On the reliability of the influence measure in the transformation method of fuzzy arithmetic

The transformation method has been proposed as a practical tool for the simulation and the analysis of systems with uncertain parameters using fuzzy arithmetic. A major advantage of this method, among others, is the fact that in the analysis part of the method, the degree of influence for each uncertain parameter can be computed with a rather simple formula. However, a thorough examination of how accurate this measure of the degree of influence really is has not yet been performed. In the paper, the influence measure provided by the transformation method is compared to a rather classical one derived from differential calculus. Furthermore, an additional measure is introduced which can serve as an indicator for the effectiveness and the reliability of the influence measure calculated by the transformation method.