An index of applicability for the decomposition method of multivariable fuzzy systems

Research on the application of fuzzy set theory to the design of control systems has led to interest in decomposition of multivariable fuzzy systems. Decomposition of multivariable control rules is preferable since it alleviates the complexity of the problem, but the inference error is inevitable because of its approximate nature. In this paper we show that a large inference error is generated when the Gupta´s decomposition method (1986) is applied to Exclusive-nor (ENOR) gate model which is used as a counter example. We define an index of applicability which can classify whether the decomposition method can be applied to a multivariable fuzzy system or not