The natural transformations with fuzzified commutativity

The natural transformation forms one of the most abstract mapping that is considered in category theory. In fact, it forms a unique transformation between the so-called functors, which operate between categories. The natural transformations are determined by the appropriate commutativity of their diagrams and their general form may be predicted by the so- called Yoneda's lemma. This paper is aimed at proposing a new concept of fuzzy natural transformation as based on fuzzified commutativity. It seems to be interesting that such a fuzzified natural transformation may be referred to coding theory. In addition, a fuzzy Yoneda's lemma is formulated and proved.