模糊賦范空間中冪集線性算子的若干研究.pdf

1、南京師范大學(xué)碩士學(xué)位論文模糊賦范空間中冪集線性算子的若干研究姓名：陶嵐申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：嚴(yán)從華20070301MastersDegreeDissertationofNanjingNormalUniversityAbstractFuzzynomedspacetheoriesareimportantpartsinfuzzyanalysis，whilepowersetlinearoperatorisareasonabl

2、eformofclassiclinearoperatorinfuzzynormedspaceThedissertationsystematiclydiscussestheimportantpropertiesofpowersetlinearoperatorsinfuzzynormedspace(asnormsofoperators，boundednessandcontinuity，convergenceofoperatorssequen

3、ces)Themaincontentsaleasfollows：1WedisnsstherelationoffuzzynornqBfortheZadeh7stypelinearoperators，specialkindsofpowersetoperators，inthesensesofKrishnaandSarma，WuandFang，respectivelyThengetapreciseterm2Wegiveoutthedefinit

4、ionoffuzzynormofpowersetlinearoperatorbasedonthesenseofWuandFang，a180wegettwocharacterizationsoftheboundedfuzzypowersetlinearoperators，whichshowouttheequivalencebetweenfuzzybounded。nessandfuzzycontinuityofpowersetlinearo

5、peratorsinfuzzynormedspacesAlso，weproofthatthecontinuitiesofZadeh‘8typelinearoperatorsinK—fuzzynormedspaceandWFfuzzynormedspacealeequivalent，fromwhichwegetsomesufficientandnecessaryconditionsoffuzzycontinuityforgeneralpo

6、wersetlinearoperatorsAndinvestigatetherelationbetweenfuzzycontinuityofpowersetlinearoperatorsandgeneraloperators3Byintroducingthedefinitionsofuniformconvergenceandstrongconvergenceofpowersetlinearoperatorssequences，weget

7、therelationbetweenthetwoconver～gencesMoveover，wegetthefuzzytopologicalstructurecorrespondingLostrongconvergenceofpowersethnearoperatorssequencesandproofthatitisHausdorffandlocalconvexfuzzylineartopologicalspaceKeywords：f