Amory Bisserier

A revisited approach to linear fuzzy regression using trapezoidal fuzzy intervals

Conventional Fuzzy regression using possibilistic concepts allows the identification of models from uncertain data sets. However, some limitations still exist. This paper deals with a revisited approach for possibilistic fuzzy regression methods. Indeed, a new modified fuzzy linear model form is introduced where the identified model output can envelop all the observed data and ensure a total inclusion property. Moreover, this model output can have any kind of spread tendency. In this framework, the identification problem is reformulated according to a new criterion that assesses the model fuzziness independently from the collected data distribution. The potential of the proposed method with regard to the conventional approach is illustrated by simulation examples.

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.

Fuzzy piecewise linear regression

Fuzzy regression using possibilistic concepts allows the identification of models from uncertain data sets. However, some limitations still exist about the possible evolution of the output spread with respect to inputs. We present here a modified form of fuzzy linear model whose output can have any kind of output spread tendency. The formulation of the linear program used to identify the model introduces a modified criterion that assesses the model fuzziness independently of the collected data. These concepts are used in a global identification process in charge of building a piecewise model able to represent every kind of output evolution.

Assimilation of D-InSAR and sub-pixel image correlation displacement measurements for coseismic fault parameter estimation

In this paper, 2 data fusion strategies from SAR images are investigated through application to measurement of displacement field due to the Kashmir earthquake (Mw=7.6, 2005). Firstly, the 3D displacement field at the Earths surface is retrieved by a linear inversion, using the measurements from sub-pixel image correlation and differential interferometry. In addition to the generalized least square method, a fuzzy approach is applied to represent the measurement uncertainty. Secondly, the geometry of the fault is optimized by a non linear inversion, using the same measurements. The inter-comparisons between strategies and approaches are performed in order to highlight the advantages and disadvantages of each strategy and approach.

Combining climate temperature models through fuzzy interval regression: Application to the La Plata Basin

This paper presents a fuzzy interval linear regression method to combine climate temperature models. The study is carried out using air temperature data recorded yearly during the 20th century in the La Plata Basin. The objective of the study is to provide realistic predictions of the air temperature in the 21st century, taking into account five climate models to envelope the predicted data. The input to the fuzzy interval model is the central value for each climate model. The output observed data if the central value, the lower and upper limits, representing 90% of the dataset within a region. The output to the fuzzy interval regression model represents the uncertainty in a trapezoid shaped membership function, in which the core interval envelop all the observed central data values and the support interval envelopes 90% of observed data. The fuzzy regression parameters may be trapezoid shaped or crisp values and are computed such that the global uncertainty is minimized. A standard linear regression model is also be used for comparison and validation. The method has shown to be useful to handle the uncertainty management in climate model better than the linear regression despite its wider uncertainty range in all cases.