A fuzzy regression model based on distances and random variables with crisp input and fuzzy output data: a case study in biomass production

Abstract

Least-squares technique is well-known and widely used to determine the coefficients of a explanatory model from observations based on a concept of distance. Traditionally, the observations consist of pairs of numeric values. However, in many real-life problems, the independent or explanatory variable can be observed precisely (for instance, the time) and the dependent or response variable is usually described by approximate values, such as “about $$\pounds300$$ ” or “approximately $500”, instead of exact values, due to sources of uncertainty that may affect the response. In this paper, we present a new technique to obtain fuzzy regression models that consider triangular fuzzy numbers in the response variable. The procedure solves linear and non-linear problems and is easy to compute in practice and may be applied in different contexts. The usefulness of the proposed method is illustrated using simulated and real-life examples.