2.3. The probability distribution of input data based on the rate of change of output

It is known that many rules are needed at or near the places where output data change quickly in fuzzy modeling. Then, how can we find the rate of output change? The probability pM (x) is one method to perform it. As shown in Eqs. (16) and (17), any input data where output changes quickly is selected with the high probability, and any input data where output changes slowly is selected with the low probability, where M is the size of range considering output change.

Based on the literature [13], the probability (distribution) is defined as follows:
