Towards Fuzzy Interpolation with “at Least–at Most” Fuzzy Rule Bases

Fuzzy interpolation property is among the most important properties of fuzzy inference systems. It has been showed that the normality plus Ruspini condition applying to the antecedent fuzzy sets is a sufficient condition with a high practical impact. Another important property is the monotone behavior of the resulting control function (after a defuzzification) derived from a monotone fuzzy rule base. Unfortunately, this goal may be often reached only when applying at least and at most modifiers which is in collision with the Ruspini condition. This paper tries to answer the question whether this collision is an unavoidable obstacle for the interpolation property or whether the “lost” Ruspini condition does not cause losing the interpolation.