二元模糊关系范畴的对称幺半范畴性

Symmetric monoid categorization of binary fuzzy relation category

结合模糊关系范畴的概念给出了二元模糊关系范畴L_(b)Rel的概念.首先,讨论了范畴L_(b)Rel的积和余积的结构.其次,定义了张量积函子■,得到了L_(b)Rel是对称幺半范畴.进而,给出了范畴L_(b)Rel中的幺半群和余幺半群结构.最后,以二元模糊关系范畴L_(b)Rel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.

The concept of binary fuzzy relation category L_(b)Rel was given by combining the concept of fuzzy relation category.Firstly,we discussed the structure of product and coproduct in the category LgRel.Secondly,we defined the tensor functor and obtained that the category L_(b)Rel is a symmetric monoid category.Furthermore,we gave the structure of monoid and comonoid in the category LypRel.Finally,we constructed a functor from fuzzy set category LSet to fuzzy relation category RelL^(L)by using binary fuzzy relation category L_(b)Rel.