Which Value \(\widetilde{x}\) Best Represents a Sample \(x_1,\ldots ,x_n\): Utility-Based Approach Under Interval Uncertainty

  • Andrzej Pownuk
  • Vladik KreinovichEmail author
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 276)


In many practical situations, we have several estimates \(x_1,\ldots ,x_n\) of the same quantity x. In such situations, it is desirable to combine this information into a single estimate \(\widetilde{x}\). Often, the estimates \(x_i\) come with interval uncertainty, i.e., instead of the exact values \(x_i\), we only know the intervals \([\underline{x}_i,\overline{x}_i]\) containing these values. In this paper, we formalize the problem of finding the combined estimate \(\widetilde{x}\) as the problem of maximizing the corresponding utility, and we provide an efficient (quadratic-time) algorithm for computing the resulting estimate.



This work was supported in part by the National Science Foundation grants HRD-0734825 and HRD-1242122 (Cyber-ShARE Center of Excellence) and DUE-0926721, and by an award “UTEP and Prudential Actuarial Science Academy and Pipeline Initiative” from Prudential Foundation.


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Authors and Affiliations

  1. 1.University of Texas at El PasoEl PasoUSA

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