fuzzy inference

Hello,

I have a question regarding fuzzy inference that I have not been able
to find the answer to on the internet, or books etc.

Simply it is:  Why is it that MIN-MAX and PRODUCT-SUM inference
options are the most commonly used? Why doesn't anyone mention
MIN-SUM?

I have been doing some work where we tried applying MIN inference
(implication) with SUM composition (aggregation of output sets).  It
provided a better result using centroid defuzzification, which allows
for the fact that the summed DoBs of the output sets can be greater
than 1.

No-one ever seems to talk about MIN-SUM and PRODUCT-MAX inference!   I
can see that there may be a problem with MAX-PRODUCT because it would
result in valleys in the output sets.    What might be wrong with
MIN-SUM?

I would very much appreciate any ideas you have or pointers to texts/
examples that could help?

Kind regards,

Steve