Abstract
In the Mamdani-Assilian models considered in this study, the linguistic values of the two input variables and the output variable are described by trapezial membership functions forming a fuzzy partition, the rule base is monotone and the t-norm TM, Tp or TL is applied, combined with either the Mean Of Maxima (MOM) or Center Of Gravity (COG) defuzzification method. For these models, monotonicity cannot be guaranteed for all non-smooth rule bases. If the rule base is smooth, a monotone input-output behaviour is obtained when applying the t-norm Tp combined with the MOM or COG defuzzification method. When applying the t-norm TM combined with the MOM defuzzification method to a model with a smooth rule base, the lengths of the intervals of non-constant membership degree should be equal for all membership functions used in the consequents of the rules, in order to obtain a monotone input-output behaviour.
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