Indicators and Partial Orders – An
Introduction
Role of Indicators
Our world will increasingly be more and more complex. Hence, evaluation of the
state (in order to find decisions for management in the future) will be correspondingly difficult. In many cases deterministic mathematical models can be sufficiently
sophisticated to support decisions. In the evaluation of chemicals, such as EUSES
(Heidorn et. al. 1997) or the former E4CHEM (Bruggemann and Drescher-Kaden
2003) are suitable examples. Even agent-based models, cannot encompass all
eventualities of our daily life. (Agent based modelling within a general context
is described in Wikipedia, 2020; within geographical simulations in Castle and
Crooks, 2006 and within an ecological context in Hüning et al. 2016.) Hence, one
can find everywhere indicators, e.g., Fragile State Index (FSI) 2019, (Carlsen and
Bruggemann 2013, 2014, 2017) or the Human Environment Interface Index (HEI),
Environment Performance Index (EPI) (for both within the Partial order context,
see (Bruggemann and Patil 2011), World happiness Index (Helliwell et al. 2019),
Human development Index (Human Development Report 2019), Gender equality
Index (Gender Equality Index 2019), Bruggemann and Carlsen 2020, Sustainable
Cities Index (Sustainable Cities Index 2018), Sustainable Society Index (Europe
Sustainable Development Report 2019), Food Sustainable Index (Barilla 2019)
or indicator helping to measure the quality of life in cities (El Din et al. 2013),
just to mention some typical indicators. The general problem is, how to quantify
these indicators (examples are mentioned above). Often sub-indicators (we will call
them “preliminary indicators”) are defined which can be measured, or estimated
by mathematical models or for which an ordinal scale is obvious. In the next step,
this series of indicators typically is condensed to form a single quantity, sometimes
called ‘the index’, or more precisely the composite indicator. In fact, this procedure,
defining subsystems of indicators, leads to hierarchies of indicator systems, for
example, that applied for the definition of the food index (Barilla 2019)).
The mathematical problem is how to carry out this condensation, or aggregation
step, in the most sensible way possible. Bruggemann and Patil (2011) denoted the
vii
Introduction
Role of Indicators
Our world will increasingly be more and more complex. Hence, evaluation of the
state (in order to find decisions for management in the future) will be correspondingly difficult. In many cases deterministic mathematical models can be sufficiently
sophisticated to support decisions. In the evaluation of chemicals, such as EUSES
(Heidorn et. al. 1997) or the former E4CHEM (Bruggemann and Drescher-Kaden
2003) are suitable examples. Even agent-based models, cannot encompass all
eventualities of our daily life. (Agent based modelling within a general context
is described in Wikipedia, 2020; within geographical simulations in Castle and
Crooks, 2006 and within an ecological context in Hüning et al. 2016.) Hence, one
can find everywhere indicators, e.g., Fragile State Index (FSI) 2019, (Carlsen and
Bruggemann 2013, 2014, 2017) or the Human Environment Interface Index (HEI),
Environment Performance Index (EPI) (for both within the Partial order context,
see (Bruggemann and Patil 2011), World happiness Index (Helliwell et al. 2019),
Human development Index (Human Development Report 2019), Gender equality
Index (Gender Equality Index 2019), Bruggemann and Carlsen 2020, Sustainable
Cities Index (Sustainable Cities Index 2018), Sustainable Society Index (Europe
Sustainable Development Report 2019), Food Sustainable Index (Barilla 2019)
or indicator helping to measure the quality of life in cities (El Din et al. 2013),
just to mention some typical indicators. The general problem is, how to quantify
these indicators (examples are mentioned above). Often sub-indicators (we will call
them “preliminary indicators”) are defined which can be measured, or estimated
by mathematical models or for which an ordinal scale is obvious. In the next step,
this series of indicators typically is condensed to form a single quantity, sometimes
called ‘the index’, or more precisely the composite indicator. In fact, this procedure,
defining subsystems of indicators, leads to hierarchies of indicator systems, for
example, that applied for the definition of the food index (Barilla 2019)).
The mathematical problem is how to carry out this condensation, or aggregation
step, in the most sensible way possible. Bruggemann and Patil (2011) denoted the
vii