Extension-Principle-Based Approach to Least Square Fuzzy Linear Regression

Abstract

The regression method is widely used in predictive analysis. Its role is to derive an analytic estimation of the outputs expected for given inputs based on observed input-output data. The objective function that is optimized within the regression model is generally the representation of the approximation error comparing to the observed data. Nowadays, the uncertainty is commonly taken into consideration when modeling real systems, and vectorizing information is an important aspect of addressing big data in computer science. Consequently, finding pertinent fuzzy regression models is of great importance within mathematical modeling. In this paper we report our findings related to the full use of the extension principle in solving the optimization model comprised in a least square fuzzy linear regression methodology. We propose a solution approach based on mathematical programming to estimate the fuzzy outputs of the observed fuzzy data; and group our experiments in two categories with respect to the crispness of the observed input data. The first category uses crisp input data and is considered to better explain the advantage of using the extension principle within the solution approach; while the second category, having fuzzy both input and output observed data, is included to prove the relevance of the new approach compared to methodologies from the recent literature.