格蕴涵代数的Ω-模糊子代数  

Ω-Fuzzy Subalgebra in Lattice Implication Algebra

作　　者：傅小波[1] 廖祖华[2] FU Xiaobo;LIAO Zuhua(Wuxi Institute of Technology, Wuxi, Jiangsu 214121, China;School of Science, Jiangnan University, Wuxi, Jiangsu 214122, China)

机构地区：[1]无锡职业技术学院,江苏无锡214121 [2]江南大学理学院,江苏无锡214122

出　　处：《计算机科学与探索》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~~

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.

关 键 词：格蕴涵代数 模糊Ω-子代数 同态 直积 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]