Singular value-based identification of fuzzy system

This paper applies a singular value decomposition based method to extract a fuzzy inference system from a given set of sampled input/output data. With data sampled at rectangular grid points, the method yields a class of irreducible fuzzy system which exactly reproduces the sampled data. Interdependency between the identified membership functions and rule consequences are apparent with the present formulation. The work characterizes input membership functions by the conditions of sum normalization and non-negativeness. The characterization can be relaxed or tightened, giving rise to various class of identified system. Under the present framework, issues like similarity transformation, model reduction, irreducible representation, etc., can be addressed for fuzzy system as well. A system with 2 inputs is used here for presentation but the method is readily extendible to systems with a general number of inputs.