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Justification and numerical realization of the uniform method for finding point estimates of interval elicited scaling constants

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Abstract

The form of the utility function over multi-dimensional consequences depends on the point estimates of the scaling constants. Fuzzy rational decision makers elicit those in the form of uncertainty intervals. The paper proposes an analytical justification and a numerical realization of the uniform method that finds point estimates of interval scaling constants. The main assumption of the technique is that constants are uniformly distributed in their uncertainty intervals. The density of the constants’ sum is constructed using preliminarily chosen knots. A new numerical procedure to calculate the I type error p value of a two-tail test for singularity of the constants’ sum is proposed. All numerical procedures are embodied into program functions. The application of the method is demonstrated in examples. The connection between precision and time for analysis is investigated. Comparison of the analytical uniform method and an earlier proposed simulation realization is also conducted.

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Authors and Affiliations

  1. Technical University–Varna, 1 Studentska Str., 9010, Varna, Bulgaria

    Kiril Tenekedjiev & Natalia Nikolova

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  1. Kiril Tenekedjiev
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  2. Natalia Nikolova
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Correspondence to Kiril Tenekedjiev.

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Tenekedjiev, K., Nikolova, N. Justification and numerical realization of the uniform method for finding point estimates of interval elicited scaling constants. Fuzzy Optim Decis Making 7, 119–145 (2008). https://doi.org/10.1007/s10700-008-9027-0

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  • DOI: https://doi.org/10.1007/s10700-008-9027-0

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