Multiobjective evolutionary optimization of quadratic Takagi-Sugeno fuzzy rules for remote bathymetry estimation

In this work we tackle the problem of bathymetry estimation using: i) a multispectral optical image of the region of interest, and ii) a set of in situ measurements. The idea is to learn the relation that between the reflectances and the depth using a supervised learning approach. In particular, quadratic Takagi-Sugeno fuzzy rules are used to model this relation. The rule base is optimized by means of a multiobjective evolutionary algorithm. To the best of our knowledge this work represents the first use of a quadratic Takagi-Sugeno fuzzy system optimized by a multiobjective evolutionary algorithm with bounded complexity, i.e., able to control the complexity of the consequent part of second-order fuzzy rules. This model has an outstanding modeling power, without inheriting the drawback of complexity due to the use of quadratic functions (which have complexity that scales quadratically with the number of inputs). This opens the way to the use of the proposed approach even for medium/high dimensional problems, like in the case of hyper-spectral images.