二元模糊关系范畴的对称幺半范畴性
Symmetric monoid categorization of binary fuzzy relation category
周鑫 1刘淼1
作者信息
- 1. 伊犁师范大学数学与统计学院,新疆伊宁 835000;伊犁师范大学应用数学研究所,新疆伊宁 835000
- 折叠
摘要
结合模糊关系范畴的概念给出了二元模糊关系范畴LbRel的概念.首先,讨论了范畴LbRel的积和余积的结构.其次,定义了张量积函子⊗,得到了LbRel是对称幺半范畴.进而,给出了范畴LbRel中的幺半群和余幺半群结构.最后,以二元模糊关系范畴LbRel作为纽带,构造了一个从模糊集范畴LSet到模糊关系范畴RelLL的忠实函子.
Abstract
The concept of binary fuzzy relation category LbRel was given by combining the concept of fuzzy relation category.Firstly,we discussed the structure of product and coproduct in the category LbRel.Secondly,we defined the tensor functor and obtained that the category LbRel is a symmetric monoid category.Furthermore,we gave the structure of monoid and comonoid in the category LbRel.Finally,we constructed a functor from fuzzy set category LSet to fuzzy relation category RelLL by using binary fuzzy relation category LbRel.
关键词
模糊关系/二元模糊关系/范畴/函子/对称幺半范畴Key words
fuzzy relation/binary fuzzy relation/category/functor/symmetric monoidal category引用本文复制引用
基金项目
新疆高校科研计划项目(XJEDU2021Y042)
新疆伊犁州科技计划项目(YZ2022Y010)
伊犁师范大学博士科研启动基金(2021YSBS011)
伊犁师范大学科研创新团队项目(CXZK2021014)
伊犁师范大学提升学科综合实力专项项目(2022XKZY08)
伊犁师范大学高级别培训项目(YSPY2022011)
出版年
2024
NETL
NSTL
万方数据