Choosing linguistic connector word models for Mamdani fuzzy logic systems

We examine ten antecedent connector models in the framework of a singleton or non-singleton fuzzy logic system (FLS) to establish which models can be used. In this work a usable connector model must lead to a separable firing degree that is a closed-form and piecewise-differentiable function of the membership function (MF) parameters and also the parameter characterizing that connector model. The. multiplicative compensatory and model that uses the product t-norm and maximum t-conorm, Φ_p^MCA, is shown to be usable for both singleton and non-singleton Mamdani-product FLSs. We also show, by examples, that the parameter of Φ_p^MCA provides additional freedom in adjusting a FLS, so that the FLS has the potential to achieve better performance than a FLS that uses the traditional product or minimum t-norm for the antecedent connections.