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N. Pankow et al.
(Bruggemann and Patil 2011). With the partial order, objects are characterized by
attributes (or in this case indicators). The sorting of variants or objects using the ≤relation results in a rating network with characteristic structures, a so-called Hasse
Diagram (HD) (Steinberg 2002). A HD displays the objects and their ≤-relation by
a directed graph (chain). In a poset not all objects are comparable, so they are not
connected by a graph (antichain). The program PyHasse was used to create those
HDs (Bruggemann 2018).
During the course of this work PyHasse showed a low validity for the assessment
of the variants because of the high number of indicators and low number of objects
(Pankow 2018; Bruggemann et al. 2014). The focus of this work was to derive a
MIS to assess variants in decision-making. Therefore, the indicators should also be
assessed in this process. For the assessment of the indicators, the indicators were
treated as objects and the variants as attributes. When the indicators are treated as
objects, the variants can be used to characterize the indicators. For the assessment
of the indicators the case examples were analysed in two different approaches. In
the first approach each case examples forms a matrix and is analysed individually.
Therefore, each case example was considered individually. The other approach is to
analyse all case example in its entirety in one matrix.
The examination tools for both approaches were identical. The indicators must
be normalized to allow forthcoming analysis. The goal of the partial order is the
mapping of indicators on a metric scale. Indicators should therefore not dominate
other indicators due to a large measure-unit. To avoid this kind of dominance a
normalization can be appropriate. After the normalization the HDs for all case
examples and the entirety of all case examples were created.
The characteristic structures formed in the HDs, especially the subsets in the
HD were of interest. With the PyHasse module “sepanal15_4” the separability of
subsets from the HD can be investigated (Restrepo and Bruggemann 2008). The
module provides a degree of separability and the attributes that cause the separability
between two subsets. The result can be displayed graphically in a so-called tripartite
graph.
All indicators were associated with a sustainability dimension (social, ecological
or economic). If one dimension dominates the other dimensions, it would point
to an unbalanced set of indicators. The module “dds_12” in PyHasse analyses the
dominance of an assigned group of attributes. With dds_12 a dominance histogram
is generated. The histogram shows the distribution of the normalized dominance of
objects. In addition to the histogram, the module calculates the dominance matrix,
the separability matrix and the degree of separability.
2.2.2 Case Example
The case examples were previous projects at the BWB. Three of those examples
were projects in different wastewater treatment plants.
The first case example is the exhaust air treatment in the wastewater treatment
plant (WWTP) 1. In the inlet area of the mechanical wastewater treatment at the
N. Pankow et al.
(Bruggemann and Patil 2011). With the partial order, objects are characterized by
attributes (or in this case indicators). The sorting of variants or objects using the ≤relation results in a rating network with characteristic structures, a so-called Hasse
Diagram (HD) (Steinberg 2002). A HD displays the objects and their ≤-relation by
a directed graph (chain). In a poset not all objects are comparable, so they are not
connected by a graph (antichain). The program PyHasse was used to create those
HDs (Bruggemann 2018).
During the course of this work PyHasse showed a low validity for the assessment
of the variants because of the high number of indicators and low number of objects
(Pankow 2018; Bruggemann et al. 2014). The focus of this work was to derive a
MIS to assess variants in decision-making. Therefore, the indicators should also be
assessed in this process. For the assessment of the indicators, the indicators were
treated as objects and the variants as attributes. When the indicators are treated as
objects, the variants can be used to characterize the indicators. For the assessment
of the indicators the case examples were analysed in two different approaches. In
the first approach each case examples forms a matrix and is analysed individually.
Therefore, each case example was considered individually. The other approach is to
analyse all case example in its entirety in one matrix.
The examination tools for both approaches were identical. The indicators must
be normalized to allow forthcoming analysis. The goal of the partial order is the
mapping of indicators on a metric scale. Indicators should therefore not dominate
other indicators due to a large measure-unit. To avoid this kind of dominance a
normalization can be appropriate. After the normalization the HDs for all case
examples and the entirety of all case examples were created.
The characteristic structures formed in the HDs, especially the subsets in the
HD were of interest. With the PyHasse module “sepanal15_4” the separability of
subsets from the HD can be investigated (Restrepo and Bruggemann 2008). The
module provides a degree of separability and the attributes that cause the separability
between two subsets. The result can be displayed graphically in a so-called tripartite
graph.
All indicators were associated with a sustainability dimension (social, ecological
or economic). If one dimension dominates the other dimensions, it would point
to an unbalanced set of indicators. The module “dds_12” in PyHasse analyses the
dominance of an assigned group of attributes. With dds_12 a dominance histogram
is generated. The histogram shows the distribution of the normalized dominance of
objects. In addition to the histogram, the module calculates the dominance matrix,
the separability matrix and the degree of separability.
2.2.2 Case Example
The case examples were previous projects at the BWB. Three of those examples
were projects in different wastewater treatment plants.
The first case example is the exhaust air treatment in the wastewater treatment
plant (WWTP) 1. In the inlet area of the mechanical wastewater treatment at the