Quadratic least square regression in fuzzy environment

Abstract

The role of the regression analysis is crucial in many disciplines. Addressing the fuzzy quadratic least square regression for observed data modeled by fuzzy numbers, we aim to emphasize how a methodology that does not fully comply to the extension principle may fail to predict fuzzy valued numbers. We also propose a solution approach that functions in full accordance to the extension principle, thus overcoming the shortcomings arisen from the practice of splitting the optimization of a fuzzy number in independent optimizations of its components.