On re-scaling in fuzzy control and genetic algorithms

It is known that in many applications of fuzzy control or genetic algorithms, appropriate re-scaling of the control parameters can drastically improve the performance. Successful applications of re-scaling are normally based on fine-tuning experiments or on the good knowledge of the area. These successes tempt justification of the use of re-scaling in situations when we do not have good knowledge and have not experimented much. Surprisingly, in such situations, re-scaling often not only does not improves the performance, but often degrades it. In this paper, we provide a simple mathematical explanation of this phenomenon