utility.aggregate.harmooff: Harmonic aggregation of values or utilities with offset

In utility: Construct, Evaluate and Plot Value and Utility Functions

Harmonic aggregation of values or utilities with offset

Description

Function to perform a harmonic aggregation (weighted harmonic mean) of values or utilities with offset. The offset is added to the arguments and subtracted from the result.

Usage

utility.aggregate.harmooff(u, par)

Arguments

u	numeric vector of values or utilities to be aggregated.
par	numeric vector of weights appended by an offset for calculating the weighted harmonic mean minus an offset of the values provided in the argument u plus the offset. The weights need not be normalized, they will be normalized before use. In case of missing values in the vector u, the weights of the non-missing components will be rescaled to sum to unity.

Details

The aggregation function is defined by

u = \frac{1}{\displaystyle \sum_{i=1}^n \frac{w_i}{u_i+\delta}} - \delta

where \delta is the last parameter appended to the weights.
The following figure shows examples of the behaviour of this aggregation function and its special case utility.aggregate.harmo for the two-dimensional case:

Value

The function returns the aggregated value or utility.

Author(s)

Peter Reichert <[e-mail]>

References

Short description of the package:

Reichert, P., Schuwirth, N. and Langhans, S., Constructing, evaluating and visualizing value and utility functions for decision support, Environmental Modelling & Software 46, 283-291, 2013.

Description of aggregation techniques:

Langhans, S.D., Reichert, P. and Schuwirth, N., The method matters: A guide for indicator aggregation in ecological assessments. Ecological Indicators 45, 494-507, 2014.

Textbooks on the use of utility and value functions in decision analysis:

Keeney, R. L. and Raiffa, H. Decisions with Multiple Objectives - Preferences and Value Tradeoffs. John Wiley & Sons, 1976.

Eisenfuehr, F., Weber, M. and Langer, T., Rational Decision Making, Springer, Berlin, 2010.

See Also

Constructor of aggregation node:

utility.aggregation.create

Aggregation techniques provided by uncsim:

utility.aggregate.add for additive aggregation (weighted arithmetic mean),
utility.aggregate.min for minimum aggregation,
utility.aggregate.max for maximum aggregation,
utility.aggregate.geo or utility.aggregate.cobbdouglas for geometric or Cobb-Douglas aggregation (weighted geometric mean),
utility.aggregate.geooff for geometric aggregation with offset,
utility.aggregate.revgeo for reverse geometric aggregation,
utility.aggregate.revgeooff for reverse geometric aggregation with offset,
utility.aggregate.harmo for harmonic aggregation (weighted harmonic mean),
utility.aggregate.harmooff for harmonic aggregation with offset,
utility.aggregate.revharmo for reverse harmonic aggregation,
utility.aggregate.revharmooff for reverse harmonic aggregation with offset,
utility.aggregate.mult for multiplicative aggregation,
utility.aggregate.mix for a mixture of additive, minimum, and geometric aggregation,
utility.aggregate.addmin for a mixture of additive and minimum aggregation.
utility.aggregate.addpower for additive power aggregation (weighted power mean),
utility.aggregate.revaddpower for reverse additive power aggregation,
utility.aggregate.addsplitpower for splitted additive power aggregation,
utility.aggregate.revaddsplitpower for reverse splitted additive power aggregation,
utility.aggregate.bonusmalus for an aggregation technique that considers some of the values or utilities of sub-objectives only as bonus or malus.

Examples

utility.aggregate.harmooff(c(0.2,0.8), par=c(1,1,0.1))

utility documentation built on Aug. 28, 2023, 1:07 a.m.