Fuzzy Rule Based Non Linear Regression

A novel non linear regression model is presented based on Fuzzy Inference System (FIS) and Fuzzy Linear Regression (FLR) model. The proposedmethod namely Fuzzy Rule Based Non-Linear Regression (FRNLR) is tested over some examples and gives us suitable results. In the FRNLR, input space isdivided to several subspaces and in the each subspace a Fuzzy Linear Regression (FLR) models data. A weighting procedure acts according to probabilitydensity function (membership function) of each subspace and gives portion of each FLRs. Input sampleswith some generated rules appropriate to eachmembership function and weights are obtained. Then results of weighted FLRs are combined and fitting isperformed. Creation of a nonlinear fuzzy regression using the proposed Fuzzy Inference System (FIS) and FLR are possible and give a fuzzy nonlinear regression. Some examples are tested at noisy condition and results are compared to Adaptive Neuro Fuzzy Inference System (ANFIS) which show superiority of the proposed approach.

Keywords:

Nonlinear regression , Fuzzy inference system , Fuzzy linear regression , Weighting procedure , Combining procedure