192
N. Y. Quintero
the number of linear extensions in a poset grows with the factorial of the number of
ways of ordering incomparable objects in a poset (Bruggemann et al. 2014). Then,
other methods or approximations are needed (Bruggemann and Annoni 2014). In
this study, two approximations for calculating average ranks of each object in study
have been applied, i.e. local partial order models (LPOM) (Bruggemann and Carlsen
2011; Bruggemann et al. 2004).
2.3 Software
The calculations described in this chapter are performed using the software PyHasse
(Bruggemann et al. 2014).
3 Application of Partial Order Theory to Data Matrix
in Study
3.1 Orientation of Attributes
In the current study, it was set up that the orientation follows the criterion that large
attribute values indicate better recovery of U, than lower one (Quintero et al. 2017).
Hence, from the original data, %M and UC were already rightly oriented, while t
required reorientation. The reason was that the larger the time for U trapping the
more undesirable for ranking by biotechnological reasons (Quintero et al. 2017).
At this last point, it is more efficient an organism trapping U in short time
compared to another spending a larger time (Quintero et al. 2017). In this regard,
in the set X gathering 83 microorganisms with potential as U trapping, it was
needed that organisms requiring less time had high values of the reoriented attribute
(Quintero et al. 2018). Then, t was multiplied by −1 and the maximum t value
added to obtain positive values of the reoriented time, eff in this study (Quintero et
al. 2018) (Quintero et al. 2017).
3.2 Hasse Diagram
Table 1 (Quintero et al. 2018) shows the presence of values not clearly defined
for %U and eff for some microorganisms, namely 7, 10, 25, 30, 48 and 75. These
microorganisms have intervals in attributes %U and eff. With the aim of studying
microorganisms having interval attributes, in (Quintero et al. 2017) it was devised a
set of hypothetical microorganisms. Likewise, it was explored how different interval
values affected their order relationships through the HDT. From Quintero et al.
N. Y. Quintero
the number of linear extensions in a poset grows with the factorial of the number of
ways of ordering incomparable objects in a poset (Bruggemann et al. 2014). Then,
other methods or approximations are needed (Bruggemann and Annoni 2014). In
this study, two approximations for calculating average ranks of each object in study
have been applied, i.e. local partial order models (LPOM) (Bruggemann and Carlsen
2011; Bruggemann et al. 2004).
2.3 Software
The calculations described in this chapter are performed using the software PyHasse
(Bruggemann et al. 2014).
3 Application of Partial Order Theory to Data Matrix
in Study
3.1 Orientation of Attributes
In the current study, it was set up that the orientation follows the criterion that large
attribute values indicate better recovery of U, than lower one (Quintero et al. 2017).
Hence, from the original data, %M and UC were already rightly oriented, while t
required reorientation. The reason was that the larger the time for U trapping the
more undesirable for ranking by biotechnological reasons (Quintero et al. 2017).
At this last point, it is more efficient an organism trapping U in short time
compared to another spending a larger time (Quintero et al. 2017). In this regard,
in the set X gathering 83 microorganisms with potential as U trapping, it was
needed that organisms requiring less time had high values of the reoriented attribute
(Quintero et al. 2018). Then, t was multiplied by −1 and the maximum t value
added to obtain positive values of the reoriented time, eff in this study (Quintero et
al. 2018) (Quintero et al. 2017).
3.2 Hasse Diagram
Table 1 (Quintero et al. 2018) shows the presence of values not clearly defined
for %U and eff for some microorganisms, namely 7, 10, 25, 30, 48 and 75. These
microorganisms have intervals in attributes %U and eff. With the aim of studying
microorganisms having interval attributes, in (Quintero et al. 2017) it was devised a
set of hypothetical microorganisms. Likewise, it was explored how different interval
values affected their order relationships through the HDT. From Quintero et al.