新型软半环
|
摘要
将软集的参数集赋予半环的代数结构,提出新型软半环的概念,并利用对偶软集的方法给出新型软半环的等价刻画;然后讨论了两个新型软半环在限制交和且等运算下仍然是新型软半环的性质;最后得到新型软半环的同态像和原像仍然是新型软半环的结论.
Firstly,The concept of a new type of soft semirings is introduced by endowing a parameter set with a semiring algebra structure and the equivalent characterizations of a new type of soft semirings are given by applying the dual soft set.Secondly,under the condition of the restricted intersection and the AND operation of soft set,two of a new type of soft semirings are still of new type of soft semirings.Finally,the theorem that homomorphism image and preimage of a new type of soft semirings are still of it are proved.
Firstly,The concept of a new type of soft semirings is introduced by endowing a parameter set with a semiring algebra structure and the equivalent characterizations of a new type of soft semirings are given by applying the dual soft set.Secondly,under the condition of the restricted intersection and the AND operation of soft set,two of a new type of soft semirings are still of new type of soft semirings.Finally,the theorem that homomorphism image and preimage of a new type of soft semirings are still of it are proved.
引文
[1]Zadeh L A.Fuzzy sets[J].Information and Control,1965,8:338-353.
[2]Pawlak Z.Rough Sets[J].International Journal of Information and Computer Sciences,1982,11:341-356.
[3]Astanassov K.Intuitionistic Fuzzy Sets[J].Fuzzy Sets and Systems,1986,20:87-96.
[4]Molodtsow D.Soft set theory-first results[J].Computers and Mathematics with AppUcations,1999,37:19-31.
[5]Maji P K,Roy A R,Biswas R.Soft set theory[J].Computers and Mathematics with Applications,2003,45(4):555-562.
[6]Irfan M,Ali Feng F,Xiaoyan L.On Some New Operations in Soft Set Theory[J].Computers and Mathematics with Applications,2009,57(9):1547-1553.
[7]Sezgin A,Atagun A O.Soft groups and normalistic soft groups[J].Computers and Mathematics with Applications,2011,62:685-698.
[8]Aktas H,Cagman N.Soft sets and soft groups[J].Information Science,2007,177(13):2726-2735.
[9]Feng F,Jun Y B,Zhao X.Soft semirings[J].Computers and Mathematics with Applications,2008,56:2621-2628.
[10]Jun Y B.Soft BCK/BCI-algebras[J].Computers and Mathematics with Appli-cations,2008,56:1408-1413.
[11]Jun Y B,Park C H.Applications of soft sets in ideal theory of BCK/BCI-algebras[J].Information Sciences,2008,178:2466-2475.
[12]Acar U,Koyuncu F,Tanay B.Soft sets and soft rings[J].Computers and Mathematics with Applications,2010,59(11):3458-3463.
[13]伏文清,李生刚.软BCK代数[J].计算机工程与应用,2010,46(10):5-6.
[14]伏文清.软BCK代数再研究[J].计算机工程与应用,2012,48(11):22-25.
[15]廖祖华,芮明力.软坡[J].计算机工程与应用,2012,48(2):30-32.
[16]温永川.关于软集的研究[D].大连:辽宁师范大学,2008.
[1 7]赵迪,廖祖华,朱晓英等.半群的软理想[J].模糊系统与数学,2014,28(4):45-50.
[1 8]殷霞,廖祖华等.软集与新型软子群[J].计算机工程与运用,2012,48(33):40-43.
[19]叶灵军,廖祖华,朱晓英等.软完全正则子半群[J].工程数学学报,2014,31(3):341-346.
[20]关贝贝,廖祖华,朱晓英等.软子半群[J].模糊系统与数学,2014,28(4):39-44.
[21]叶婷,廖祖华,朱晓英等.半群的软完全素理想[J].模糊系统与数学,2014,28(3):1-5.
[22]Yin X,Liao Z H.Study on soft groups[J].Journal of Computers,2013,8:960-967.
[23]Zheng G P,Liao Z H,Wang N N.et al.Soft Lattice ImplicationSubalgebras[J].Applied Mathematics and Information Sciences,2013,7(3):1181-1186.
[24]Jonathan S G.Semirings and Affine Equations over Them:Theory and Applications[M].Kluwer Academic Publishers,2003.
[2]Pawlak Z.Rough Sets[J].International Journal of Information and Computer Sciences,1982,11:341-356.
[3]Astanassov K.Intuitionistic Fuzzy Sets[J].Fuzzy Sets and Systems,1986,20:87-96.
[4]Molodtsow D.Soft set theory-first results[J].Computers and Mathematics with AppUcations,1999,37:19-31.
[5]Maji P K,Roy A R,Biswas R.Soft set theory[J].Computers and Mathematics with Applications,2003,45(4):555-562.
[6]Irfan M,Ali Feng F,Xiaoyan L.On Some New Operations in Soft Set Theory[J].Computers and Mathematics with Applications,2009,57(9):1547-1553.
[7]Sezgin A,Atagun A O.Soft groups and normalistic soft groups[J].Computers and Mathematics with Applications,2011,62:685-698.
[8]Aktas H,Cagman N.Soft sets and soft groups[J].Information Science,2007,177(13):2726-2735.
[9]Feng F,Jun Y B,Zhao X.Soft semirings[J].Computers and Mathematics with Applications,2008,56:2621-2628.
[10]Jun Y B.Soft BCK/BCI-algebras[J].Computers and Mathematics with Appli-cations,2008,56:1408-1413.
[11]Jun Y B,Park C H.Applications of soft sets in ideal theory of BCK/BCI-algebras[J].Information Sciences,2008,178:2466-2475.
[12]Acar U,Koyuncu F,Tanay B.Soft sets and soft rings[J].Computers and Mathematics with Applications,2010,59(11):3458-3463.
[13]伏文清,李生刚.软BCK代数[J].计算机工程与应用,2010,46(10):5-6.
[14]伏文清.软BCK代数再研究[J].计算机工程与应用,2012,48(11):22-25.
[15]廖祖华,芮明力.软坡[J].计算机工程与应用,2012,48(2):30-32.
[16]温永川.关于软集的研究[D].大连:辽宁师范大学,2008.
[1 7]赵迪,廖祖华,朱晓英等.半群的软理想[J].模糊系统与数学,2014,28(4):45-50.
[1 8]殷霞,廖祖华等.软集与新型软子群[J].计算机工程与运用,2012,48(33):40-43.
[19]叶灵军,廖祖华,朱晓英等.软完全正则子半群[J].工程数学学报,2014,31(3):341-346.
[20]关贝贝,廖祖华,朱晓英等.软子半群[J].模糊系统与数学,2014,28(4):39-44.
[21]叶婷,廖祖华,朱晓英等.半群的软完全素理想[J].模糊系统与数学,2014,28(3):1-5.
[22]Yin X,Liao Z H.Study on soft groups[J].Journal of Computers,2013,8:960-967.
[23]Zheng G P,Liao Z H,Wang N N.et al.Soft Lattice ImplicationSubalgebras[J].Applied Mathematics and Information Sciences,2013,7(3):1181-1186.
[24]Jonathan S G.Semirings and Affine Equations over Them:Theory and Applications[M].Kluwer Academic Publishers,2003.