Heyting代数的扰动模糊滤子
|
摘要
结合扰动模糊集和滤子理论,引入Heyting代数的扰动模糊滤子的概念,讨论它的性质,给出了扰动模糊滤子的几个等价刻画,在Heyting代数的同态映射下,研究扰动模糊滤子的同态象和同态原象.其次,提出了由Heyting代数的一个扰动模糊集生成的扰动模糊滤子的概念,获得了它的表示定理.
In combination with the theories concerning the disturbing fuzzy sets and filters,the concept of disturbing fuzzy filters of Heyting algebras is introduced,some of its properties are discussed,and several equivalent characterizations of disturbing fuzzy filters are presented.Under the homomorphic mapping of Heyting algebras,the homomorphic image and homomorphic inverse image of disturbing fuzzy filters are investigated.Next,the concept of the disturbing fuzzy filter,generated by a disturbing fuzzy set in Heyting algebras,is proposed and its representation theorem is obtained.
In combination with the theories concerning the disturbing fuzzy sets and filters,the concept of disturbing fuzzy filters of Heyting algebras is introduced,some of its properties are discussed,and several equivalent characterizations of disturbing fuzzy filters are presented.Under the homomorphic mapping of Heyting algebras,the homomorphic image and homomorphic inverse image of disturbing fuzzy filters are investigated.Next,the concept of the disturbing fuzzy filter,generated by a disturbing fuzzy set in Heyting algebras,is proposed and its representation theorem is obtained.
引文
[1]王国俊.Heyting代数成为Boole代数的条件及特征[J].陕西师范大学学报,1991,19(4):1-6.
[2]郑崇友,樊磊,崔宏斌.Frame与连续格[M].北京:首都师范大学出版社,2000.
[3]徐晓泉,熊华平,杨金波.近性Heyting代数[J].数学年刊:A辑,2000,21(2):165-174.
[4]包洪亮,李生刚.Heyting代数上的上的运算与Nucleus[J].内蒙古师范大学学报,2005,34(1):23-25.
[5]李志伟,郑崇友.Heyting代数与模糊蕴涵代数[J].数学杂志,2002,22(2):237-240.
[6]石慧君.Heyting系统及其相关性质的研究[D].西安:陕西师范大学,2012.
[7]苏忍锁,张馨文.Heyting代数与剩余格[J].陕西理工学院学报,2009,25(4):63-69.
[8]张花荣,李骏,谢强军.MTL代数的性质及其滤子[J].兰州理工大学学报,2005,31(5):147-149.
[9]王守印,王永忠.Stone代数的同余理想与Stone代数滤子[J].新乡师范高等专科学校学报,2001,15(1):67-70.
[10]Zhu W H,Xu Y.On filter theory of residuated lattices[J].Information Sciences,2000,180:3614-3632.
[11]刘春辉,徐罗山.Fuzzy蕴涵代数的MP滤子[J].模糊系统与数学,2009,23(2):1-6.
[12]Gierz G,Hofmann K,Keimel K,et al.A compendium continuous lattices[M].New York:Spring Verlag,1980.
[13]路玲霞.Heyting代数中的模糊滤子[J].内江师范学院学报,2007,22(2):15-16.
[14]刘春辉.Heyting代数的模糊滤子格[J].山东大学学报,2013,48(12):57-60.
[15]Zadeh L A.Fuzzy sets[J].Information Control,1965,8(3):338-353.
[16]Lin T Y.A set theory for soft computing:a unified view of fuzzy sets via neighborboods[C]//Fuzzy Systems.Proceedings of the Fifth IEEE International Conference on IEEE,1996,2:1140-1146.
[17]Ying M S.Perturbation of fuzzy reasoning[J].IEEE Transactions on Fuzzy Systems,1995,1(5):625-629.
[18]Rosenfeld A.Fuzzy group[J].Journal Of Mathematical Analysis And Applications,1971,35:512-517.
[19]Dib K A,Galhum N.Fuzzy ideals and fuzzy bi-ideals in fuzzy semigroups[J].Fuzzy Sets and Systems,1997,92:103-111.
[20]彭家寅.BCK-代数的(s,t]-模糊子代数与R-模糊代数[J].内江师范学院学报,2015,30(6):1-10.
[21]彭家寅.BCK-代数的Ω-模糊代数理想[J].内江师范学院学报,2008,23(4):5-7.
[22]彭家寅.Vague B-代数(英文)[J].内江师范学院学报,2012,27(4):1-5.
[23]彭家寅.LA-半群中的区间值(∈,∈∨q)-模糊理想[J].内江师范学院学报,2015,30(10):1-9.
[24]彭家寅.区间值(∈,∈∨q)-模糊B-代数(英文)[J].内江师范学院学报,2012,27(2):1-4.
[25]彭家寅.拟BCK代数的双枝值模糊理想(英文)[J].内江师范学院学报,2015,30(8):1-10.
[26]刘心,陈图云.扰动模糊逻辑及其“非算子”[J].模糊系统与数学,2002,16(2):179-182.
[27]韩莹,陈森发,陈胜.TD型扰动模糊正规子群[J].模糊系统与数学,2006,20(5):25-29.
[28]陈图云,孟艳平.扰动模糊集相似度限定推理方法[J].辽宁工程技术大学学报:自然科学版,2004,23(4):564-566.
[2]郑崇友,樊磊,崔宏斌.Frame与连续格[M].北京:首都师范大学出版社,2000.
[3]徐晓泉,熊华平,杨金波.近性Heyting代数[J].数学年刊:A辑,2000,21(2):165-174.
[4]包洪亮,李生刚.Heyting代数上的上的运算与Nucleus[J].内蒙古师范大学学报,2005,34(1):23-25.
[5]李志伟,郑崇友.Heyting代数与模糊蕴涵代数[J].数学杂志,2002,22(2):237-240.
[6]石慧君.Heyting系统及其相关性质的研究[D].西安:陕西师范大学,2012.
[7]苏忍锁,张馨文.Heyting代数与剩余格[J].陕西理工学院学报,2009,25(4):63-69.
[8]张花荣,李骏,谢强军.MTL代数的性质及其滤子[J].兰州理工大学学报,2005,31(5):147-149.
[9]王守印,王永忠.Stone代数的同余理想与Stone代数滤子[J].新乡师范高等专科学校学报,2001,15(1):67-70.
[10]Zhu W H,Xu Y.On filter theory of residuated lattices[J].Information Sciences,2000,180:3614-3632.
[11]刘春辉,徐罗山.Fuzzy蕴涵代数的MP滤子[J].模糊系统与数学,2009,23(2):1-6.
[12]Gierz G,Hofmann K,Keimel K,et al.A compendium continuous lattices[M].New York:Spring Verlag,1980.
[13]路玲霞.Heyting代数中的模糊滤子[J].内江师范学院学报,2007,22(2):15-16.
[14]刘春辉.Heyting代数的模糊滤子格[J].山东大学学报,2013,48(12):57-60.
[15]Zadeh L A.Fuzzy sets[J].Information Control,1965,8(3):338-353.
[16]Lin T Y.A set theory for soft computing:a unified view of fuzzy sets via neighborboods[C]//Fuzzy Systems.Proceedings of the Fifth IEEE International Conference on IEEE,1996,2:1140-1146.
[17]Ying M S.Perturbation of fuzzy reasoning[J].IEEE Transactions on Fuzzy Systems,1995,1(5):625-629.
[18]Rosenfeld A.Fuzzy group[J].Journal Of Mathematical Analysis And Applications,1971,35:512-517.
[19]Dib K A,Galhum N.Fuzzy ideals and fuzzy bi-ideals in fuzzy semigroups[J].Fuzzy Sets and Systems,1997,92:103-111.
[20]彭家寅.BCK-代数的(s,t]-模糊子代数与R-模糊代数[J].内江师范学院学报,2015,30(6):1-10.
[21]彭家寅.BCK-代数的Ω-模糊代数理想[J].内江师范学院学报,2008,23(4):5-7.
[22]彭家寅.Vague B-代数(英文)[J].内江师范学院学报,2012,27(4):1-5.
[23]彭家寅.LA-半群中的区间值(∈,∈∨q)-模糊理想[J].内江师范学院学报,2015,30(10):1-9.
[24]彭家寅.区间值(∈,∈∨q)-模糊B-代数(英文)[J].内江师范学院学报,2012,27(2):1-4.
[25]彭家寅.拟BCK代数的双枝值模糊理想(英文)[J].内江师范学院学报,2015,30(8):1-10.
[26]刘心,陈图云.扰动模糊逻辑及其“非算子”[J].模糊系统与数学,2002,16(2):179-182.
[27]韩莹,陈森发,陈胜.TD型扰动模糊正规子群[J].模糊系统与数学,2006,20(5):25-29.
[28]陈图云,孟艳平.扰动模糊集相似度限定推理方法[J].辽宁工程技术大学学报:自然科学版,2004,23(4):564-566.