This paper introduces a new fuzzy modeling of an unknown system. The heart of the proposed modeling is fuzzy interpolation involving resolution reduction that generates two different types of information to define single-input, single-output subsystems for an unknown system. Input is identified using a heuristic based on the proposed technique. System behavior is defined as a curve corresponding to individual input. These curves are found using fuzzy curve fitting applied to data points. Behavior curves are saved one of three ways. When the first is geometrical, the second and third use a neural network as a linear prediction coder. Convergence of the linear prediction coder specifies the membership function domain. Inference rules are extracted by observing the exactness of single-input behavior using a fuzzy method. The combination rule is new and combines single-input, single-output behavior to obtain the system model. Our proposal cancels noise well, recognizes actual input, and expresses complicated nonlinear systems with a very small number of rules.