A transformation-based framework for
nonlinear combination operators

Sergio A. Alvarez

Department of Computer Science
Worcester Polytechnic Institute
Worcester, MA 01609


In many different contexts, including knowledge aggregation in knowledge-based systems, relevance ranking in information retrieval, and lateralization measurement in neurobiology, the need arises to combine several quantitative measures of a given phenomenon into a single measure that uses the information encoded in each of them. This may be achieved by constructing an appropriate combination operator. Various ad-hoc approaches are currently in use for this purpose in different domains. This paper introduces a rational framework that systematically provides families of combination operators from a single canonical form by choosing different geometric frames of reference in the space of measurement values. We show that previously used combination operators may be obtained through our approach in a natural way, that they may be easily modified and generalized for increased flexibility, and that new combination operators may be systematically generated. We provide a characterization of the differentiable combination operators that are expressible via a frame transformation in terms of the canonical form and give an algorithm to construct an appropriate reference frame if one exists.

For related work see:

Research Report No. 97-NA-010
Center for Nonlinear Analysis
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