Building fuzzy graphs from samples of nonlinear functions

Abstract

This paper considers the problem of constructing fuzzy graphs from samples of multi-dimensional nonlinear functions to meet a precision requirement. It starts by defining the basic notions of fuzzy granulation, fuzzy graph, fuzzification and defuzzification. The formulation of the problem is then stated in a fuzzy granulation and function approximation framework. This is followed by the development of a recursive scheme that builds a fuzzy graph by generating a set of fuzzy rules and membership functions from the samples of a nonlinear function. Rigorous analysis is carried out to establish the convergence of such a recursive scheme. A few illustrative examples are also used to assess both the efficacy and the efficiency of the proposed scheme. © 1998 Elsevier Science B.V.