极小集在完备情况下的基本性质,并给出其若干等价刻画.上述结论推广相关文献的有关结论.
Firstly,the concept of fuzzy uniform posets is introduced according to the definition of uniform po-sets,and some properties of fuzzy uniform posets are studied under complete conditions. A new fuzzy way-below relationship is defined on the fuzzy uniform complete posets,and then the concept of fuzzy uniform con-tinuous posets is given and studied.In addition,the definition of fuzzy uniform minimal posets is proposed ac-cording to the definition of uniform minimal posets,and the basic properties are discussed and some equiva-lent characterizations are obtained under complete conditions. Some conclusions of the related literatures areextended.
Firstly,the concept of fuzzy uniform posets is introduced according to the definition of uniform po-sets,and some properties of fuzzy uniform posets are studied under complete conditions. A new fuzzy way-below relationship is defined on the fuzzy uniform complete posets,and then the concept of fuzzy uniform con-tinuous posets is given and studied.In addition,the definition of fuzzy uniform minimal posets is proposed ac-cording to the definition of uniform minimal posets,and the basic properties are discussed and some equiva-lent characterizations are obtained under complete conditions. Some conclusions of the related literatures areextended.
引文
[1]ZADEH L A.Fuzzy sets[J].Information and control,1965,8(3):338-353.
[2]张奇业.L-Fuzzy Domain理论[D].北京:首都师范大学,2002.
[3]YAO Wei,SHI Fugui.Quantitative domain via fuzzy sets:Part I:Continuity of fuzzy directed complete posets[J].Fuzzy Sets and Systems,2010,161(7):973-987.
[4]白仲林.一致连续偏序集理论[J].西北师范大学学报(自然科学版),1996,32(2):60-65.
[5]阮小军,张小芝.关于一致连续偏序集的若干性质[J].南昌大学学报(理科版),2008,32(2):119-120.
[6]阮小军.一致连续偏序集上的序同态[J].南昌大学学报(理科版),2013,37(2):117-118.
[7]阮小军,徐晓泉.一致极小集及其对一致连续偏序集的应用[J].模糊系统与数学,2014,28(4):80-83.
[8]李海龙.一致半连续格的理论研究[D].淮北:淮北师范大学,2015.
[9]吴玉英.一致连续偏序集的若干性质[D].南京:南京师范大学,2011.
[10]刘东明,姜广浩,李辉.可数一致集及其应用[J].齐齐哈尔大学学报(自然科学版),2018,34(4):71-74.
[11]王李锋,赵彬.模糊Domain上的模糊序同态及其性质[J].陕西师范大学学报(自然科学版),2014,42(2):13-17.
[12]姜广浩,周丽.模糊可数连续格上的序同态[J].模糊系统与数学,2016,30(6):39-46.
[13]周丽,姜广浩.模糊可数连续格的基理论研究[J].模糊系统与数学,2017,31(2):50-56.
[14]姚卫.模糊偏序集上的模糊Scott拓扑及模糊拓扑空间的特殊化L-序[D].北京:北京理工大学,2008.
[15]饶三平.模糊Domain的基理论研究及其推广[D].长沙:湖南大学,2014.
[2]张奇业.L-Fuzzy Domain理论[D].北京:首都师范大学,2002.
[3]YAO Wei,SHI Fugui.Quantitative domain via fuzzy sets:Part I:Continuity of fuzzy directed complete posets[J].Fuzzy Sets and Systems,2010,161(7):973-987.
[4]白仲林.一致连续偏序集理论[J].西北师范大学学报(自然科学版),1996,32(2):60-65.
[5]阮小军,张小芝.关于一致连续偏序集的若干性质[J].南昌大学学报(理科版),2008,32(2):119-120.
[6]阮小军.一致连续偏序集上的序同态[J].南昌大学学报(理科版),2013,37(2):117-118.
[7]阮小军,徐晓泉.一致极小集及其对一致连续偏序集的应用[J].模糊系统与数学,2014,28(4):80-83.
[8]李海龙.一致半连续格的理论研究[D].淮北:淮北师范大学,2015.
[9]吴玉英.一致连续偏序集的若干性质[D].南京:南京师范大学,2011.
[10]刘东明,姜广浩,李辉.可数一致集及其应用[J].齐齐哈尔大学学报(自然科学版),2018,34(4):71-74.
[11]王李锋,赵彬.模糊Domain上的模糊序同态及其性质[J].陕西师范大学学报(自然科学版),2014,42(2):13-17.
[12]姜广浩,周丽.模糊可数连续格上的序同态[J].模糊系统与数学,2016,30(6):39-46.
[13]周丽,姜广浩.模糊可数连续格的基理论研究[J].模糊系统与数学,2017,31(2):50-56.
[14]姚卫.模糊偏序集上的模糊Scott拓扑及模糊拓扑空间的特殊化L-序[D].北京:北京理工大学,2008.
[15]饶三平.模糊Domain的基理论研究及其推广[D].长沙:湖南大学,2014.