Abstract
Among many research areas to which Ron Yager contributed are decision making under uncertainty (in particular, under interval and fuzzy uncertainty) and aggregation—where he proposed, analyzed, and utilized ordered weighted averaging (OWA). The OWA algorithm itself provides only a specific type of data aggregation. However, it turns out that if we allow several OWA stages, one after another, we obtain a scheme with a universal approximation property—moreover, a scheme which is perfectly equivalent to modern ReLU-based deep neural networks. In this sense, Ron Yager can be viewed as a (grand)father of ReLU-based deep learning. We also recall that the existing schemes for decision making under uncertainty are also naturally interpretable in OWA terms.
Highlights
In order to start analyzing the relation between ordered weighted averaging (OWA), deep learning, and decision making under uncertainty—several computer topics—let us first recall why computers are needed in the first place
In the 1980s, Ron Yager proposed a new averaging operator—in which we first order the averaged inputs, and take a linear combination of these inputs with weights, depending on the rank in this ordering. This OWA operator has turned out to be very useful in data processing and decision making
We show that OWA operators naturally appear if we consider algorithms consisting of stages of two types: linear combinations and nonlinear functions, which are invariant with respect to any linear or nonlinear re-scaling
Summary
In order to start analyzing the relation between OWA, deep learning, and decision making under uncertainty—several computer topics—let us first recall why computers are needed in the first place. The main objective of computers is to process data. Data processing is usually performed in several stages. Which processing algorithms should we select for each stage?. At each stage of a deterministic data processing, the result, y, is uniquely determined by the inputs, x1, . In mathematical terms, this means that, at each stage, we are computing a function of the inputs, y = f
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