Fix-Mundis for Fuzzy IF-THEN Rule Bases with T-Norm Based Compositional Rule of Inference Interpretation

In [TeFa00] we have presented fixpoints and fix-mundis when interpreting fuzzy IF-THEN rules and rule bases by the simplest (standard) form of the Compositional Rule of Inference (CRI) [Zade73]. In this paper we extend our investigation to the t-norm based form of the CRI. We give solutions for fixpoints of single rules and, when using the standard aggregation operator maximum, we show, that the solution for a fixpoint of a single rule can be canonically extended to fix-mundis of rule bases. For dedicated t-norms we give examples and for a small rule base an application possibility.