A Midpoint–Radius approach to regression with interval data

In this paper, a revisited interval approach for linear regression is proposed. In this context, according to the Midpoint–Radius (MR) representation, the uncertainty attached to the set-valued model can be decoupled from its trend. The estimated interval model is built from interval input–output data with the objective of covering all available data. The constrained optimization problem is addressed using a linear programming approach in which a new criterion is proposed for representing the global uncertainty of the interval model. The potential of the proposed method is illustrated by simulation examples.

► We propose a Midpoint–Radius revisited interval approach for linear regression.
► We design an identification technique from interval input–output data.
► The uncertainty attached to the identified model is decoupled from its trend.
► To deal with inclusion constraints, a new optimization criterion is proposed.
► The optimization procedure is made according to a linear programming approach.