Besides the ecological issues, recycling of plastics involves economical matters that encourage industrial firms to invest in the field. Part of them have focused on the waste sorting phase by designing optical device able to discriminate on line among plastics categories. For achieving ecological and economical objectives, sorting errors must be minimized to avoid serious recycling problems and significant quality degradation of the final recycled product. Even with the most recent acquisition technologies based on spectra imaging, plastic recognition remains a tough task due to the presence of imprecision and uncertainty, e.g., variability in the measurement due to atmospheric disturbances, ageing of plastics, dark or black coloured materials etc. The enhancement of the recent sorting techniques based on classification algorithms leads to rather good performance results, however for such applications, the remaining errors have serious consequences. In this article, we propose an imprecise classification algorithm to minimize sorting errors of standard classifiers when dealing with incomplete data by both integrating the processing of classification's doubt and hesitation in the decision process and improving the classification performances. To this aim, we propose a relabelling procedure that allows to better represent the imprecision of the learning data and we introduce the belief functions framework to represent the posterior probability provided by a classifier. Finally, the performances of our approach compared to existing imprecise classifiers is illustrated on the sorting problem of four plastics categories from mid-wavelength infra-red spectra acquired in an industrial context.

Belief functions are quite generic models when it comes to represent uncertain data, as it extends a wide range of uncertainty models (possiblity and probability distributions, among others). Usually, belief functions are defined over finite spaces, however many real word problems require to deal with beliefs over a continuous space while maintaining computational efficiency. This paper discusses the case of focal sets on the unit simplex, and proposes efficient inference tools to manipulate them. Such sets can be used to represent unknown proportions that one may face in various fields like soil contamination managing, plastic sorting or image reconstruction. In this paper, we illustrate their use on an industrial problem of plastic sorting, where the proportion of material impurities must not go over a limit while minimizing the rejection of sorted materials, whose nature is uncertain.

With the increase in waste streams, industrial sorting has become a major issue. The main challenge is to minimise sorting errors to avoid serious recycling problems and significant quality degradation of the final recycled product. Making use of near infrared (NIR) technology, some industrialists have already designed sorting machines able to discriminate between several types of plastics with good reliability. However, these devices are not suited to dark plastics, which are very common in WEEE (Waste Electronic and Electrical Equipment). In order to overcome this obstacle, mid-wavelength infrared (MIR) technology can be used instead of NIR. Nevertheless, the new spectral range is poorer in terms of wavelength for some plastics of interest (2712 − 5274nm), which makes the sorting task harder in an industrial context where spectrum identification is subject to imprecision and uncertainty. This article shows the benefit of combining this promising optical technology with a cautious machine learning procedure to optimise recycling. When the information provided by the device regarding a plastic fragment to be sorted is insufficient to discriminate between candidate materials, the pro-posed procedure, taking advantage of the belief functions theory, blows the fragment into a container dedicated to more than one specific material. This cautious sorting enables the containers dedicated to the specific ma-terials to contain less impurities, which leads to higher-quality secondary raw materials. The proposed sorting procedure is illustrated and compared with a more conventional approach using real industrial data.

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Predictions from classification models are most often used as final decisions. Yet, there are situations where the prediction serves as an input for another constrained decision problem. In this paper, we consider such an issue where the classifier provides imprecise and/or uncertain predictions that need to be managed within the decision problem. More precisely, we consider the optimisation of a mix of material pieces of different types in different containers. Information about those pieces is modelled by a mass function provided by a cautious classifier. Our proposal concerns the statement of the optimisation problem within the framework of belief function. Finally, we give an illustration of this problem in the case of plastic sorting for recycling purposes.