Mixed fuzzy least absolute regression analysis with quantitative and probabilistic linguistic information

Abstract

Regression analysis is widely used in evaluation and prediction, and fuzzy least absolute regression is preferred when data is fat-tailed or out-linear. Given that the probabilistic linguistic term set is a powerful tool in expressing evaluators' complex linguistic perceptions, this paper incorporates the probabilistic linguistic term set to the fuzzy least absolute regression and builds a fuzzy regression model with mixed types of inputs. To achieve this goal, this paper introduces the concept of double-cut set of the probabilistic linguistic term set. Then, new operations of probabilistic linguistic term sets based on the double-cut sets are investigated. A mixed fuzzy least absolute regression model is proposed and a linear programming is introduced to work out the fuzzy regression parameters. A numerical example concerning the house lease price evaluation under the shared economy is provided to validate the applicability of the proposed model. The study ends with some concluding remarks.