Least squares identification of monotonic fuzzy systems

This paper introduces a least squares (LS) based identification method of fuzzy systems constrained by monotonic input-output relationship. We first present sufficient conditions on the parameters of a fuzzy system under which the output of the system is monotonic with respect to its input. We then formulate monotonic fuzzy systems identification method as LS problem with a nonnegativity constraint, which represents the derived sufficient conditions. Using Lawson and Hanson's nonnegative LS algorithm [2], we suggest a systematic identification method that guarantees monotonicity of the identified fuzzy system. Moreover, using the recursive LS algorithm, we suggest a recursive fuzzy identification technique that keeps monotonicity at every identification step.