Generation of polyline reference sets on quantized supports

A key step in fuzzy relational modeling is the generation of appropriate reference sets. The membership functions used to define these reference sets are often based on heuristics. However, more attention must be paid to how these reference sets are created if the actual statistical characteristics of the system signals are to be reflected in the shape of the membership functions. A new algorithm which automatically generates reference sets without neglecting important information hidden in the data statistics is described in this paper. The method employs a Scalar Quantization (SQ) algorithm to partition the universe of discourse, and a parametric polyline technique to generate the membership functions on the partitioned universe. The performance of the reference set generator algorithm is analyzed by modeling and simulating a stochastic process.