learning algorithm for tuning fuzzy rules based on the gradient descent method

The paper reference is 

A learning algorithm for tuning fuzzy rules based on the gradient
descent method
Shi, Y.; Mizumoto, M.; Yubazaki, N.; Otani, M.; 
Fuzzy Systems, 1996., Proceedings of the Fifth IEEE International
Conference on , Volume: 1 , 8-11 Sept. 1996
Page(s): 55 -61 vol.1

assume the input is X = [ 12,13,14,15]
and estimated output is y =[12.345, 13.215, 14.871, 15.654]
we know that the error occoured is the difference 
So 
we have,
   Y' = [0.345,0.215,0.871,0.654]
how do we go about doing this  using the above?

any help with this will be appreciated
thanks.