山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (2): 119-126.doi: 10.6040/j.issn.1671-9352.0.2015.156
• • 上一篇
彭家寅
PENG Jia-yin
摘要： 利用一元模糊谓词逻辑和连续格值逻辑语义方法来发展格蕴涵代数的不分明化滤子。引入格蕴涵代数的不分明化滤子的概念,讨论其相关性质,研究了在格蕴涵同态映射下格蕴涵代数的不分明化滤子的象与原象之间的关系。
中图分类号:
| [1] 宋振明. 基于格蕴涵代数的智能控制中的不确定性推理的研究[D]. 成都:西南交通大学,1998: 14-15. SONG Zhengming. Research on the uncertainty reasoning of intelligent control based on lattice implication algebra[D]. Chengdu: Southwest Jiaotong University, 1998: 14-15. [2] 徐杨. 格蕴涵代数[J]. 西南交通大学学报, 1993, 28(1):20-27. XU Yang. Lattice implication algebras[J]. Journal of Southwest Jiaotong University, 1993, 28(1):20-27. [3] 徐杨. 格蕴涵代数中的同态[C] //中国第五届多值逻辑学术会议论文集,1992: 206-210. XU Yang. The homomorphism of the lattice implication algebras[C]. Proceedings of the fifth conference on multi valued logic conference in China, 1992: 206-210. [4] 宋振明,徐杨. 格蕴涵代数上的同余关系[J].应用数学,1997,10(3):121-124. SONG Zhenming, XU Yang. Congruence relations on lattice implication algebra[J]. Mathematica Applicata, 1997,10(3):121-124. [5] 徐杨,秦克云. 格H蕴涵代数与格蕴涵代数类[J]. 河北煤炭建筑工程学院学报,1992,3:139-143. XU Yang, QIN Keyun. Lattice H implication algebras and class of lattice implication algebras[J]. Journal of Hebei Coal Building Engineering Institute, 1992, 3:139-143. [6] 赵丽. 格蕴涵代数及其乘积结构研究[D]. 成都:西南交通大学,2012: 12-49. ZHAO Li. Research on lattice implication algebra and its product structure[D]. Master Thesis of Southwest Jiaotong University, 2012: 12-49. [7] XU Yang, QIN Keyun. On the filters of lattice implication algebras[J]. Journal of Fuzzy Mathematics, 1993, 1(2):251-260. [8] QIN Keyun, XU Yang. On the super filters of lattice implication algebras[J]. Journal of Southwest Jiaotong University, 1999, 34(1):52-54. [9] JUN Youngbae. Implication filter of lattice implication algebras[J]. Bulletin of the Korean Mathematical Society, 1997, 34(2):193-198. [10] JUN Youngbae, XU Yang. Qin Keyun. Positive implicative and associative filter of lattice implication algebras[J]. Bulletin of the Korean Mathematical Society, 1998, 35(1):51-61. [11] JUN Youngbae. The prime filters theorem of lattice implication algebras[J]. International Journal of Mathematics and Mathematical Science, 2001, 25(2):115-118. [12] 吴明慧,徐杨. 格蕴涵代数的布尔滤子[J]. 毕节学院学报, 2011, 29(4):1-5. WU Minghui,XU Yang. Boolean filters of lattice implication algebras[J]. Journal of Bijie University, 2011, 29(4):1-5. [13] 郭玲. 格蕴涵代数及生成滤子结构研究[D]. 成都:西南交通大学, 2012: 19-27. GUO Ling. Research on lattice implication algebra and structures of generated filters[D] , Master Thesis of Southwest Jiaotong University, 2012: 19-27. [14] ZADEH L A. Fuzzy sets[J]. Information Control, 1965, 8(3):338-353. [15] 徐扬,秦克云.模糊格蕴涵代数[J].西南交通大学学报, 1995,30(2):121-127 XU Yang, QIN Keyun. Fuzzy lattice implication algebras[J]. Journal of Southwest Jiaotong University, 1995, 30(2):121-127. [16] QIN Keyun, XU Yang. On some properties of fuzzy filters of lattice implication algebras[M] // Liu Y M. Fuzzy Set Theory and its Application Baoding: Press of Hebei University, 1999: 179-182. [17] JUN Youngbae. Fuzzy positive implicative and fuzzy associative filters of lattice implication algebras[J]. Fuzzy Sets and Systems, 2001, 121(2):353-357. [18] ZADEH L A. The concept of a lingnist variable and its application to approximate reasoning-I[J]. Information Sciences, 1965, 8(3):338-353. [19] 秦亚, 钟纯真, 刘熠.格蕴涵代数的T-模糊滤子[J]. 西南民族大学学报:自然科学版, 2010,36(5):730-734. QIN Ya, ZHONG Chunzhen, LIU Yi. On T-fuzzy filter of lattice implication algebras[J]. Journal of Southwest University of Nationalities: Natural Science Edition, 2010, 36(5):730-734. [20] 傅小波, 战学秋, 廖祖华.格蕴涵代数的(∈,∈∨q(λ,μ))-模糊滤子[J]. 计算机科学与探索, 2014, 8(3):376-384. FU Xiaobo, ZHAN Xueqiu, LIAO Zuhua.(∈,∈∨q(λ,μ))-fuzzy filter of lattice implication algebras[J]. Journal of Frontiers of Computer Science and Technology, 2014, 8(3):376-384. [21] 刘熠,钟纯真. 格蕴涵代数的区间值J-模糊滤子理论[J]. 模糊系统与数学, 2013, 27(4):74-83. LIU Yi, ZHONG Chunzhen. Interval-valued J-fuzzy filters on lattice implication algebras[J]. Fuzzy Systems and Mathematics, 2013, 27(4):74-83. [22] 裴峥. 格蕴涵代数中的直觉模糊滤子[J]. 西华大学学报(自然科学版), 2007, 26(2):17-20. PEI Zheng. Intuitionistic fuzzy filter of lattice implication algebra[J]. Journal of Xihua University(Natural Science), 2007, 26(2):17-20. [23] 彭家寅, 莫智文. 格蕴涵代数滤子的粗糙性[J]. 数学的实践与认识, 2012, 42(20):217-222. PENG Jiayin, MO Zhiwen. Roughness of filters in lattice implication algebras[J]. Mathematics in Practice and Theory, 2012, 42(20):217-222. [24] 廖祖华, 王妮妮, 郑高平, 等. 格蕴涵代数的软滤子[J]. 计算机工程与应用, 2015,51(9):72-76. LIAO Zuhua, WANG Nini, ZHENG Gaoping, et al. Soft filters of lattice implication algebra[J]. Computer Engineering and Applications, 2015, 51(9):72-76. [25] 吴望名. 模糊推理的原理和方法[M].贵阳:贵州科技出版社,1994. WU Wangming. Principles and methods of fuzzy resoning[M]. Guiyang: Science and Technology Press in Guizhou, 1994. [26] 王国俊. 非经典数理逻辑与近似推理[M]. 北京:科学出版社,2003. WANG Guojun. Non classical mathematical logic and approximate reasoning[M]. Beijing: Science Press, 2003. [27] ROSSER J B, TURQUETTE A R. Many-valued logics[M]. New York: Springer, 1952. [28] YING Mingsheng. A new approach for fuzzy topology(I)[J]. Fuzzy Sets and Systems, 1991, 39(3):303-321. [29] YING Mingsheng. A new approach for fuzzy topology(II)[J]. Fuzzy Sets and Systems, 1992, 47(2):201-231. [30] YING Mingsheng. A new approach for fuzzy topology(III)[J]. Fuzzy Sets and Systems, 1993, 55(2):193-207. |
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