292
R. Bruggemann et al.
Within the field of MCDA two problems arise:
(i) How to quantify the many parameters needed beyond the data matrix, and how
to understand their roles.
(ii) The final quantity on which a decision should be based is often a mathematical
complex combination of entries of the data matrix and other (supporting)
parameters. Therefore it is difficult to trace back how a decision was found
and what was the role of the different inputs of the MCDA.
Partial order theory can be a helpful tool. Although partial order is often seen
as a MCDA too, its very idea is that only the entries of the data matrix should
be considered. Often partial order leads to graphical representations, the so-called
Hasse diagrams (see e.g. Bruggemann and Patil 2011). The examination of the
Hasse diagrams lead to evaluation (finally to a decision) and to an exploration
(finally a trace back identifying the role of the single indicators and of their
values). Although both, evaluation and exploration are simply with respect to the
mathematics need, the manual management can be very tedious and error-prone.
This fact caused the development of software. Beside others, the software PyHasse
was developed. This contribution is thought of as a brief introduction into PyHasse
and its further development.
2 The Mathematical Basis of PyHasse
The idea behind the software package PyHasse was to support the interested
researcher in the evaluation of a data matrix, consisting of several rows, (several
objects) which are characterized by several indicators, the columns of the matrix. In
that sense an object x is characterized by a set of indicator values, which is ordered
and considered as a data profile for each object. Partial order comes into play, by
a simultaneous analysis of the data profiles of the objects, i.e., by evaluating the
central equation (of the Hasse diagram technique (HDT)):
x ≤ y : ⇐⇒ q (i, x) ≤ q (i, y) for all indicators, q (i) , (syn.attributes)
(1)
The indicators characterize the objects x, y with respect to the criterion under
which the decision is to be performed. We call X the set of objects. (For details
about HDT, see e.g. Bruggemann et al. 2001; Bruggemann and Patil 2010, 2011;
Newlin and Patil 2010; Patil and Taillie 2004).
If for any two objects x, y Eq. (1) does not hold, then it is said: x is incomparable
with y, denoted in most mathematical papers as
x
y.
R. Bruggemann et al.
Within the field of MCDA two problems arise:
(i) How to quantify the many parameters needed beyond the data matrix, and how
to understand their roles.
(ii) The final quantity on which a decision should be based is often a mathematical
complex combination of entries of the data matrix and other (supporting)
parameters. Therefore it is difficult to trace back how a decision was found
and what was the role of the different inputs of the MCDA.
Partial order theory can be a helpful tool. Although partial order is often seen
as a MCDA too, its very idea is that only the entries of the data matrix should
be considered. Often partial order leads to graphical representations, the so-called
Hasse diagrams (see e.g. Bruggemann and Patil 2011). The examination of the
Hasse diagrams lead to evaluation (finally to a decision) and to an exploration
(finally a trace back identifying the role of the single indicators and of their
values). Although both, evaluation and exploration are simply with respect to the
mathematics need, the manual management can be very tedious and error-prone.
This fact caused the development of software. Beside others, the software PyHasse
was developed. This contribution is thought of as a brief introduction into PyHasse
and its further development.
2 The Mathematical Basis of PyHasse
The idea behind the software package PyHasse was to support the interested
researcher in the evaluation of a data matrix, consisting of several rows, (several
objects) which are characterized by several indicators, the columns of the matrix. In
that sense an object x is characterized by a set of indicator values, which is ordered
and considered as a data profile for each object. Partial order comes into play, by
a simultaneous analysis of the data profiles of the objects, i.e., by evaluating the
central equation (of the Hasse diagram technique (HDT)):
x ≤ y : ⇐⇒ q (i, x) ≤ q (i, y) for all indicators, q (i) , (syn.attributes)
(1)
The indicators characterize the objects x, y with respect to the criterion under
which the decision is to be performed. We call X the set of objects. (For details
about HDT, see e.g. Bruggemann et al. 2001; Bruggemann and Patil 2010, 2011;
Newlin and Patil 2010; Patil and Taillie 2004).
If for any two objects x, y Eq. (1) does not hold, then it is said: x is incomparable
with y, denoted in most mathematical papers as
x
y.