Uncertainty in Weights for Composite
Indicators Generated by Weighted Sums
Rainer Bruggemann and Lars Carlsen
1 Introduction
Checking the literature with respect to decision support systems (for an overview
see for example Colorni et al. 2001; Figueira et al. 2005; Munda 2008; Munda and
Nardo 2008), the concepts of partial order theory seem to play a minor role or are at
best interim results (cf. ELECTRE family (Roy 1972, 1990) or PROMETHEE (in
step I) (Brans and Vincke 1985)). There are two arguments why partial order theory
does not play the role which it could have: (1) The appearance of incomparability,
i.e., the fact that a ranking, i.e., a total order cannot be obtained, because of nonresolved conflicts in data and (2) the inability to include stakeholders’ knowledge.
Originally, the fact that data beyond the data matrix are not needed was
considered by the authors of this paper as an advantage, because partial order theory
based purely on the data matrix leads to “data driven results” and is therefore free
of any subjectivisms, beside those which already were included in the data matrix.
All parameters used in ELECTRE (Roy 1990) or PROMETHEE (Brans and Vincke
1985) or other decision support systems beyond the data matrix are considered as
subjective and are often difficult to be obtained. Nevertheless, the stakeholder’s
qualitative knowledge should be included within the framework of partial order
theory.
One method in the area of decision support systems is the weighted sum of
(normalized) indicator values for each object. Objects are the issue of interest for
which a decision is to be found. The advantage of the weighted – sum – approach
R. Bruggemann ()
Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Berlin, Germany
e-mail: brg_home@web.de
L. Carlsen
Awareness Center, Roskilde, Denmark
e-mail: LC@AwarenessCenter.dk
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
R. Bruggemann et al. (eds.), Measuring and Understanding Complex Phenomena,
https://doi.org/10.1007/978-3-030-59683-5_4
45
Indicators Generated by Weighted Sums
Rainer Bruggemann and Lars Carlsen
1 Introduction
Checking the literature with respect to decision support systems (for an overview
see for example Colorni et al. 2001; Figueira et al. 2005; Munda 2008; Munda and
Nardo 2008), the concepts of partial order theory seem to play a minor role or are at
best interim results (cf. ELECTRE family (Roy 1972, 1990) or PROMETHEE (in
step I) (Brans and Vincke 1985)). There are two arguments why partial order theory
does not play the role which it could have: (1) The appearance of incomparability,
i.e., the fact that a ranking, i.e., a total order cannot be obtained, because of nonresolved conflicts in data and (2) the inability to include stakeholders’ knowledge.
Originally, the fact that data beyond the data matrix are not needed was
considered by the authors of this paper as an advantage, because partial order theory
based purely on the data matrix leads to “data driven results” and is therefore free
of any subjectivisms, beside those which already were included in the data matrix.
All parameters used in ELECTRE (Roy 1990) or PROMETHEE (Brans and Vincke
1985) or other decision support systems beyond the data matrix are considered as
subjective and are often difficult to be obtained. Nevertheless, the stakeholder’s
qualitative knowledge should be included within the framework of partial order
theory.
One method in the area of decision support systems is the weighted sum of
(normalized) indicator values for each object. Objects are the issue of interest for
which a decision is to be found. The advantage of the weighted – sum – approach
R. Bruggemann ()
Leibniz-Institute of Freshwater Ecology and Inland Fisheries, Berlin, Germany
e-mail: brg_home@web.de
L. Carlsen
Awareness Center, Roskilde, Denmark
e-mail: LC@AwarenessCenter.dk
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
R. Bruggemann et al. (eds.), Measuring and Understanding Complex Phenomena,
https://doi.org/10.1007/978-3-030-59683-5_4
45