Conceptual Graphs (CG) are a graph-based knowledge representation and reasoning formalism; fuzzy Conceptual Graphs (fCG) constitute an extension that enriches their expressiveness, exploiting the fuzzy set theory so as to relax their constraints at various levels. This paper proposes a comparative study of existing approaches over their respective advantages and possible limitations. The discussion revolves around three axes: (a) Critical view of each approach and comparison with previous propositions from the state of the art; (b) Presentation of the many possible interpretations of each definition to illustrate its potential and its limits; (c) Clarification of the part of CG impacted by the definition as well as the relaxed constraint.