L-值随机变量与Heyting代数上的运算

《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