欢迎来到天天文库
浏览记录
ID:39105468
大小:765.46 KB
页数:34页
时间:2019-06-24
《L-值随机变量与Heyting代数上的运算》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、L·valuedRandomVariablesandtheOperationoonHeytingAlgebrasBAOHong-liangAbstract:Researchesofthisthesisincludingtworespects(bothrelatetolatticetheoryandtopology).Ononehamd,wehaveinvestigatedL-valuedrandomvariables(Lisaclosed一8etlatticeormoleculelygeneratedlattice).Receivingal—readyha
2、sinspirationofthought、methodandskillstudyingL-topologicalspaceindocuments,wehavedefinedacrisptopology哂on硭(Ⅳ)={A∈LⅣJforeachainCopr(L),{z∈丑tIA@)≥△)isnon—emptycompactsetofR“}andseveralkindsofmetriconL-subsetgroups,somepropertieshavediscussedofthem.Onthisbasis。wehavedefinedseveralL-va
3、luedrandomvariablesanddiscussedprelim—inarynatureofthem.Atthesallletime,wehavestudledbediefmeasureinducedbyL-valuedrandomvariablesanditsnature.Ontheotherhand,akindofoperationoisdefinedonHeytingalgebraswithminimalelements,andpropertiesofoandnucleus,includingrelationshipsbetweenoand
4、nugleus,areinvestigated.Thecontentofthistextdividesintofourchaptersaltogether:Thechapteroneisprepareknowledge,whichhasintroducedthetopologyonsuperspaceandtheconceptofmeasurablemultivaluedmappingandrandomsets.OnrandomF—set’Sbasis,wehavegiyentheconceptofrandomL—setanditsnature.Thech
5、aptertwoismainpartofthispaper,L—valuedrandomvariablesarestudied(Lisaclosedsetlatticeormoleculelygeneratedlattice).Atfirst,wehaveintroducedtheconceptsof跆(础),硭。(础),掣(R1,磷(R8),andhaveprovedthat(/Co,h)isacompletemetricspace.Nextwehavedefinedacrisptopology嘞on硭(R-)andthreekindofmetricon
6、L-subsetgroups,andWehaveprovedthat(譬(酣),7每)isaseparablespaceandunderthemapping霄=k)倒(丌o:j}(R,n)——'‰,JisCopr(L)),wehavegottenthatif8∈仃(7≈),7r(日)∈盯(7;h);ifA∈口(7魏),7r一1(4)∈盯(7≈)(phisametricontheproductspace£olJ
7、,7赫istheproducttopologyinducedbythemetric劬).Finally,wehavedefinedseveralki
8、ndsofL-valuedrandomvariablesOilthisbasisanddiscussedpreliminarynatureofthem.3Inthechapterthree,wehavemainlystudiedbiliefmeasureinducedbyL-valuedrandomvariablesanditsproperties.Inthischapter,wehavegivenbeliefmeasureinducedbyKwakernaakL—valuedrandomvariableanditsnatureusingthemethod
9、oflatticetheoryandtopology.thecha
此文档下载收益归作者所有