However when a fact fuzzy set is not included in only one rule fuzzy set, several generalized modus ponens are computed for this fact fuzzy set, one for each rule fuzzy set intersecting it.

This problem can be formalized by the following schematic form where rules contain the same variables in premises and in conclusions:

Rules	: IF	X is THEN	Y is i=1,n
Fact	:	X is
Conclusion	:		Y is

One way of processing a collection of rules could consist, first in making as many inferences as there are rules and, second in combining the results provided by each of them with formula 6 as [4]:

However, if (with and ), the final fuzzy set is the total uncertainty (e=1) with formula 8 because

• implies and ,
• implies and and finally
• (total uncertainty).

It would be logic to obtain the final fuzzy set . Equally if It would be logic to obtain .

Some researches [4, 6] show that the combination/projection principle performed globally behaves better than performed locally. So, it is better to minimize fuzzy implications involved by generalized modus ponens and combine this result with the fact to provide a more specific conclusion as :