Rule-based modeling of nonlinear relationships

We discuss a problem of rule-based fuzzy modeling of multiple-input single-output nonlinear relationships f: R_n→R. The model under investigation is viewed as a collection of conditional statements “if state Ω, then y=g _i(x,at)”, i=1,2,...N with Ω_i being a fuzzy relation defined in the space of the input variables. In contrast to the commonly encountered identification approach, based exclusively upon discrete experimental data, the one proposed in this study is concerned with the rule-based modeling exploiting the available nonlinear input-output relationship. The main thrust is in the development of a relevant fuzzy partition of the input variables. We introduce and study criteria of separability and variability as the key means guiding a distribution and granularity of the linguistic labels forming the condition part of the local models