Ridge fuzzy regression modelling for solving multicollinearity

Abstract

This paper proposes an a-level estimation algorithm for ridge fuzzy regression modeling, addressing the multicollinearity phenomenon in the fuzzy linear regression setting. By incorporating a-levels in the estimation procedure, we are able to construct a fuzzy ridge estimator which does not depend on the distance between fuzzy numbers. An optimized α-level estimation algorithm is selected which minimizes the root mean squares for fuzzy data. Simulation experiments and an empirical study comparing the proposed ridge fuzzy regression with fuzzy linear regression is presented. Results show that the proposed model can control the effect of multicollinearity from moderate to extreme levels of correlation between covariates, across a wide spectrum of spreads for the fuzzy response.