There are many contexts in which several quantitative measures that provide in- formation about a given phenomenon are available and it is desired to combine these measures into a single measure that uses the information encoded in each of them. Examples include knowledge aggregation in knowledge-based systems , , lateralization measurement in neurobiology , , and relevance ranking in information retrieval. Mostly ad-hoc approaches are currently in use for this purpose in different domains. The objective of this paper is to introduce a rational framework that systematically provides families of combination operators for the integration of disparate measures in a variety of situations. Our approach uses a single canonical form to produce a multitude of different combination functions by choosing different geometric frames of reference in the space of measurement values. We show that previously used combination functions 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 functions that are expressible via conjugacy in terms of the canonical form and give an algorithm to construct an appropriate reference frame if one exists. We also address the asymptotic behavior of the combination functions produced by our framework when the number of source measures grows without bound.
Alvarez, Sergio A.
(1998). A transformation-based combination framework for approximate reasoning. .
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