Identification of fuzzy rules from learning data

Fuzzy identification means to find a set of fuzzy if-then rules with well defined attributes, that can describe the given $\text{I}\text{O}\text{-}\text{behaviour}$ of a system. In the identification algorithm proposed here the subject of learning are the rule conclusions i.e. the membership functions of output attributes in form of singletons. For fixed input membership functions learning is shown to be a least squares optimization problem linear in the unknown parameters. Examples show applications of the algorithm to the linguistic formulation of a PI control strategy and to identification of a nonlinear time-discrete dynamic system.