群逆伪BCI-代数与群逆滤子（英文）.pdf

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1、模糊系统与数学Vo1．28．No．2第28卷第2期2014年4月FuzzySystemsandMathematicsApr．．2014ArticleID：1OO1-7402(2014)02-0021-13Anti—groupedPseudo—BCIAlgebrasandAnti—groupedFiltersZHANGXiao—hong．YoungBaeJun(1．DepartmentofMathematics，CollegeofArtsandSciences，ShanghaiMaritimeUniversity，S

2、hanghai201306，China；2．DepartmentofMathematicsEducation，GyeongsangNationalUniversity，Chinju660—701，Korea)Abstract：ThenotionofPseudo—BCKalgebrascanberegardedasanalgebraicframework(implicationalfragment)ofnon-cc}mmutativefuzzylogics．Thispaperinvestigatesthestruct

3、uresofpseudo—BCIalgebraswhicharegeneralizationpseudoBCKalgebras．First，acharacterizationofpseudoBCIalgebraisconstructedbvthenotionofBZ—algebra(orweakBCC—algebra)．Second，therelationshipbetweenpseudo-BCIalgebrasand(non—commutative)groupsareinvestigatedbyintroduci

4、ngthenotionofanti-groupedDseudo—BCIalgebra．Third，thenotionsofanti—grouped(well，norma1)filterareintroduced，andbvthesenotionsthenecessaryandsufficientconditionsforpseudo—BCIalgebratObeantigrouped(andfiltertobep-fiher)aregiven．Finally，thefollowingresultsareproved

5、：(1)medialpseudo—BCIalgebraiseauivalenttopsemisimp1eBCIatgebra；(2)everyfilterofapseudo—BC1algebraXisP—filter，ifandonlyif，Xisanti—groupedandeverysubgroupofadjointgroupofXisnormalsubgroup·Kevwords：Pseudo—BCIA1gebra；BZ—algebra；Anti—groupedPseudo—BCIAlgebra；Anti—g

6、roupedFilter；P—filterCLCnumber10153Documentcode：A1IntroductionIntheareaofmodernfuzzylogictheory，relatedalgebraicsystemsl5．1’8。playanimportantrole．G．GeorgescuandA．Iogulescuintroducedpseudo—BCKalgebrasasanextensionofwell—knownBCK—algebras[4·6]．BCI—algebraisanimp

7、ortantgeneralizationofBCK—algebra[]．AsageneralizationofBCI—algebra。thenotionofpseudo—BCIalgebraisintroducedinEli，andsomepropertiesofpseudo—BCIalgebrasareinvestigated．Y．B．Juneta1．[introducedtheconceptof(pseudo—BCI)idealinpseudo—BCIalgebras，andtheydisplayeditsch

8、aracterizations．Recently，in[23]，westudiedtherelationshipbetweenweaklyintegralresiduatedpomonoidandDseudo-BCIalgebras．Theresultsshowthatpseudo—BCIalgebrasarebasisstructuresofweaklyi