Accurate similarity analysis and computing of Gaussian membership functions for FNN simplification

This paper provides a complete solution for the problem how to accurately compute the similarity between fuzzy sets with Gaussian membership functions, which is a fundamental issue for the identification and simplification of FNNs. It is shown that there are three different types of similarities between a pair of Gaussian membership functions dependent on the relative positioning between the given pair of membership functions, and the accurate and detailed computing formulas are given in each type. A simulation example is given to compare the proposed accurate similarity analysis method with the existing approximation approaches and to show how much more accuracy can be obtained than the approximation one in terms of absolute percentage approximation error.