Higher-Degree Fuzzy Polynomial Regression Model Estimation Stability: A Comparative Study

Abstract

Estimating fuzzy nonlinear regression models is an essential problem when observed responses are inaccurate and represented by fuzzy numbers. Fuzzy least squares regression based on shape conservation (FLSR-SPO) and the proposed ridge-based improved fuzzy nonlinear regression (PR-FNR) are two estimators that are available for this problem.

In this study, three sample sizes (n = 25, 75, 150) and two error variance levels (σ² = 0.5, 2.5) are simulated across two true polynomial scores (k = 3, 4). The estimators' performance was assessed using the root mean squared fuzzy error on independent, noise-free test sets after the experiment was performed 1000 times.

The results of the experiment indicate that, under all experimental settings, with increasing polynomial score and decreasing sample size, the PR-FNR obtains a much lower RMSE than the FLSR-SPO. These results show that the estimation instability caused on by higher-score fuzzy polynomial models is well reduced by the cross-validated ridge penalty implemented in the PR-FNR method.