格的模糊素理想的度量
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摘要
本文主要研究了模糊代数中格的模糊素理想的度量。首先给出了模糊素理想的新概念,并利用模糊素理想度讨论了格的模糊子集是模糊素理想的程度。其次,利用格的模糊集的(强)水平集得到了模糊素理想的等价刻画。最后,讨论了任意多个模糊子集的交、直积的模糊素理想度以及格的模糊子集在同态映射下像与原像的模糊素理想度的性质。
In this paper,we mainly deal with the measure of fuzzy prime ideals on Lattices in fuzzy algebra.Firstly,the new concept of the measure of fuzzy prime ideals was given and use measures of fuzzy prime ideals to discuss that the fuzzy subset is the degree of fuzzy prime ideals. Second,equivalently describe of the measures of fuzzy prime ideals was gotten by using the( strong) level set of fuzzy sets.Finally,we discuss the fuzzy prime ideal degrees of the intersection and the direct product of fuzzy subsets. Meanwhile,the measures of fuzzy prime ideals properties about the homomorphism image and inverse image of the fuzzy subset of lattice was obtained.
In this paper,we mainly deal with the measure of fuzzy prime ideals on Lattices in fuzzy algebra.Firstly,the new concept of the measure of fuzzy prime ideals was given and use measures of fuzzy prime ideals to discuss that the fuzzy subset is the degree of fuzzy prime ideals. Second,equivalently describe of the measures of fuzzy prime ideals was gotten by using the( strong) level set of fuzzy sets.Finally,we discuss the fuzzy prime ideal degrees of the intersection and the direct product of fuzzy subsets. Meanwhile,the measures of fuzzy prime ideals properties about the homomorphism image and inverse image of the fuzzy subset of lattice was obtained.
引文
[1] 孙道德.离散数学[M].北京:清华大学出版社,2013.
[2] Rosenfeld A.Fuzzy groups[J].Journal of Mathematical Analysis and Applications,1971,35:512～517.
[3] Hájek P.Meta mathematics of fuzzy logic[M].Kluwer Academic Publishers,1998.
[4] 王国俊.数理逻辑引论与归结原理(第二版[M].北京:科学出版社,2006.
[5] 张小红.模糊逻辑及其代数分析[M].北京:科学出版社,2008.
[6] 方进明.剩余格与模糊集[M].北京:科学出版社,2012.
[7] Ahsan J,Mordeson J N,Shabir M.Fuzzy semirings with applications to automata theory[M].Berlin:Springer-Verlag,2014.
[8] 刘溶滨.模糊子格的代数性质探讨[J].四川师范大学(自然科学版),1987,20(1):24～27.
[9] Yuan B,Wu W M.Fuzzy ideals on a distribute lattice[J].Fuzzy Sets and Systems,1990,35:231～240.
[10] Swamy U.M.,Raju D.V..Fuzzy ideals and congruences of lattices[J].Fuzzy Sets and Systems,1998,95:249～253.
[11] Attallah M.Completely fuzzy prime ideals of distributive lattices[J].The Journal of Fuzzy Mathematics,2000,8(1):151～156.
[12] 杨云.格的L-fuzzy理想的代数性质[J].模糊系统与数学,2001,15(1):81～84.
[13] Koguep B B N,Nkuimi C,Lele C.On fuzzy prime ideals of lattice[J].SJPAM,2008,3:1～11.
[14] 吴广庆.格的L-fuzzy素理想[J].模糊系统与数学,2008,22(4):62～67.
[15] 刘银萍,辛小龙.模糊子格与模糊子格上的模糊理想[J].模糊系统与数学,2014,28(1):39～45.
[16] 刘春辉.格的模糊软理想[J].数学的实践与认识,2014,44(18):283～289.
[17] 郑高平等.格蕴涵代数的软LI-理想[J].计算机工程与应用,2015,51(8):42～46.
[18] 王德江,梁久祯,廖祖华.R-广义模糊子格的理想[J].计算机科学,2014,41(1):271～296.
[19] Mezzomo I,Bedregal B C,Santiago R H N.Types of fuzzy ideals in fuzzy lattices[J].Journal of Intelligent and Fuzzy Systems,2015,28(2):929～945.
[20] 韩元良,杨文光,文小艳.L-fuzzy子格上L-fuzzy 素理想的研究[J].模糊系统与数学,2016,30(3):143～148.
[21] Shi S R.Measures of fuzzy subgroups[J].Proyecciones Journal of Mathematics,2010,29:41～48.
[22] 郝晓琳,王绪柱.基于t-模的模糊子群度[J].模糊系统与数学,2014,28(4):11～18.
[23] 冯娟.关于模糊子半群度的一些结论[D].成都四川师范大学,2014.
[24] 郝瑶媛,王绪柱.模糊子环的度量[J].模糊系统与数学,2016,30(2):22～31.
[25] 王绪柱,武彩萍,薛娜.模糊偏好关系及其应用[M].北京:科学出版社,2016.
[26] Wang X Z,Ruan D,Kerre E E.Mathematics of fuzziness-Basic issues[M].Berlin:Springer-Verlag,2005.
[27] 胡宝清.模糊理论基础[M].武汉:武汉大学出版社,2010.
[28] Li J,Shi F G.L-fuzzy convexity induced by L-convex fuzzy sublattice degree[J].Iranian Journal of Fuzzy Systems,2017,14(5):83～102.
[29] Dan Y X,Hu B Q,Qiao J S.Some results on the degree of symmetry of fuzzy relations[J].Fuzzy Sets and Systems,2018.
[2] Rosenfeld A.Fuzzy groups[J].Journal of Mathematical Analysis and Applications,1971,35:512～517.
[3] Hájek P.Meta mathematics of fuzzy logic[M].Kluwer Academic Publishers,1998.
[4] 王国俊.数理逻辑引论与归结原理(第二版[M].北京:科学出版社,2006.
[5] 张小红.模糊逻辑及其代数分析[M].北京:科学出版社,2008.
[6] 方进明.剩余格与模糊集[M].北京:科学出版社,2012.
[7] Ahsan J,Mordeson J N,Shabir M.Fuzzy semirings with applications to automata theory[M].Berlin:Springer-Verlag,2014.
[8] 刘溶滨.模糊子格的代数性质探讨[J].四川师范大学(自然科学版),1987,20(1):24～27.
[9] Yuan B,Wu W M.Fuzzy ideals on a distribute lattice[J].Fuzzy Sets and Systems,1990,35:231～240.
[10] Swamy U.M.,Raju D.V..Fuzzy ideals and congruences of lattices[J].Fuzzy Sets and Systems,1998,95:249～253.
[11] Attallah M.Completely fuzzy prime ideals of distributive lattices[J].The Journal of Fuzzy Mathematics,2000,8(1):151～156.
[12] 杨云.格的L-fuzzy理想的代数性质[J].模糊系统与数学,2001,15(1):81～84.
[13] Koguep B B N,Nkuimi C,Lele C.On fuzzy prime ideals of lattice[J].SJPAM,2008,3:1～11.
[14] 吴广庆.格的L-fuzzy素理想[J].模糊系统与数学,2008,22(4):62～67.
[15] 刘银萍,辛小龙.模糊子格与模糊子格上的模糊理想[J].模糊系统与数学,2014,28(1):39～45.
[16] 刘春辉.格的模糊软理想[J].数学的实践与认识,2014,44(18):283～289.
[17] 郑高平等.格蕴涵代数的软LI-理想[J].计算机工程与应用,2015,51(8):42～46.
[18] 王德江,梁久祯,廖祖华.R-广义模糊子格的理想[J].计算机科学,2014,41(1):271～296.
[19] Mezzomo I,Bedregal B C,Santiago R H N.Types of fuzzy ideals in fuzzy lattices[J].Journal of Intelligent and Fuzzy Systems,2015,28(2):929～945.
[20] 韩元良,杨文光,文小艳.L-fuzzy子格上L-fuzzy 素理想的研究[J].模糊系统与数学,2016,30(3):143～148.
[21] Shi S R.Measures of fuzzy subgroups[J].Proyecciones Journal of Mathematics,2010,29:41～48.
[22] 郝晓琳,王绪柱.基于t-模的模糊子群度[J].模糊系统与数学,2014,28(4):11～18.
[23] 冯娟.关于模糊子半群度的一些结论[D].成都四川师范大学,2014.
[24] 郝瑶媛,王绪柱.模糊子环的度量[J].模糊系统与数学,2016,30(2):22～31.
[25] 王绪柱,武彩萍,薛娜.模糊偏好关系及其应用[M].北京:科学出版社,2016.
[26] Wang X Z,Ruan D,Kerre E E.Mathematics of fuzziness-Basic issues[M].Berlin:Springer-Verlag,2005.
[27] 胡宝清.模糊理论基础[M].武汉:武汉大学出版社,2010.
[28] Li J,Shi F G.L-fuzzy convexity induced by L-convex fuzzy sublattice degree[J].Iranian Journal of Fuzzy Systems,2017,14(5):83～102.
[29] Dan Y X,Hu B Q,Qiao J S.Some results on the degree of symmetry of fuzzy relations[J].Fuzzy Sets and Systems,2018.