半群上的L-模糊同余  

L-Fuzzy Congruences on Semigroups

作　　者：李倩倩 LI Qianqian(School of Science,Lanzhou University of Technology,Lanzhou 730050,China)

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《甘肃科学学报》2023年第1期23-25,共3页Journal of Gansu Sciences

摘　　要：半群S上的模糊关系是特殊的映射,它将S×S映到[0,1]区间。[0,1]区间是全序集,是特殊的格。通过将[0,1]换成完全格推广模糊关系的定义得到L-模糊关系的定义。在此基础上给出L-模糊等价关系、L-模糊同余的定义。研究了半群S上的L-模糊同余的部分性质,证明了两个L-模糊同余他们的圈乘是L-模糊同余当且仅当他们的圈乘是L-模糊等价关系当且仅当他们的圈乘是L-模糊对称的当且仅当他们的圈乘满足交换律。最终证明了μ^(-1)(1)={(a,b)∈S×S|μ(a,b)=1}是半群S上的同余。The Fuzzy relations on semigroups S are special mappings,which maps S×S to[0,1].The interval is an overall ordered set and a special lattice.By replacing[0,1]with complete lattice,the definition of L-fuzzy relation is established,based on which,the concept of L-fuzzy equivalence relation and L-fuzzy congruence are defined.This article studied on some properties of L-fuzzy congruences on semigroups which proves that two L-fuzzy congruences whose circle multiplication is L-fuzzy congruence if and only if their circle multiplication is L-fuzzy equivalence if and only if their circle multiplication is L-fuzzy symmetric if and only if their circle multiplication satisfies commutative law.Eventually,it has been proved thatμ^(-1)(1)={(a,b)∈S×S|μ(a,b)=1}is a congruence on the semigroup S.

关 键 词：半群 L-模糊关系 L-模糊同余 

分 类 号：O152[理学—数学]