12
J. Wittmann
Fig. 4 The general structure of an indicator (s system quantity, i indicator value, w weight, op
aggregation/weighting operation)
tem variables. In fact, indicators can have a complex internal structure, represented
by
– a set of different sub-indicators
– the hierarchical structure of these sub-indicators
– a weighting system
– a freely definable aggregation function.
The conclusion of the deliberations is the fact, that indicators themselves are
constructs that model a valuating system within a more comprehensive system
structure. If we transfer the terms and definitions from modelling and simulation
to the process of building complex indicators, the specification of the indicator
seems to be very analogue to the building of a dynamic model. In fact, indicators
can be considered as a “valuation model” that complements the original “dynamic
model” with its defining parts as declaration of model quantities and the dynamic
description.
For indicator purposes, the dynamic model has to provide a set of model
quantities MQ, thus the indicator part for the model has to include.
A. the set of model quantities
MQ.
B. the set of indicator quantities with
IQ = {iq 1 , . . . , iq n |iq i εMQ|}.
C. the set of weights
W = {w 1 , . . . , w n |w i ε|}.
D. The aggregated indicator value AIV as result of the aggregation function AF
AIV = AF(iq 1 , . . . , iq n , w 1 , . . . , w n ).
J. Wittmann
Fig. 4 The general structure of an indicator (s system quantity, i indicator value, w weight, op
aggregation/weighting operation)
tem variables. In fact, indicators can have a complex internal structure, represented
by
– a set of different sub-indicators
– the hierarchical structure of these sub-indicators
– a weighting system
– a freely definable aggregation function.
The conclusion of the deliberations is the fact, that indicators themselves are
constructs that model a valuating system within a more comprehensive system
structure. If we transfer the terms and definitions from modelling and simulation
to the process of building complex indicators, the specification of the indicator
seems to be very analogue to the building of a dynamic model. In fact, indicators
can be considered as a “valuation model” that complements the original “dynamic
model” with its defining parts as declaration of model quantities and the dynamic
description.
For indicator purposes, the dynamic model has to provide a set of model
quantities MQ, thus the indicator part for the model has to include.
A. the set of model quantities
MQ.
B. the set of indicator quantities with
IQ = {iq 1 , . . . , iq n |iq i εMQ|}.
C. the set of weights
W = {w 1 , . . . , w n |w i ε|}.
D. The aggregated indicator value AIV as result of the aggregation function AF
AIV = AF(iq 1 , . . . , iq n , w 1 , . . . , w n ).