  Since categories are graphs with additional "structure", one should start
from fuzzy graphs in order to define a theory of fuzzy categories. Thus is
makes sense to introduce categories whose morphisms are associated with a
plausibility degree that determines to what extend it is possible to "go" from
one object to another one. These categories are called {\em fuzzy categories}.
Of course, the basic properties of these categories are similar but not
identical to their ordinary counterparts. Thus, it is necessary to introduce
notion like fuzzy commutative diagrams, fuzzy initial and fuzzy terminal
objects, etc.
