Type-2 Fuzzy Robust Regression with Two-Step Construction

Abstract

Regression models that describe the relationship between independent and dependent variables are widely used owing to their simple structure, ease of handling, and ease of interpretation. One such model is the interval fuzzy regression model that uses fuzzy sets. This model represents the possibility distribution of an analysis target in terms of interval predictions. Generally, the vagueness of a dependent variable is represented by the intervals of type-1 fuzzy sets. However, these observations contain errors, and the interval predictions are considered vague. Therefore, research has been conducted on fuzzy regression using type-2 fuzzy sets. A type-2 fuzzy regression model has been proposed to illustrate possibility distribution of an analysis target through possibilistic and necessity regressions. To investigate reliable and robust fuzzy regression models, this study constructs a type-2 fuzzy robust regression model for possibilistic regression, which illustrates the possibility distribution of the analyte, and a fuzzy robust regression model, which illustrates the robust possibility of the analyte. Numerical examples are used to confirm the characteristics of the proposed model and identify future research directions.