准模糊图拟阵模糊基的研究

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1、TheStudyonBasesofQuasi-FuzzyGraphMatriodsTheThesisSubmittedtoChongqingUniversityinPartialFulfillmentoftheRequirementfortheMaster’sDegreeofScienceByXiaJunSupervisedbyProf.WuDeyinSpecialty:OperationalResearchandCyberneticsCollegeofMathematicsandStatist

2、icsofChongqingUniversity,Chongqing,ChinaApril,2013重庆大学硕士学位论文中文摘要摘要在现有拟阵和模糊拟阵理论的基础上，本文主要研究了模糊拟阵模糊基，特别是准模糊图拟阵模糊基的性质。1)研究了模糊拟阵的闭、正规与其模糊基的存在性之间的关系，给出了闭模糊拟阵的一类模糊基的构造方法；2)分析了准模糊图拟阵与闭正规模糊拟阵之间的关系，找到了准模糊图拟阵是闭正规模糊拟阵的一个充分条件；3)研究了准模糊图拟阵模糊基的性质，得到了准模糊图拟阵的模糊基结构定理。还

3、证明了准模糊图拟阵的模糊基与其导出拟阵M的基有一一对应关系。最后r1还得到了准模糊图拟阵模糊基的对称交换定理；4)研究了准模糊图拟阵的模糊基有序问题，得到了准模糊图拟阵是模糊基有序的一个充要条件。本文比较深入的研究了准模糊图拟阵的模糊基及其与导出拟阵M的基之间r1的关系等。这些研究对丰富准模糊图拟阵的理论有重要意义。关键词：模糊拟阵，准模糊图拟阵，正规模糊拟阵，基，模糊基I重庆大学硕士学位论文英文摘要ABSTRACTOnthebaseoftheoriginaltheoryofcrispmatro

4、idsandfuzzymatroids,thepaperstudiesmainlyaboutthepropertiesofbasesoffuzzymatroids,especially,andstudiesthepropertiesofbasesofquasi-fuzzygraphmatroids.1)Thepaperstudiestherelationshipbetweentheclosedorregularpropertiesoffuzzymatroidsandtheexistenceoff

5、uzzybasesoffuzzymatroids.Wehaveobtainedamethodtostructureafuzzybaseintheclosedfuzzymatroid；2)Therelationshipbetweenquasi-fuzzygraphmatroidsandclosedregularfuzzymatroidshadbeenanalyzed,wehavegotoneofsufficientconditionswhichquasi-fuzzygraphmatroidsisc

6、losedregularfuzzymatroids；3)Thepropertiesofbasesofquasi-fuzzygraphmatroidswerestudied,andwehavealsoobtainedthestructure-theormofbasesofquasi-fuzzygraphmatroids.Wehaveprovedtheexistenceofthebijectionbetweenbasesofquasi-fuzzygraphmatroidsandbasesofindu

7、cedmatroidsM.Lastly,wehavestudiedthesymmetry-exchanger1propertiesoffuzzybasesofquasi-fuzzygraphmatroids；4)Fromfutherresearchonordere-basesofquasi-fuzzygraphmatroids,wehavefoundtwosufficientconditionswhichquasi-fuzzygraphmatroidsisorder-basesfuzzymatr

8、oids.Thispaperworkoverdeeplythebasesofquasi-fuzzygraphmatroids,alongwiththerelationshipbetweenthebasesofquasi-fuzzygraphmatroidsanditsinducedmatroidsM.Thesehavebeenimportanttoenrichtheoryfoundationfortheresearchr1ofquasi-fuzzygraphmatroids.Keywords：f