thank you for your question.
There seems to be some differences in the names used by the different players in fuzzy logic control, but the differences are only in the names. The centre of area or gravity that you are asking for is the Centroid in fuzzylite (and also in matlab). In jfuzzylogic, they make a difference between centre of area and centre of gravity, where the centre of area refers to the Bisector (in fuzzylite and matlab), and the centre of gravity refers to the Centroid (in fuzzylite and matlab).
Let me know if this answers your question.