Because there are many possibilities for the set of basic functions, parameters and operators used in the design of an adaptive-network-based fuzzy inference system (ANFTS), the search for the most suitable operators and functional blocks, together with their characterization and evaluation, is also an important topic in the field of neuro-fuzzy design. As shown in papers dealing with real applications, the designer has to select the operator to be used in each phase in the design of a neuro-fuzzy system, and this decision is usually taken in terms of the most common operations performed. Nevertheless, it is very important to determine which factors have the greatest influence on the behaviour and performance of the neuro-fuzzy system. Therefore, the designer should pay close attention to the phase in which the selection of the operator is most statistically significant. In this way, it is possible to obviate a detailed analysis of different configurations that lead to systems with very similar performance. In order to perform this analysis, an appropriate statistical tool has been used: the multifactorial analysis of the variance (ANOVA) which consists of a set of statistical techniques that enable the analysis and comparison of experiments, by describing the interactions and interrelations between either the quantitative or the qualitative variables of the neural network system. By applying this methodology to a great variety of neuro-fuzzy systems, it is possible to obtain general results about the most relevant factors defining the neural network design.
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