摘要
给定一个集合Ω,将Ω-模糊集与格蕴涵代数相结合,引入了格蕴涵代数Ω-模糊子代数的概念,并研究了其相关性质;给出了格蕴涵代数Ω-模糊子代数的若干等价刻画,讨论了格蕴涵代数Ω-模糊子代数与格蕴涵代数子代数之间的相互关系;研究了格蕴涵代数Ω-模糊子代数在Ω-模糊集下交、并等运算下的基本性质;讨论了格蕴涵代数Ω-模糊子代数的同态像与同态原像的基本性质;最后研究了格蕴涵代数Ω-模糊子代数的直积与投影。
LetΩbe a set.By combining theΩ-fuzzy sets and the lattice implication algebras,this paper introduces the concepts ofΩ-fuzzy subalgebra in the lattice implication algebra,and investigates some related properties.Beside,this paper obtains some equivalent descriptions of theΩ-fuzzy subalgebra in the lattice implication algebra,and gives the relations betweenΩ-fuzzy subalgebra and the subalgebra in the lattice implication algebra.Then this paper studies some basic properties of theΩ-fuzzy subalgebra under the intersection,union and other operations ofΩ-fuzzy sets,and discusses some basic properties of homomorphic image and homomorphic preimage ofΩ-fuzzy subalgebra.Finally,this paper studies theΩ-fuzzy subalgebra direct product in the lattice implication algebra.
作者
傅小波
廖祖华
FU Xiaobo;LIAO Zuhua(Wuxi Institute of Technology, Wuxi, Jiangsu 214121, China;School of Science, Jiangnan University, Wuxi, Jiangsu 214122, China)
出处
《计算机科学与探索》
CSCD
北大核心
2017年第7期1183-1190,共8页
Journal of Frontiers of Computer Science and Technology
基金
国家自然科学基金Nos.611702121
11401259
江苏省自然科学基金No.BK2015117~~
关键词
格蕴涵代数
模糊Ω-子代数
同态
直积
lattice implication algebra
Ω - fuzzy subalgebra
homomorphic
direct product
