utility.aggregate.mult {utility}

Multiplicative aggregation of values or utilities

Description

Function to perform a multiplicative aggregation of values or utilities.

Usage

utility.aggregate.mult(u, par)

Arguments

u

numeric vector of values or utilities to be aggregated.

par

numeric vector of weights for calculating the multiplicative combination of the values provided in the argument u. Note that for this aggregation technique, the result depends on the sum of the weights that need not be unity.

Details

To derive the aggregated value, we first solve the implicit equation

k + 1 = \prod_{i=1}^n (1 + k w_i)

for k and then calculate the aggregated value as

u = \frac{\displaystyle \prod_{i=1}^n (1 + k w_i u_i)}{k}

See Keeney and Raiffa, Decisions with multiple objectives, 1976, pp. 307, 347-348 for details.
The following figure shows examples of the behaviour of this aggregation function for the two-dimensional case:

Value

numeric value corresponding to the multiplicative aggregation of the values provided in the vector u.

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.mult(c(0.2,0.8),par=c(0.3,0.3))