基于连续值逻辑上的不分明化拓扑线性空间

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1Vol.26,No.120062JOURNALOFMATHEMATICALRESEARCHANDEXPOSITIONFeb.,2006ArticleID:1000-341X(2006)01-0089-07Documentcode:ABaseandSubbaseinI-FuzzyTopologicalSpacesFANGJin-ming,YUEYue-li(Dept.ofMath.,OceanUniversityofChina,Qingdao266071,China)(E-mail:fangjm@public.qd

2、.sd.cn)Abstract:Inthispaper,wegivetheconceptsofthebaseandsubbaseinI-fuzzytopologicalspaces,andusethemtoscorecontinuousmappingandopenmapping.WealsostudythebaseandsubbaseintheproductspaceofI-fuzzytopologicalspaces.Keywords:I-fuzzytopology;I-fuzzyquasi-coincidentneighborhood

3、system;base;subbase;productspace.MSC(2000):54A40CLCnumber:O1891.IntroductionIn1980,H•ohle[1]introducedtheconceptofthefuzzymeasurablespaceswiththeideaofgivingdegreesin[0,1]tosometopologicaltermsratherthan0and1.In1991,fromalogicalpointview,Ying[2]introducedtheconceptoffuzzi

4、fyingtopologyandgaveitsbaseandsubbase,whichisestablishedonthecrispsetsnotonthefuzzyset.ItisvaluedtonotethatYing[2]alsointroducedanotherfuzzytopologicalspacewhichiscalledbifuzzytopologicalspace(inthispaperwecallitI-fuzzytopologicalspace).Brie yspeaking,anI-fuzzytopologyona

5、setXassignstoeveryfuzzysetonXacertaindegreeofbeingopen,otherthanbeingdenitelyopenornot.HeonlygavetheconceptofI-fuzzytopology,butdidnotstudyit.Itisverymeaningfultostudythiskindoffuzzytopologicalspace,soFang[3]introducedtheI-fuzzyquasi-coincidentneighborhoodsysteminI-fuzzy

6、topologicalspaces.InordertostudytheI-fuzzytopologicalspaces,weusetheI-fuzzyquasi-coincidentneighborhoodsystemtogivetheconceptsofbaseandsubbaseofI-fuzzytopologyandusethemtodepictthecontinuousandopenmapping.WealsostudytheproductspaceofI-fuzzytopologicalspacesandgainmanyimpo

7、rtantresults.LetXbeauniversaldiscourseandthefamilyofallfuzzysetsonXwillbedenotedbyIX(whereI=[0;1]).By0Xand1X,wedenoterespectivelytheconstantfuzzysetonXtakingthevalue0and1.Thesetofallfuzzypointsx(i.e.,afuzzysetA2IXsuchthatA(x)=6=0andA(y)=0fory6=x)isdenotedbypt(IX).Givena

8、mappingf:X!Y,wewritefforthefunctionIY!IXdenedbyf(A)=Afandwritef!forthefunctionIX!IYdenedWbyf!