Fuzzy rules, implicative fuzzy models, defuzzification, monotonicity

Frequent practical problems lead to intuitively monotone fuzzy rule bases. By the monotone fuzzy rule base we mean a rule base consisting of such fuzzy rules expressing the monotone dependence of consequent fuzzy sets on antecedent fuzzy sets. Very often real-world applications require some defuzzification to be employed at the end of the inference process. The problem is that after the defuzzification we obtain a crisp input-output function which is not necessarily monotone anymore. Most of the attention has been paid to the Mamdani-Assilian conjunctive kind of models of fuzzy rule bases built with help of particular t-norms. This paper focuses on the implicative approach for arbitrary residual implication.