BCK/BCI-代数的(∈,∈∨q)-模糊软理想
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摘要
在BCK/BCI-代数中引入(∈,∈∨q)-模糊软理想的概念,研究并获得了若干代数性质.定义了BCK/BCI-代数的模糊软同态和模糊软同构的概念,证明了(∈,∈∨q)-模糊软理想的模糊软同构(态)像(原像)仍为(∈,∈∨q)-模糊软理想这一结论.
The notion of(∈,∈∨q)-fuzzy soft ideals of BCK/BCI-algebras is introduced.Their algebraic properties are discussed and obtained.Concepts of fuzzy soft homomorphism and isomorphism between two BCK/BCI-algebras are defined.It is proved that the fuzzy soft isomorphism(resp.homomorphism)image(resp.inverse image)of a(∈,∈∨q)-fuzzy soft ideal is also a(∈,∈∨q)-fuzzy soft ideal.
The notion of(∈,∈∨q)-fuzzy soft ideals of BCK/BCI-algebras is introduced.Their algebraic properties are discussed and obtained.Concepts of fuzzy soft homomorphism and isomorphism between two BCK/BCI-algebras are defined.It is proved that the fuzzy soft isomorphism(resp.homomorphism)image(resp.inverse image)of a(∈,∈∨q)-fuzzy soft ideal is also a(∈,∈∨q)-fuzzy soft ideal.
引文
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[11]陈娟娟,李生刚.BCI代数上的反模糊软理想与模糊软理想[J].计算机工程与应用,2013,49(9):10-12.CHEN Juanjuan,LI Shenggang.Anti-fuzzy soft ideals and fuzzy soft ideals in BCI-algebras[J].Computer Engineering and Applications,2013,49(9):10-12.
[12]刘璐璐.软拓扑的确定以及有限拟阵的确定[D].西安:陕西师范大学,2012.LIU Lulu.Determination of Soft Topologies and Finite Matroids[D].Xi’an:Shaanxi Normal University,2012.
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[14]JUN Y B,LEE K J,PARK C H.Fuzzy soft sets theory applied to BCK/BCI-algebras[J].Computers Mathematics with Applications,2009,57:367-378.
[15]ZHANG G J,ZHANG C,LIU Z X.New kinds of fuzzy ideals in BCI-algebras[J].Fuzzy Optim Decis Making,2006(5):177-186.
[2]IORGULESCU A.Some direct ascendants of Wajsberg and MV-algebras[J].Scientiae Mathematics Japonica,2003,57(3):583-647.
[3]MOLODTSOV D.Soft set theory-first results[J].Computers Mathematics with Applications,1999,37(4):19-31.
[4]MAJI P K,BISWAS R,ROY A R.Fuzzy soft sets[J].Journal of Fuzzy Mathematics,2001,9(3):589-602.
[5]ZADEH L A.Fuzzy sets[J].Information&Control,1965(8):338-353.
[6]AKTAS H,CAGMAN N.Soft sets and soft groups[J].Information Sciences,2007,177:2726-2735.
[7]JUN Y B.Soft BCK/BCI-algebras[J].Computers Mathematics with Applications,2008,56:1408-1413.
[8]JUN Y B,CHUL P H.Applications of soft sets in ideals theory of BCK/BCI-algebras[J].Information Sciences,2008,178:2466-2475.
[9]刘春辉.软格[J].模糊系统与数学,2013,27(5):40-46.LIU Chunhui.Soft lattices[J].Fuzzy Systems and Mathematics,2013,27(5):40-46.
[10]刘春辉.滤子化软FI代数[J].山东大学学报:理学版,2012,47(11):94-98.LIU Chunhui.Filteristic soft FI-algebras[J].Journal of Shandong University:Natural Science,2012,47(11):94-98.
[11]陈娟娟,李生刚.BCI代数上的反模糊软理想与模糊软理想[J].计算机工程与应用,2013,49(9):10-12.CHEN Juanjuan,LI Shenggang.Anti-fuzzy soft ideals and fuzzy soft ideals in BCI-algebras[J].Computer Engineering and Applications,2013,49(9):10-12.
[12]刘璐璐.软拓扑的确定以及有限拟阵的确定[D].西安:陕西师范大学,2012.LIU Lulu.Determination of Soft Topologies and Finite Matroids[D].Xi’an:Shaanxi Normal University,2012.
[13]JUN Y B,LEE K J,PARK C H.Fuzzy soft sets theory applied to ideals in d-algebras[J].Computers Mathematics with Applications,2010,59:3180-3192.
[14]JUN Y B,LEE K J,PARK C H.Fuzzy soft sets theory applied to BCK/BCI-algebras[J].Computers Mathematics with Applications,2009,57:367-378.
[15]ZHANG G J,ZHANG C,LIU Z X.New kinds of fuzzy ideals in BCI-algebras[J].Fuzzy Optim Decis Making,2006(5):177-186.