模糊理论与Kleisli范畴  

Fuzzy Theory and the Kleisli Category

作　　者：周鑫 ZHOU Xin(School of Mathematics and Statistics,Yili Normal University,Yining 835000,China;School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,China)

机构地区：[1]伊犁师范大学数学与统计学院,新疆伊宁835000 [2]东北师范大学数学与统计学院,吉林长春130024

出　　处：《模糊系统与数学》2021年第2期37-42,共6页Fuzzy Systems and Mathematics

基　　金：新疆维吾尔自治区自然科学基金资助项目(2020D01C269)。

摘　　要：运用范畴论的观点和语言,讨论了几种真值集不同的模糊集,得出它们都是特殊的模糊理论。更进一步,指出了模糊理论所对应的范畴与由模糊理论诱导的单子所构造的Kleisli范畴的等价关系。最后,通过一个实例,描述了伴随函子诱导的单子,并构造了相应的Kleisli范畴,指出了Kleisli范畴在模糊理论中的应用。Using the viewpoint and language of category theory, we discuss several fuzzy sets with different truth-value sets, and point out that they are special fuzzy theories essentially. Furthermore, we establish equivalence relation between the category of fuzzy theory and the Kleisli category which is constructed by monad induced by the fuzzy theory. Finally, through a example, we describe the monad induced by adjoint functor and construct its Kleisli category, and show that the Kleisli category can be applied to the fuzzy theory.

关 键 词：模糊理论 单子 Kleisli范畴 伴随函子 

分 类 号：O159[理学—数学]