Parameterized continuous models of fuzzy reasoning

Abstract

In this paper, the ideas of universal logic is introduced into fuzzy systems. After giving the definitions of the softened fuzzy reasoning models based on Schweizer-Sklar t-norms and Schweizer-Sklar implications, i.e., α-models and β-models, we give the sufficient and necessary conditions for these models to be continuous, and discuss the continuity of some commonly used models. We also prove that when an α-model or a β-model is used as a fuzzy controller, it has universal property with respect to function approximation. The results we obtained show that α-models and β-models are more flexible than the existing models in applications.

Key words： Schweizer-Sklar t-norms; Schweizer-Sklar implications; continuous fuzzy reasoning models