Abstract:
The concept of binary fuzzy relation category
\mathbbL_bRel was given by combining the concept of fuzzy relation category. Firstly, we discussed the structure of product and coproduct in the category
\mathbbL_bRel . Secondly, we defined the tensor functor and obtained that the category
\mathbbL_bRel is a symmetric monoid category. Furthermore, we gave the structure of monoid and comonoid in the category
\mathbbL_bRel . Finally, we constructed a functor from fuzzy set category
\mathbbLS et to fuzzy relation category
Rel_\mathbbL\mathbbL by using binary fuzzy relation category
\mathbbL_bRel .